2^3 Design
 Mathews Malnar and Bailey, Inc.

Quality engineering, applied statistical consulting,
and training services for R&D, product, process,
and manufacturing engineering organizations.		 Run Chart

Meeting announcements are in reverse order with the most recent meeting at the top. All meetings are free and everyone is welcome to present or to recommend a topic. Please e-mail me at paul@mmbstatistical to be added to the mailing list.

Use these meetings to earn recertification units (RUs) for your ASQ certifications.


Debugging the Real-Time Data Collection and Processing Functions of a Hobby Electronics Project, 7:30-9:00AM, 1 November 2024 via Zoom
In the QMN meeting back on 5 August 2022 I described some of the real-time data processing problems I was having on my hobby electronics project to replace the instruments on my sailboat. At that time I was focussed on fixing a distracting time lag problem between when an event occurred and when it would appear on the instrument display. I was using a simple exponentially-weighted moving average (EWMA) filter which comes from SPC to smooth the noisy data. A known down-side of the EWMA filter is that it introduces a time lag in the response. I made the mistake of attributing the time lag that I was observing to the EWMA filter so I was investigating other filters with shorter time lags but sufficient smoothing. This sailing season I discovered that the time lag problem was coming from a combination of two different causes: 1) my code wasn't processing the data stream correctly and 2) the Raspberry Pi computer I was using to process the data and display the results wasn't fast enough for the job in its original configuration. I was able to fix both problems and now the system does an excellent job collecting, processing, and displaying data.


Paradoxes in Statistics, 7:30-9:00AM, 4 October 2024, by Zoom
Statistical methods can be confusing enough, but they are aggravated by a set of common traps/mistakes that get clustered into a family of "statistical paradoxes". (See the list in Wikipedia: https://en.wikipedia.org/wiki/Category:Statistical_paradoxes.) With training and practice you can learn how to recognize and avoid these potential analysis errors. We'll consider some of these paradoxes at this month's QMN meeting.


An Introduction to Blue Sky Statistics Statistical Software, Sanjay Kumar, CEO, Blue Sky Statistics, 7:30-9:00AM, 2 August 2024, by Zoom.
Sanjay Kumar, CEO and co-founder of BlueSky Statistics, a Chicago-based company, will introduce BlueSky Statistics Software through a live demo and Q&A. BlueSky Statistics is a comprehensive, easy-to-use, point-and-click statistics and data analytics software to meet the needs of all process and quality improvement initiatives (based on well-known DMAIC methodology). The software is designed for quality engineers, process improvement professionals, and Six Sigma practitioners of all levels for a fraction of the cost compared to MINITAB, JMP, and other expensive software licenses. The software has been used in over 135 countries. Many organizations across industries have switched to BlueSky Statistics from JMP, MINITAB, SPSS, and others. Join the session to see a live demo of the important features such as process capability analysis, measurement system analysis, SPC charts, distribution fit analysis, hypothesis testing, regression analysis, graphs and plots, DOE, and more as time permits.


Pugh Concept Selection Matrix, 7 June 2024, 7:30-9:00AM, by Zoom
Following the Analyze phase of the Six Sigma DMAIC process (for improving an existing process) or the DMADV process (for designing a new product or service) it is necessary to leverage the process model developed in the Analyze phase to choose the best solution to implement in the Improve or Design phase, respectively. Sometimes a single solution will stand out and there are no questions about how to proceed; however, when there are multiple competing candidate solutions it will be necessary to select the best one. There are many methods available (e.g. multi-voting) to assist in the solution selection process but in particularly difficult situations a more rigorous method like the Pugh Concept Selection Matrix method may be required. This method uses a two-way classification matrix of performance criteria versus candidate solutions and scoring relative to a standard solution to identify the best of the candidate solutions.

Acronyms:
DMAIC   Define, Measure, Analyze, Improve, and Control
DMADV   Define, Measure, Analyze, Design, Verify


The Ramirez-Runger Test: Do my data come from a single stable population?, 3 May 2024, 7:30-9:00AM, by Zoom
When we're collecting data from some process, we usually make the assumption that the process is stable in time, that is, that its distribution location, variation, and shape are all constant. If a process is not stable in time then we can't expect to fit a distribution model to the data. We need a method to discriminate between stable and unstable processes.

We often test for the stability of a process by inspecting a run chart of the data; however, this method is subjective and may not detect subtle problems so we need a more discriminating test. Enter the Ramirez-Runger test. I only learned about this test recently from a Quality Digest article by Don Wheeler (link below) and the test has only been around since 2006 so it doesn't appear in any of my archaic reference materials.

The Ramirez-Runger test works by comparing two measures of the process variation using an F test for two standard deviations. The first of the two measures is simply the standard deviation of all of the sample data. The second measure is the standard deviation estimated from the moving ranges where moving ranges are the absolute values of the differences between consecutive observations. If the data come from a time stable process, then the two standard deviation estimates should be comparable to each other. If the data don't come from a time stable process, then the two standard deviation estimates will diverge and we can't expect to fit a distribution to the data. I'm planning to adopt this test in my process capability study protocol and other procedures that require the stability assumption.

Wheeler, https://www.qualitydigest.com/inside/lean-article/test-use-all-other-tests-040324.html
Ramirez and Runger, Quantitative Techniques to Evaluate Process Stability, June 2006, Quality Engineering 18(1):53-68


The Many Uses of the Sign Test, 5 April 2024, 7:30-9:00AM, by Zoom
The nonparametric sign test is one of the few statistical methods that have a simple instinctive interpretation. It appears any time you're expecting binary observations to have a 50/50 split. Consider what is perhaps its best known example:

    A balanced coin is tossed 10 times. How would you feel if the coin delivered 5 heads and 5 tails? 4 heads and 6 tails? 3 heads and 7 tails? ...

Hopefully you can see where this is going. At some point, certainly for a 1/9 or 0/10 split, you would get suspicious and check the coin to see if there is any evidence against the "balanced" claim.

When binary observations, like the heads or tails results in the coin toss example, are coded as plus (+) and minus (-) signs, then we just have to count the experimental number of plus and minus signs and test for significance using the "sign test". The number of heads x in n trials under the null hypothesis that the coin is balanced (p = 0.50) follows the binomial distribution b(x;n,p = 0.50). Knowledge of this distribution allows us to determine the statistical significance of the data.

At first the scope of problems where you would expect the sign test to be appropriate might seem pretty narrow; however, it turns up in a lot of places:
The sign test is usually not the most powerful test method available, but it is so simple to learn and easy to apply that it is invaluable as an exploratory or quick test. With some practice you'll learn to recognize the many places that it appears and how to interpret its results.


Accelerated Life Test of a Hand Sanitizer Product, 2 February 2024, 7:30-9:00AM, by Zoom
In our December and January meetings we discussed many ways to analyze the data for an accelerated life test. This month we'll consider another type of life test. In the previous discussions, the life response was measured in hours or cycles to failure with the possibility of right censoring. This month we will consider the determination of the shelf life for a biomedical hand sanitizer product that must comply to FDA Guidance Document ICH Q1E Evaluation of Stability Data. The product's response that determines its shelf life is the chemical concentration of its sanitizing active ingredient. The concentration is high at the time of manufacture but decays slowly over time approaching the concentration's lower spec limit. ICH Q1E specifies the shelf life-determining condition and allows for both real time room temperature and temperature accelerated testing. We'll show that by evaluating samples stored at 25 and 40C it is possible to demonstrate a two year shelf life claim using 6 month data.


Design, Analysis, and Sample Size Calculations for an Accelerated Life Test - Part 2, 5 January 2024, 7:30-9:00AM, by Zoom
We didn't finish our discussion of accelerated life tests last month so we will continue our discussion in January. See the December abstract for the planned scope of the discussion.


Design, Analysis, and Sample Size Calculations for an Accelerated Life Test, 1 December 2023, 7:30-9:00AM, by Zoom
I am working on an experiment design and sample size calculation for an accelerated life test for a customer. MINITAB has methods for the the data analysis and the sample size calculation; however, I'm having difficulty configuring the sample size calculation menu. I thought that I would talk through these issues at this month's meeting. The abstract from our last discussion on this topic (minus the sample size calculation) is here:

Use Accelerated Testing to Reduce the Length of Life Tests (5 May 2017)
In an ordinary life test, where the response (such as the fraction of units surviving or the concentration of a chemical) changes with time, the units under test are operated at the same conditions as are expected in actual use until they reach a defined end-of-useful-life condition. The downside of this approach is that if the life of the product is expected to be very long then the duration of your life test will also need to be that long. And iterations of the design could result in several consecutive life test cycles that will surely exceed the limits of any manager's patience. Thankfully the duration of many life tests can be reduced by operating the units under test at a higher stress level than they would see in normal use, thereby accelerating the rate of change of the response. Common stress variables are temperature, pressure, and voltage. Through careful design of the life test experiment - with particular attention paid to resolving the effect of the accelerating variable - we can build a model for the life test response that allows us to make life predictions for normal operating conditions from the accelerated life test data. This approach can reduce the duration of a life test to just a fraction of the time it would take to perform the same test under unaccelerated conditions.


Goodness of Fit Tests for Linear Regression, 3 November 2023, 7:30-9:00AM, by Zoom
One of the assumptions of the linear regression method is that the form of the model is appropriate for the data. This condition is referred to as "goodness of fit" or "lack of fit". Many people make the mistake of assuming that goodness of fit is indicated by the R-squared metric; however, R-squared and goodness of fit address different issues so other methods of assessing goodness of fit are necessary.

The easiest way to assess whether a model fits the data is to create a plot showing the model superimposed on the data. If the model tracks the data well then we probably have a good fit. This assessment "by eye" works well but it can be insufficient when subtle discrepancies are present or the model is too complicated to display in graphical form. In these cases formal quantitative goodness of fit tests are required. At this week's QMN meeting we will consider some of these goodness of fit tests and implement them manually and using MINITAB's built in capabilities.


Examples of Equivalence, Superiority, and Noninferiority Tests,  6 October 2023, 7:30-9:00AM via Zoom
At last month's QMN meeting we discussed the formulation of equivalence, superiority, and noninferiority test hypotheses. We'll continue that topic this month by discussing detailed examples of these cases. If you've run any of these tests yourself, please consider volunteering to explain your work.


Formulating Equivalence, Superiority, and Noninferiority Test Hypotheses, 1 September 2023, 7:30-9:00AM, by Zoom
After learning the basic significance test methods we often find ourselves with the need to perform equivalence, superiority, and noninferiority tests. The analyses and interpretation of these methods borrow heavily from significance testing but they introduce new issues that complicate their formulation. We'll consider these issues at September's QMN meeting.


Sample Size Calculations for One-way, Two-way, and Multi-way Classification Designs, 4 August 2023, 7:30-9:00AM, by Zoom
In our previous sessions we discussed how to adapt the sample size calculation for the two-sample t test using Bonferroni's correction to the more general case of testing for biases between three or more treatment groups in one-way and multi-way classification designs; however, we never looked at the exact sample size calculation methods for those designs. In this month's meeting we will start with the sample size calculation method for F tests for two-way and multi-way classification designs and then compare their results to those from the Bonferroni-corrected two-sample t test method.


Connections Between Sample Size Calculations for the Two-sample T Test, Two-level Factorial Designs, and Linear Regression, 2 June 2023, 7:30-9:00AM, by Zoom
In recent past QMN meetings we've discussed sample size calculations for the two-sample t test, the two-level factorial designs, and linear regression. All sample size calculations have similar structure, but these three methods have particularly close relationships that deserve to be discussed in more detail. The benefit of understanding these relationships is that it can make it easier to choose the necessary inputs for the calculations and there may be opportunities to perform a calculation for one method by using another method's solution or software implementation.


Sample Size Calculations for Linear Regression, 5 May 2023, 7:30-9:00AM, by Zoom
The next topic in our ongoing discussion of sample size calculation methods is linear regression. This is probably one of the most abused and ignored sample size calculation methods in engineering, science, business, and industry. Proper consideration of sample size for linear regression must take into account the goal of the experiment - usually to quantify (with a confidence interval) or test the value of (with a hypothesis test) the slope of the regression line; however, there are other crucial inputs to the problem including the range of observations on the independent variable (i.e. x) scale and the distribution of observations over that range. Given all of these inputs and an estimate for the noise/repeatability of the response (i.e. y) variable, an objective sample size can be determined for the experiment to build a regression model. These calculation methods are relatively simple; however, they are not supported in MINITAB and other common software.


Sample Size Calculations: Poisson Count Responses, 7:30-9:00AM, Friday, 7 April 2023, by Zoom
At this month's QMN meeting we will discuss sample size calculations for Poisson count responses. Poisson counts appear whenever you are counting the number of events per unit area of opportunity, such as:
We will consider sample size calculations for Poisson counts for the following situations:
Thankfully MINITAB supports most of these methods.


Sample Size Calculations: Two Proportions, 7:30-9:00AM, 3 March 2023 by Zoom
One of the most common and important experiment design categories is the two populations design. This design can be used to generically compare any two populations but it is especially important when comparing a gold standard or "control" method to a competing test method. This test versus control design has the benefit that it considers the test and control methods under the same conditions compared to the relative weakness of evaluating a test method in a one sample test without direct comparison to the control. The two populations design can be applied to measurement and attribute responses.

When the observed response in a two populations design is a binomial count, such as when we count the number of pass/fail events observed in a predetermined number of trials, then the statistical analysis is done using a two proportions test. There are two such tests available: Fisher's Exact Test and a normal approximation test. Fisher's test works under all circumstances but the calculations can be difficult. The normal approximation method is applicable under some common conditions and is easier to apply. Both analysis methods are implemented in good statistical software, such as in MINITAB's Stat> Basic Statistics> 2 Proportions menu.

As with all data collection and analysis exercises for the purpose of studying or improving a process, the two populations study deserves to be preceded with a sample size calculation to get the sample size correct. An uninformed choice of sample size runs the risk of 1) being too large and wasting time and resources or 2) being too small risking an incorrect decision. Given appropriate inputs about the history of the processes under study and the goals of the experiment, an objective sample size can be calculated. MINITAB provides support for those cases that can be analyzed using the normal approximation method with its Stat> Power and Sample Size> 2 Proportions method. When the normal approximation conditions aren't satisfied the custom FishersPower.mac MINITAB macro can be used. At this month's QMN meeting will consider both of these tools.


Sample Size Calculations: One Proportion, 7:30-9:00AM, 3 February 2023 by Zoom
Near the top of the list on the Pareto chart of most-used statistical analysis methods are methods for one proportion. These methods include the generic confidence intervals and hypotheses tests for one proportion but they also include specialized quality engineering applications such as attribute acceptance sampling and reliability demonstration tests. At this month's QMN meeting we will look at sample size calculations for the following one-sample proportion goals:
Thankfully MINITAB provides support for all of these methods but you can also perform these calculations with Russ Lenth's free Piface sample size calculator (https://homepage.divms.uiowa.edu/~rlenth/Power/) if you don't have MINITAB.


Sample Size Calculations: Standard Deviations and Process Capability, 7:30-9:00AM, 6 January 2023 by Zoom
At our December meeting we discussed sample size calculations for the two-sample means problem and the associated many-sample means problem. At our January QMN meeting we will discuss sample size calculations for standard deviations and MINITAB's support for the method. We will also study how those methods can be adapted for sample size calculations for process capability metrics. The result is quite depressing.


An Introduction to Sample Size Calculations - Part 3, 7:30-9:00AM, 2 December 2022, by Zoom
At our November meeting we discussed sample size calculations for the one-sample and two-sample Student t tests for location and at the end of that discussion we rushed into the extension of the two-sample t test to many samples. This month we'll go back and take the sample size calculation for the many-samples case more slowly. We'll review the sample size calculation for the two-sample t test, we'll extend its scope to many samples using Bonferroni's correction, and then we'll compare that result to the sample size for one-way ANOVA. We'll also look at how the sample size calculation for one-way ANOVA relates to ANOVA for two-way and multi-way classification designs.


An Introduction to Sample Size Calculations - Part 2, 7:30-9:00AM, 4 November 2022, by Zoom
At last month's meeting we started a discussion of sample size calculation methods. We started all the way back at the beginning of the topic and took our time with the material. We got through the z- and t-based one-sample tests and confidence intervals for the population mean - less than I'd planned but that's a good thing. This month we'll review those methods and then continue on with the two-sample test and confidence interval for the difference between two population means. We'll also extend the solution for the two-sample case to three or more samples. I plan to go over this material as slowly as you like, so please come prepared to ask lots of questions. We will continue with this topic in future meetings.


An Introduction to Sample Size Calculations, 7:30-9:00AM, 7 October 2022, by Zoom
We frequently address the topic of sample size calculations in this forum, usually taking on a specific method of interest. I recently heard a request to backtrack from the advanced material a bit and take the topic from the very beginning, so at the October QMN meeting we will discuss the sample size calculations for a few of the most basic statistical analyses:
I plan to go over this material as slowly as you like so please come prepared to ask lots of questions. We can continue on with this topic in future meetings.


Diagnostic Tests and ROC Curves, 7:30-9:00AM, 2 September 2022, by Zoom
A diagnostic test is used to distinguish two populations, for example, between diseased and healthy subjects, using a quantitative measurement compared to a threshold value. Observations that fall on one side of the threshold are judged to have the disease and observations that fall on the other side of the threshold are judged to be healthy. Diagnostic tests are also common in engineering, manufacturing, and other non-medical situations.

When the tails of the distributions of diseased and healthy subjects overlap on the measurement scale, the diagnostic test will misclassify some of the subjects. For example, the test will produce some false positives (subjects who are healthy but whose test indicates that they have the disease) and false negatives (subjects who have the disease but whose test indicates that they are healthy). Both types of errors have associated costs that must be taken into account when choosing the threshold value.

The overall performance of a diagnostic test is evaluated in terms of its true negative rate or specificity (the fraction of healthy subjects who are classified correctly) and its true positive rate or sensitivity (the fraction of diseased subjects who are classified correctly). The trade-offs associated with different threshold values can be evaluated using a receiver operating characteristic (ROC) curve - a plot of the true positive rate or sensitivity versus the false positive rate or 1 - specificity.


Smoothing Noisy Time Series Data - A Solution from the Technical Trading Stock Market Community, 7:30-9:00AM, 5 August 2022, by Zoom
Most of you know that my wife and I have a sailboat that we race and cruise on Lake Erie. The boat's instrument system is over 20 years old now and its LCD displays have lost their contrast so are effectively useless. I could/should just replace the instrument system but where is the fun in that? The boat speed, depth, and wind sensors all still work great, so as a hobby electronics project I set out to re-use the sensors and build everything else from scratch. I'm using an Arduino-like microcontroller to read the raw instrument data and a Raspberry Pi to process the data and write responses to a waterproof sunlight readable touchscreen display. Needless to say, there have been a lot of stumbling points along the way - little things like learning Arduino, Raspberry Pi, Python, and Kivy. I've learned a lot though so I keep telling myself that this is fun.

At this point all of the basic functionality of the system is working but I have encountered another unexpected stumbling point: I expected the sensor data to be noisy but assumed that filtering out the noise in software would be easy. NOT! My early filtering attempts came from simple statistical methods for time series data. Those methods do successfully filter the data but introduce a long, unnerving, distracting delay between a sudden change on the boat (such as wind speed) and when the effect of that change shows up on the displays. I knew there would be a trade off between the degree of smoothing and the time lag but I haven't able to find an acceptable compromise. I had to find a better way to filter the data without introducing long time lags. I initially looked to the electronics community for a solution but was surprised to find that the solutions I needed come from "technical" stock market trading. Technical traders write algorithms to identify reliable patterns in stock market data and then buy and sell stocks on that basis. Recognizing a change in a process quickly and reliably is crucial to their success. Many of the most successful methods are proprietary but the basic methods are well known and implemented in commonly available trading software. At this month's QMN meeting I will describe some of the time series filtering methods that I've discovered. The basic methods are native in MINITAB but I'll describe some other simple algorithms that can be implemented in MINITAB code or other software.


The Rank-Order Transform and Nonparametric Analysis Methods for When Your Data Aren't Normal, 3 June 2022, 7:30-9:00AM, by Zoom
We all know that the classical statistical analysis methods like the one-sample t test, two-sample t test, and ANOVA require that the data be normally distributed. Those methods aren't particularly sensitive to deviations from normality, especially when the sample sizes are large (yeah Central Limit Theorem!), but when you're not sure if a deviation from normality is too much then robust alternatives to the classical methods are provided by analogous nonparametric ones. The nonparametric methods (for the three tests mentioned) involve rank transforming the observations - that is, replacing the original measurement values with their rank order. The analogous nonparametric analysis methods for rank ordered data are provided by the one-sample Wilcoxon test, the Mann-Whitney test, and the Kruskal-Wallis test. MINITAB supports all of these methods from its Stat> Nonparametrics menu. Also remember that the nonparametric methods can be applied to any rank ordered data, even when a measurement scale isn't available.


Fitting Multiple Regression Models with Inputs Expressed in Physical Units, 7:30-9:00AM, 6 May 2022, by Zoom
When we build a designed experiment in MINITAB, MINITAB prompts us to enter the physical values of our process input variables (PIV); however, when it reports the results of the analysis it expresses the PIVs in coded units. For example, we might specify Temperature as a PIV with physical levels 30 and 50C, but MINITAB recodes those levels to -1 and +1, respectively, when it reports the regression equation. Why does it do that? Why doesn't it just report the regression equation in physical units? This seeming quirk isn't unique to MINITAB either. Every other reputable statistical software does the same thing. The need to "code" the PIVs to +/-1 values (or some other coding scheme) is required to determine independent and accurate regression coefficients that can be used to judge the effect of and the statistical significance of the PIVs. A regression equation CAN be expressed in terms of the physical units; however, those regression coefficients may be contaminated with contributions from other PIVs that will lead to confusion and misinterpretation of the effects of the PIVs on the response. Proper coding of the PIVs solves that problem. At this month's QMN meeting we will look at the root cause of the need to code PIVs when doing multiple regression and we will identify the properties of models that permit or don't permit expressing a multiple regression model in terms of the physical values of the PIVs.


Double and Multiple Sampling Plans Versus Bonferroni-Corrected Single Sampling Plans Adapted for Double and Multiple Sampling, 1 April 2022, 7:30-9:00AM, by Zoom
At our last meeting I described how to use Bonferroni's method to expand a zero acceptance number sampling plan to allow one or more defectives in double or multiple inspection episodes. The Bonferroni method is technically valid; however, it overlooks a structural issue in adapting single sampling plans into double or multiple sampling plans that makes its sample sizes larger - sometimes much larger - than they need to be. At this month's meeting we will compare the Bonferroni-corected single sampling plans adapted for double and multiple sampling to the formal methods available for designing double and multiple sampling plans.


Use of Bonferroni's Method to Account for Early Defectives in Attribute Sampling, 7:30-9:00AM, 4 March 2022, by Zoom
At last month's QMN meeting we discussed the application of Bonferroni's correction to the post-ANOVA multiple comparisons test problem; however, applications of Bonferroni's method have much broader applications. I was recently helping a customer design a single sampling plan for attributes to demonstrate that the proportion defective of a process is less than 5% with 95% confidence. The required sample size for the zero acceptance number sampling plan comes from the well known Rule of 3: n = 3/pmax where pmax is the allowed upper limit on the proportion defective. To meet the 95% confidence of less than 5% defectives goal, the required sample size is n = 3/0.05 = 60. But my customer was rightly concerned about the possibility of finding a defective unit before reaching the n = 60 sample size so we revised the sampling plan design using Bonferroni's method to allow a two-stage sampling process that allows for an early defective. The nature of this problem is also present in interim analysis and double sampling plans. We'll look at the applications of Bonferroni's method in sampling plan design and these related methods at this month's QMN meeting.


Bonferroni's Correction for Multiple Comparisons Tests, 7:30-9:00AM, 4 February 2022, by Zoom
When we're planning a statistical analysis by hypothesis test or confidence interval one of the decisions we have to make is what type 1 or false alarm error rate to tolerate. The most common choice is 5%; however, that choice must be reconsidered when more than one test is planned. This problem arises naturally and is very common. For example, if we need to test for a difference between two treatment groups then only one test is necessary and a 5% error rate is appropriate, but if there are more than two treatment groups then we will have to test for differences between all possible pairs of treatments and the number of tests can grow very large. For example, in the simple case of tests to compare five treatment groups there will be 10 tests: 12, 13, 14, 15, 23, 24, 25, 34, 35, and 45 where the numbers 1, 2, ..., 5 indicate treatment group IDs and a pair of numbers indicates a test between those treatments. The large number of tests, each with a 5% error rate, makes it more likely that we will commit one or more errors among the many tests required. This forces us to reconsider the choice of a 5% error rate per test. The first solution to deal with this multiple comparisons testing problem was offered by Bonferroni who observed that we can control the error rate for a family of tests by setting the individual test error rate equal to the family error rate divided by the number of tests we intend to perform. In our previous example of 10 tests to compare five treatment groups, Bonferroni's method advises that to hold a 5% error rate for the family of 10 tests we need to use a 0.05/10 = 0.005 or 0.5% error rate for individual tests. This approach is simple, conservative, and very flexible so it is used more often than every other type of multiple comparisons test.


Weighted ANOVA and Weighted Regression (What To Do When You Can't Find a Variable Transform), 7:30-9:00AM, 7 January 2022, by Zoom
When we perform ANOVA or regression we always analyze the model residuals to determine if the assumptions of normality and homoscedasticity (aka equal variances) are satisfied. When they're not, a variable transform - such as taking the log, square root, power function, or reciprocal of the response - may resolve the problem and we can go on with our planned analysis. However, there are times when the residuals are heteroscedastic and we just can't find a variable transform that fixes the problem. A common example is when the experimental data are collected using two or more different measurement instruments or methods that have different inherent measurement precision. ANOVA and regression fail under these conditions; however, they can be salvaged by proper weighting of the residuals. This sounds complicated but it's quite simple: weighted ANOVA or regression requires you to identify a function that accounts for the differences in standard deviations, use the function to determine weights, and then re-run the ANOVA or regression with the weights incorporated into the model. We can even use the original residuals diagnostic methods for checking assumptions by analyzing the weighted residuals instead of the original/raw residuals. We'll take a look at these methods in this month's meeting.


Resampling Methods, 7:30-9:00AM, 3 December 2021, by Zoom
I'm so used to my old habits when working in MINITAB that I often don't notice additions that have been made to the program. Recently I was talking a customer through an analysis and did a double-take when I noticed the Calc> Resampling menu. I'm not sure when this menu was added, but it's a great addition to MINITAB and definitely worth talking about in a QMN session.

The traditional methods for constructing confidence intervals and performing hypothesis tests are based on the z, t, chi-square, F, and other distributions that can feel abstract and, frankly, much like magic to novices. Even after we get those methods under control there are often situations in which we can be uncertain or uncomfortable that the assumptions required for their use are satisfied. In such circumstances, the family of resampling methods, which rely only on sample data and special but intuitive resampling procedures, can provide a comforting and useful alternative set of analysis tools that have fewer assumptions and constraints than the traditional methods. So at this month's QMN meeting we will discuss the use of resampling methods for confidence intervals and hypothesis tests and compare their results to those from the traditional methods. This topic is likely to span more than one session so make sure you join us next week so that you're not behind in the following sessions.


Tests and Sample Size Calculations for Poisson Count Responses, 7:30-9:00AM, 5 November 2021, by Zoom
We've spent a lot of time discussing tests and sample size calculations for measurement responses and for proportions (e.g. proportions defective or yield); however, we haven't taken up the topic of tests and sample size calculations for Poisson distributed counts, such as defect counts or pretty much any count-per-unit-something. At this month's QMN meeting we will discuss the one-sample, two-sample, and many-sample tests for Poisson counts and their associated sample size calculations.



Tests for Homoscedasticity (aka Equal Variances) by F, Bonett, and Levene Test Methods, 7:30-9:00AM, 1 October 2021, by Zoom
At this month's QMN meeting we will review the F test for homoscedasticity and consider two alternative tests: Bonett's and Levene's tests.

One of the most frequently checked assumptions when working with two or more independent populations is the assumption of equal variances or homoscedasticity (from the Greek for "same dispersion"). In the simplest case of two treatment groups, the classical method for testing the homoscedasticity assumption is the F test where the F statistic is given by the ratio of the two sample variances. The F test works very well when the two populations being studied are normally distributed; however, errors creep in when those distributions deviation from normality. This issue is sufficiently serious that modern versions of MINITAB default to more robust methods (Bonett and Levene) and bury the F test in its submenus. Levene's method also has the added benefit of being applicable when there are two, three, or more treatment groups.


The Two-Sample T Test and the Paired-Sample T Test, 7:30-9:00AM, 3 September 2021 by Zoom
Two of the most frequently used hypothesis testing methods are the two-sample t test and the paired-sample t test. Both methods are tests of means so they're obviously closely related which makes them easily confused but they deal with very specific situations and it's crucial to choose the correct method for an analysis
Example 1. Suppose that you need to test for a difference in the operating lifetime of a device on batteries supplied by two different manufacturers. To perform the experiment you would collect random samples from the two manufacturers, operate the device on those samples and record the battery lifetimes, and then use the two-sample t test to determine if they are different from each other.

Example 2. Suppose that you need to test for a difference between two nondestuctive test methods that are supposed to deliver the same results. To perform the experiment you would collect a sample of units to be tested, measure them under both test methods, and then use the paired-sample t test to determine if there is a bias between the two test methods.

This all sounds pretty simple; however, it's not always so easy. I was recently working on a complicated test plan for a customer. We designed the experiment and I immediately recognized the opportunity for using the two-sample t test; however, I failed to recognize that the data collection scheme also provided the opportunity for using the paired-sample t test. I was uncomfortable with the two-sample t test analysis that I recommended and eventually considered a simplified version of the experiment that revealed the paired-sample t test opportunity. As it turned out, the paired-sample t test required a smaller sample size than the two-sample t test, so the extra sample size that we planned for the two-sample t test just provides greater power for the paired-sample t test.


Organizational Statistical Maturity Checklist, 7:30-9:00AM, 6 August 2021 by Zoom
As a consultant I see a wide range of statistical and quality engineering skills and practices among my many customers. Invariably they all want to know how their company compares to others. An appropriate instrument or measurement tool to make such comparisons is an organizational statistical maturity checklist. I started such a checklist long ago intending to get back to it some day and now is the time. At this month's QMN meeting I'll present my draft and notes on the topic. Please join our discussion to contribute your own thoughts on what should be included in the checklist, how it should be organized, and how it should be scored. Maybe we'll follow up by executing the checklist at work and then comparing results at a future meeting.


Modeling Standard Deviations, 7:30-9:00AM, 4 June 2021 by Zoom
When we're doing experimental work our first concern is for understanding how process input variables (PIV) affect the process's mean response. The statistical analysis methods used to compare two or more means or many means under diverse conditions are the two-sample t test, ANOVA, and regression. There is an assumption required of those methods that the standard deviation of the noise in the process is constant under all conditions - a state referred to as homoscedasticity. When that condition is not satisfied (i.e. when the noise is heteroscedastic) we can often deal with the problem by applying an appropriate variable transform to the response. A logarithmic transform (log or ln) usually works. The are times, however, when such transforms fail and it becomes necessary to build experiments to study how the standard deviation of a process's response changes as a function of the PIVs. These analyses for standard deviations are performed using methods that are analogous to those used for analyzing means. At this month's meeting we will consider the tests and analysis methods available to study how standard deviations vary in the context of experiments with two treatment groups, many treatment groups, and in designed experiments.


The Slipped Confidence Intervals Method versus the Two-Sample t Test Method, 7:30-9:00AM, 7 May 2021, by Zoom
My friend Mark is planning a clinical trial for which we designed an appropriate experiment to be analyzed using a two-sample t test with a matching sample size calculation; however, his sponsors, who have limited statistical knowledge and skills, were confused by how "statistical power" enters the sample size calculation and have demanded that we perform the analysis by the slipped confidence intervals method instead. In this method, the data from two independent populations are collected and confidence intervals are calculated for their population means. If the two confidence intervals are slipped, i.e. don't overlap, then we reject the null hypothesis H0: the two population means are equal in favor of the alternate hypothesis HA: the two population means are different. While this analysis method is simple - it certainly has a very easy-to-understand graphical presentation - it suffers from some serious flaws that discourage its use. I learned to avoid the slipped confidence intervals method long ago, but until now I was never forced to look into it seriously. So this week we will compare the wrong way to do the analysis (the slipped confidence intervals method) to the right way to do the analysis (the two-sample t test method).

Follow-up: After our discussion in this meeting we figured out that when the confidence levels of the two confidence intervals is adjusted to 84% the slipped confidence intervals method has Type 1 error rate of 5% and matches the statistical power of the two-sample t test. That is, the two slipped confidence intervals test methods using 84% confidence intervals is equivalent to the two-sample t test.


Normality - When Does It Matter and When Does It Not? (Part 3), 7:30-9:00AM, 2 April 2021, by Zoom
At the last two QMN meetings we've been talking about where the normality assumption applies and where it does not, especially in the context of process capability analysis. We weren't quite done with that conversation so we're going to take it up again in this third - and hopefully last - session on this topic. I'll come to the meeting with a collection of examples that demonstrate the difficulties that we've been having to prime the discussion. Hopefully after this meeting we can achieve some better understanding if not clarity on these issues.


Normality - When Does It Matter and When Does It Not? (Part 2), 7:30-9:00AM, 5 March 2021, by Zoom
Many statistical analysis methods require or work better when the data follow a normal distribution; however, in experiments with complex structure it can be difficult to decide what to check for normality. One example that we talked about last month - one that instigated this discussion topic - is the very important problem of process capability analysis when the data set contains samples from several lots when there are biases between lots. There are three distributions that could be tested for normality: the distribution of the original data set, the distribution of the noise within lots, and the distribution of the biases between lots. At this month's meeting we'll discuss how to run the analysis in this situation and some more complex ones.


Normality - When Does It Matter and When Does It Not?, 7:30-9:00AM, 5 February 2021, by Zoom
I ran into two recent instances of mistakes made in testing for normality to support another analysis:
These are just two of many possible ways that a simple normality test is inappropriate and may mislead you. We'll talk about these two and many other cases at this month's meeting.


Development, Validation, and Use of Subjective Measurement/Observation Scales Using Ordinal Data, 7:30-9:00AM, 8 January 2021, by Zoom
Way back at our 4 August 2017 QMN meeting we discussed the development of a pseudo-measurement system for making subjective observations on an ordinal scale. The specific application was Joe R's need for developing a measurement system for interpreting the severity of material corrosion. Ordinal scales have a sense of size (e.g. this is bigger than that) but don't have a fixed unit of measurement (e.g. inches, seconds, ...). Generally when presented with an inspection made on a subjective ordinal scale we try to upgrade the ordinal observations to a true quantitative interval scale; however, there are many situations in which the upgrade is impossible and we must live with the subjective ordinal data. When this problem comes up we talk about it in the context of solving a specific problem (like Joe R's in that QMN meeting); however, at this month's QMN meeting let's talk about the general steps required to develop, validate, and use measurements made on an ordinal scale. We'll also talk about designing experiments for use with an ordinal response and the associated issue of determining the sample size for such an experiment.

Quality, Statistics, Engineering, and Science Reading List, 7:30-9:00AM, Friday, 4 December 2020, by Zoom
On the small chance that anyone else out there still reads (yes, I still read actual physical books with paper pages), let's discuss our favorite quality engineering, statistics, engineering, and science books. I keep a list of the books that I frequently recommend posted here that we can start from but come ready with your own recommendations.


Why We Randomize, 7:30-9:00AM, 6 November 2020,  by Zoom
One of the good indicators of you or your organization's "statistical maturity" is your understanding and insistence on the use of randomization when you're collecting experimental data. As is often the case, this discussion topic was instigated by a recent customer experience. This customer performed a simple experiment to compare four different treatment groups for possible differences in their means and standard deviations and asked for my help in running the analysis. (I wasn't involved in the design of the experiment at all.) When I ran the analysis, which indicated the presence of statistically significant differences between the treatment groups, I included a disclaimer that because the run order of the observations was not reported to me I couldn't say for certain whether the observed differences were truly due to the treatment groups or if they were due to an unobserved lurking variable if the observations were not run in random order. Initially my customer didn't notice or comment on my disclaimer, but when they looked at the differences between the treatment groups those differences were completely contradictory to what they expected but correlated well with the non-random run order that they used to collect the data. The experiment was expensive and time consuming to perform; however, they can't deny that the observed effects are better explained by a run order effect than by differences between the treatment groups so they are reluctantly committing to repeat the experiment, this time using a randomization plan to control for lurking variables and run order effects. Lessons like this are hard to learn. Instructors and advisors and technical experts can tell you again and again and again that you should be randomizing but until you get burned in a major, traumatic way, you never really understand or appreciate the necessity of randomizing the order of the runs in your experimental work.


Configuring MINITAB's Stat> ANOVA> General Linear Model Menu (Part 2) and Related Methods, 7:30-9:00AM, 2 October 2020, by Zoom
Last month we discussed how to configure MINITAB's Stat> ANOVA> General Linear Model menu. I was rushing at the end of the presentation, skipping some of the examples and advanced methods that I intended to cover, so we'll pick up this topic again this month. We'll also look at the related methods/menus that MINITAB provides for including:


Configuring MINITAB's Stat> ANOVA> General Linear Model Menu, 7:30-9:00AM, 4 September 2020, by Zoom
One of the most powerful tools that MINITAB provides for data analysis is its Stat> ANOVA> General Linear Model menu. This menu can be used to analyze a quantitative response as a function of one or more predictor variables in a wide variety of experiment designs. MINITAB does offer some menus to analyze some simple experiments like Stat> ANOVA> One-Way; however, the Stat> ANOVA> General Linear Model menu is not that much more difficult to configure and its capabilities encompass those of all of the other methods and much, much more. My take on this is that I'd rather learn to use one very powerful tool to do the vast majority of my work than have to learn the intricacies of many simple tools. So this month we will discuss how to configure Stat> ANOVA> General Linear Model for the following issues:


Fitting Curved Functions to Y versus X Data, 7:30-9:00AM, 7 August 2020, by Zoom
At this month's QMN meeting we will discuss methods for fitting curved functions to experimental y versus x data from a scatterplot.
The most frequently used method to fit a function to y versus x data in a scatter plot is linear regression which has a linear model of the form y = b0 + b1x where b0 and b1 are regression coefficients determined from the sample data; however, when the y versus x plot shows curvature we have to consider a different model. There are three approaches which might be appropriate:
The choice of which form of model to use should be driven by first principles understanding when possible. We will use MINITAB to fit models to example data using all of these methods.


Sample Size Calculations for One- and Two-Sample Proportions - Examples, 7:30-9:00AM, 5 June 2020, by Zoom
Given the great interest in last month's topic (sample size calculations for proportions), let's do a follow-up session. Last month I felt that I rushed through the material, spent too much time covering too many methods, and not enough time looking at examples. So let's go back this month and quickly review each method but spend more time carrying out example sample size calculations. We'll use MINITAB's Stat> Power and Sample Size menu as much as we can but we'll also work out by hand or by other methods sample size calculations that MINITAB doesn't support. In particular we'll look at sample size calculations for the following problems:


Sample Size Calculations for One- and Two-Sample Proportions with Applications to Managing Defective Rate and Reliability, 7:30-9:00AM, 1 May 2020, by Zoom
I've had a recent flurry of requests for help with sample size calculations for attribute pass/fail responses. These are very common problems and many companies have internal expertise to get these calculations done, but for the rest of us they can be a challenge. Note that these problems can be expressed in terms of a defective rate goal, such as "We need to be 95% confident that the defective rate is less than 1%" or as a reliability goal "We need to be 95% confident that the reliability is at least 99%". The two forms are just simple complements of each other because reliability is equal to 1 minus the defective rate. The two types of responses, fraction defective and reliability, are generically referred to as proportions.

At this month's meeting we will look at the sampling plan design and sample size calculations for the following one-sample and two-sample problems for proportions. The cases we will consider are:
* A one-sided upper confidence limit for the proportion when that proportion is small
* The special case of the Rule of Three
* A two-sided confidence interval for the proportion when that proportion is moderate (say between 10 and 90%)
* Hypothesis test for one proportion
* Hypothesis test for two proportions by Fisher's Exact Test and the normal approximation

We will talk about how to perform these calculations by hand (they're generally pretty simple) using mostly approximation methods and we will confirm our answers using MINITAB where we can; however, there are several problems that MINITAB doesn't do that we'll also consider.


An Introduction to MINITAB Macros, 7:30-9:00AM, 3 April 2020, by Zoom
You have all seen in class or meetings that I frequently use the MINITAB command line or macros to do some tasks. I find the command line is often faster than using the mouse and GUI to configure analyses and it can be very convenient when you have to repeat the same analysis several times. And when you have a series of commands that you need to perform frequently, MINITAB makes it easy to collect those commands and re-run them or to make them into an EXEC macro that you can run as needed. When you exceed the capabilities of EXEC macros, you can modify an EXEC macro to create a LOCAL macro that can be easier to use and capable of more complex operations. At this month's meeting I'll demonstrate this analysis development sequence: how to run an analysis from the GUI, how to run the same analysis from the MINITAB command line, how to capture those operations to create an EXEC macro, and how to modify the EXEC macro to create a LOCAL macro.


Taguchi's Contributions to Quality Engineering, Paul Pastor, 7:30-9:00AM, 6 March 2020, Lakeland Community College, Room T136
Dr. Genichi Taguchi was a mechanical engineer who made several important advancements in Quality Engineering. Among them, Taguchi introduced “Robust Design” to the quality world.  Robustness in the Taguchi sense is to identify the process input variables that are uncontrollable and to minimize their effects on critical to quality (CTQ) characteristics. Taguchi also created a “Loss Function” which merges process variation, cost, and process targets into a key metric used to determine lost value passed on to society. This metric considers specifications as a minor factor in determining lost value. Taguchi also made significant contributions to “parameter design” techniques used in quality improvement of products and processes.
Today we will present Taguchi's Robust Design, Loss Function, and "Off-line” Quality improvement process consisting of: 1) System Design, 2) Parameter Design, and 3) Tolerance Design. We will discuss a Parameter Design problem that looks at control factors, noise factors, and the use of orthogonal arrays to perform a designed experiment. The Signal-to-Noise (S/N) ratio concept that Taguchi developed will also be discussed.


Goodness-of-Fit (aka Lack-of-Fit) Tests, 7 February 2020, 7:30-9:00AM, Lakeland Community College, Room T136
The most common model-fitting task most of us perform is fitting a simple linear regression model of the form y = b0 + b1x where y is the response, x is the predictor, and b0 and b1 are regression coefficients. An appropriate - and necessary - follow-up analysis is to question whether the linear model provides a good fit to the experimental data. Most people check the R-squared value and conclude that if R-squared is sufficiently large then the linear model fits the data and if R-squared is too small then the linear model does not fit the data, but that's an incorrect use of R-squared. (We've talked about how R-squared values are often misused in a past meeting.) Whether a model fitted to data has the correct form or not is a question dealt with by a special set of model fitting diagnostic tools called goodness-of-fit, aka lack-of-fit, tests.

The general strategy of a goodness-of-fit test has three steps:
1) Fit your desired model to the data.
2) Propose a logical complication to your model that could fit the data better. Fit the more complicated model.
3) Compare the two models by testing for statistical significance of the added complication. If the complication is statistically significant, then the original model provides an insufficient fit to the data. If the complication is not statistically significant, then the original model provides a sufficient fit to the data.

This strategy can be easily applied to our simple linear regression problem:
1) Fit a linear model to the data.
2) A deviation from a linear model could involve curvature in y versus x, so fit a quadratic model of the form y = b0 + b1x + b2x2 to the data.
3) Check the quadratic regression coefficient b2 for statistical significance. If b2 is statistically significant, then the linear model was insufficient and the quadratic model fits the data better. If b2 is not statistically significant, then the quadratic term can be dropped from the model and the linear model is a sufficient fit to the data.

Fitting a quadratic model to test a linear model provides a very simple goodness-of-fit test but there are even better methods available and the same strategy can be applied to more complicated cases. We'll look at these and other examples of goodness-of-fit tests at our February meeting.


Fixed and Random Variables in Statistical Analysis, 10 January 2020, 7:30-9:00AM, Lakeland Community College, Room T136
American Statistical Association's (ASA) Statistical Consulting Section is currently hosting a discussion about the distinction between fixed and random variables in ANOVA and regression models. This issue comes up any time you're analyzing a data set which involves a qualitative/categorical predictor variable with two or more levels. In the process of setting up the statistical analysis, you have to specify whether such a variable is fixed or random. Sometimes the distinction is obvious but other times not so much. In the simplest cases, if an experiment includes all possible levels of a qualitative variable, then that variable is a fixed variable in the analysis. However, if the experiment only contains a random sample of many possible levels of that variable, then that variable is a random variable in the analysis. It's important to correctly specify the nature of each qualitative variable in an analysis as fixed or random because 1) the choice affects how the ANOVA or regression calculations are performed and 2) the interpretation of the analysis results are different.

As a practical example of the fixed versus random choice, consider operators in a gage error study. If the operators included in the study are the only operators who ever make that measurement, then operator must be treated as a fixed variable. However, if the operators included in the study are a random sample from a large population of operators, then operator must be treated as a random variable.

So at this month's QMN meeting we will begin with a review of fixed and random variables, how they're specified when setting up an analysis, and how they are interpreted. Then we will read and discuss some of the more interesting postings in the Statistical Consulting Section's discussion of the topic.


Like Nails On A Chalkboard, 6 December 2019, 7:30-9:00AM, Lakeland Community College, Room T136
As creators and consumers of information presented using statistical methods we've all suffered through instances of the abuse and misuse of those methods. At this month's QMN meeting let's discuss the phrases and mistakes we hear that make us cringe. Candidate topics are:


Critique of a YouTuber's Experiment to Test the Mechanical Properties of 3D Printed Parts, 1 November 2019, 7:30-9:00AM, Lakeland Community College, Room T136
My brother is a hobbyist woodworker and uses a 3D printer to make jigs and fixtures for some of his fancier work. A while ago he pointed me to the YouTuber CNCKitchen who posts videos on building and using 3D printers, CNC equipment, and other neat home-made hardware. Among CNCKitchen's projects is a home-made tensile tester that he uses to evaluate the mechanical properties of 3D printed test samples. He's posted studies of many different 3D printing process variables but in a recent posting he studied extrusion width. In this posting he's very thorough in his descriptions of the responses, study variable, and other variables and even mentions Design of Experiments but his DOE, statistical analysis, and data presentation skills still infuriated me. I thought it would be fun (cathartic?)  to watch his video together and then go back through it to critique his work and identify opportunities to improve his future experiments.


Equivalence, Superiority, and Non-inferiority Tests - Part 2, 4 October 2019, 7:30-9:00AM, Lakeland Community College, Room T136
At this month's QMN meeting we will continue our discussion of equivalence tests and their related methods. We'll start with a quick review of equivalence tests, especially of the two one-sided tests (TOST) method using confidence intervals, and we'll look at the one-sample, two-sample, and many-sample cases with examples. We'll follow up with discussion and examples of superiority and non-inferiority tests.


Equivalence Tests, 6 September 2019, 7:30-9:00AM, Lakeland Community College, Room T136
The hypothesis testing method that all of us learned first and use almost exclusively is the method of significance tests. The goal of significance testing is to reject the null hypothesis of no difference or no effect in favor of the alternate hypothesis that a difference or effect is present. As an example, suppose that the goal of an experiment is to demonstrate that the population mean for a new process (#2) is different from the population mean for the old process (#1). Then we would test the hypotheses H0: µ1 = µ2 versus HA: µ1  ≠ µ2 and reject H0 in favor of HA if µ1 and µ2 were statistically far apart. Under the strict rules of hypothesis testing there is no opportunity to accept H0. We can only reject it in favor of HA or else the test is inconclusive. This approach puts the burden of proof on the data. It forces us to honor Sagan's guidance that the extraordinary claim (HA) requires extraordinary evidence. But what if the goal of the experiment is to demonstrate that there is no difference between the two population means? To honor Sagan's requirement we must put the burden of proof on the data by inverting the original hypotheses, writing the new hypotheses as H0: µ1 ≠ µ2 versus HA: µ1 = µ2 with the intention of rejecting H0 in favor of HA. This test belongs to the family of equivalence tests. Slight modifications to these hypotheses give rise to related methods called superiority tests and non-inferiority tests. All of these testing methods: significance tests, equivalence tests, superiority tests, and non-inferiority tests, can be easily interpreted using simple confidence intervals. So if you've ever needed a test other than a significance test come join us at this month's meeting to discuss the use of these other testing methods.


Paper Helicopter Experiments, 2 August 2019, 7:30-9:00AM, LCC Room T136
In the theme of summer vacation, let's do something fun at next week's QMN meeting: Let's run paper helicopter experiments! Because of its low cost, ease of construction, and myriad design variables, the paper helicopter provides a valuable vehicle for learning design of experiments (DOE) methods. I'll bring printed copies of the paper helicopter template, scissors, tape, and everything else we'll need to make paper helicopters. And Lakeland has some great balconies for dropping them.

We'll start the session by quickly reviewing the DOE process. Then we'll execute a three step DOE program to study paper helicopter flight time as a function of several design and process variables:
1) A preliminary experiment with one paper helicopter design to estimate the standard deviation of flight time. This standard deviation will be used as an input for the sample size calculation of the next step.
2) A two-level factorial or response surface design that will be used to determine the paper helicopter geometry and operating conditions that maximize flight time.
3) A follow-up experiment using the optimal paper helicopter design to confirm the predicted maximal flight time.


SPC and Process Capability for Processes with a Drifting Mean - Part 2, 7 June 2019, 7:30-9:00AM, LCC Room T136
At last month's QMN meeting we discussed SPC and process capability methods for processes with drifting means such as tool wear processes. Our discussion was limited to the simplest cases so this month we'll resume the conversation to talk about more difficult and diverse situations. The abstract from last month's meeting is presented below to provide more background on the topic.


SPC and Process Capability for Processes with a Drifting Mean, Such as Tool Wear, 3 May 2019, 7:30-9:00AM, LCC Room T136
The ideal conditions for the use of a traditional Shewhart SPC control chart is when the process being studied is producing units that come from a single stable process with a constant mean, constant standard deviation, and follow a normal distribution. It makes sense in this simple case that the control limits for the sample mean are calculated as +/- deviations about a fixed center line. One of the more malicious of the many exceptions to these conditions is when the process mean drifts steadily with time (or number of operation cycles). A common example of this behavior is the tool wear problem which causes a sawtooth pattern of part sizes on a chart for sample means made up periods of linear drift in part size between tool replacement or adjustment events. Thankfully there are special control charts, called acceptance charts, for such processes that use control limits that are placed inside of and relative to the upper and lower specification limits instead of being referenced to the chart centerline. Alternatively, a variant of a traditional xbar chart can be used with a sloping, instead of horizontal, center line. At this month's QMN meeting we'll discuss process control methods for processes with drifting process means and some ideas for evaluating their process capability.


Reliability Test Planning, Part 2, 5 April 2019, 7:30-9:00AM, LCC Room T136
At last month's meeting we discussed the basic concepts of reliability test planning and considered some of the simplest experiment designs. (See last month's abstract below.) This month we will review those topics (to catch up anyone who didn't make last month's meeting) and then we will look at some more complicated cases. We'll wrap up with a discussion of how to execute the planned experiment and how to perform the data analysis.


Reliability Test Planning, 1 March 2019, 7:30-9:00AM, LCC Room T136.
At this month's QMN meeting we will discuss reliability test planning. The response of interest in a reliability test can be either the time (or number of cycles to failure) when a specified failure fraction occurs or the failure fraction at a specified time and the goal of a reliability test can be to either demonstrate that a minimum acceptable condition is satisfied or to estimate the value of a reliability parameter. Common examples of these problems are:
We'll look at these four cases and others, their associated experiment designs, sample size and acceptance criteria requirements, and how to analyze their experimental data.


A Tour of Micro Laboratories, 4 February 2019, 8:00-9:30AM, at Micro Labs.
Keith Kokal, the President and Owner of Micro Laboratories in Mentor, has invited us for a tour of the Micro Laboratories facilities. Micro Laboratories is a calibration services provider with capabilities including dimensional, mechanical, and electrical measurements. You can see a detailed list of their capabilities here. One of Keith's newest toys that he's excited to show off is their MasterScanner - a highly automated state-of-the-art thread measurement and calibration instrument. NIST comes to Micro Labs to use their Master Scanner.

We have to ask you to make a reservation for this event so that Keith can plan how they're going to manage a crowd in his labs. Please e-mail me if you would like to come. We'll send more details as we get closer to the event date.


Use Propagation of Error to Focus Your Process Improvement Activities, 4 January 2019, 7:30-9:00AM, Room T136.
To continue our recent theme of process capability and tolerancing, at this month's QMN meeting we will consider propagation of error - a method used to determine how variation in a process's input variables induces variation in its output variable or variables.

When a critical to quality (CTQ) characteristic depends on one or more process input variables (PIV) any variation in the PIVs will also cause variation in the CTQ. This effect, the transmission of variation from the PIVs to the CTQ, is called propagation of error. Propagation of error is easy to understand in simple cases, such as when the PIVs are arranged in a simple linear stack-up; however, the problem becomes more difficult when the CTQ is a complex function of the PIVs. 

Suppose that you're in the business of making coiled steel springs and you have a customer who is pissed off because of excessive variability in your product. Your customer's CTQ is the spring constant - the spring's change in force per unit change in length. The spring constant's PIVs are the modulus of the steel, the diameter of the steel wire, the diameter of the wire coil, and the number of coil turns and the spring constant is related to the PIVs by a known theoretical equation. If you know the process capabilities of the PIVs, which one or ones should you improve to make this customer happy? Unless you get very lucky, the easiest answer - improve those PIVs that have the worst process capability - is probably wrong. The correct answer requires that, in addition to considering the process capabilities of the PIVs, you must also consider the CTQ's sensitivity to them. Propagation of error combines the PIV's process capabilities and the CTQ's sensitivities to them to determine the true contributions to CTQ variability coming from its PIVs. Only after performing the propagation of error analysis can you correctly determine which PIV to take action on.

In addition to the spring problem we'll look at three others:


Strength-Load Interference, Interference Fits, and Stack-up Tolerances, 7 December 2018, 7:30-9:00AM, Room T136.
In our discussions from the last two months on process capability evaluation with variable tolerances (such as for GD&T true position with bonus tolerances) one of the fundamental topics that kept coming up was the treatment of interference fits. In hindsight that would have been a good background discussion for us before we took on the much harder variable tolerances topic, but we'll take care of that now. So at this month's meeting we'll discuss the statistics of interference fits, stack-up tolerances, and the related topic of strength-load interference. We'll look at three cases with analytical solutions: normal-normal interference, exponential-exponential interference, and Weibull-Weibull interference and we'll address the many other cases using Monte Carlo simulation.


Process Capability for GD&T True Position, Part 2, 2 November 2018, 7:30-9:00AM, Room T136.
At last month's very well attended meeting we discussed some basics of Geometric Dimensioning and Tolerancing (GD&T) and the complications of assessing process capability in the presence of true position bonus tolerances. Thanks to Scott H for describing the problem and his preferred solution by the residuals method and to everyone who attended for the lively discussion. This is a huge, murky topic so we'll resume our discussion at this month's meeting. We'll take a more careful look at how the residuals method calculations are performed, at some of the process capability statistics reported in common software, and at some real data volunteered by Alyssa W.


Process Capability for GD&T True Position, Part 1, 5 October 2018, 7:30-9:00AM, Room T136.
My (Paul) understanding of GD&T is weak so Scott H is going to open this month's session with an introduction to GD&T True Position. There's a good introduction to the topic, including a painfully slow video, posted here. From that posting:

True Position – Location of a Feature
Position in terms of an axis, point, or plane defines how much variation a feature can have from a specified exact true location. The tolerance is a two- or three-dimensional tolerance zone that surrounds the true location where a feature must lie. Usually when specifying true position, a datum is referenced with x and y coordinates that are basic dimensions (i.e. do not have tolerances). This means that you will have an exact point defined where the position should be and your tolerance specifies how far from this you can be. The location is most often positioned with two or three datums to exactly locate the reference position.   The true position is usually called out as a diameter to represent a circular or cylindrical tolerance zone.

One of the complications inherent in tolerancing by True Position is that the positional tolerance changes based on the feature’s size. For example, if several raised cylindrical posts on your rectangular plate must engage with matching holes in your customer's part, then how well you can hold the diameter of posts affects how much their location can vary. As the posts approach their minimum allowed diameter (least material condition or LMC) then their location tolerance increases proportionally and, of course, this complicates the calculation of process capability statistics.

This example demonstrates just one of many difficulties associated with performing process capability for True Position. We'll look at this and related issues at this month's meeting.


Design of Gage R&R Studies Part 3, 7 September 2018, 7:30-9:00AM, Room T136.
After our second meeting on August 10th on the topic of gage R&R studies we still have some unresolved questions to discuss so we will pick up the topic for a third time.

During the last meeting we discussed the use of MINITAB's Stat> Quality Tools> Gage Study> Gage R&R Study (Extended) menu for experiments with more variables than parts and operators; however, there are still some GR&R study experiment designs that MINITAB's extended and standard menus cannot handle and that require hands-on analysis using ANOVA and variance components analysis (VCA). We'll look at at least one such example: when there are no operators or other reproducibility variables in the measurement process.

In the second half of the meeting we'll discuss the number of parts, operators, and trials for attribute studies with special attention paid to the selection of the number of parts containing each defect category that the attribute measurement system is intended to detect.


Design of Gage R&R Studies Part 2, 10 August 2018, 7:30-9:00AM, Room T136.
We had a great - and somewhat terrifying - discussion about gage R&R study design at our June 1st QMN meeting but there were many related issues that we didn't get to so we will take up the topic again at our August meeting. We'll do a quick review of the motivations for deviating from the classic 3 operator, 10 part, and 2 trial gage R&R crossed experiment design. Then we'll discuss how to design and analyze gage studies with additional variables such as instrument type, measurement procedure, and the use of a jig or fixture. We'll also consider gage study design issues associated with attribute (pass/fail) responses. If you have data from an out-of-the-ordinary gage R&R study that you're willing to share please send it to me before the meeting and come prepared to describe the study and its implications.


Design of Gage R&R Studies, 1 June 2018, 7:30-9:00AM, Room T136.
The best known GR&R study design is the classic operator by part crossed design with 3 operators, 10 parts, and 2 trials. Most of the references out there don't give any guidance about why those numbers are used but good guidance is available in books like Design and Analysis of Gauge R&R Studies by Burdick, Borror, and Montgomery. This month we'll talk about how to choose the number of operators, parts, and trials for your GR&R studies and we'll also discuss other issues like randomization and blocking in the experiment design, consequences for the interpretation of the GR&R study report, and how to integrate instrument type, measurement procedure, the use or not of a jig or fixture, and other variables into your GR&R study design.


Report from the ASA Spring Conference: Successful Data Mining in Practice by Dick De Veaux, 4 May 2018, 7:30-9:00AM, Room T136.
Recently network members Paul P., Jim G., and I attended Dick De Veaux's presentation Successful Data Mining in Practice at the ASA Spring Conference. At this month's QMN meeting the three of us will present an overview of what we learned about data mining from Dick. We'll discuss what distinguishes problems that require data mining methods from traditional methods in statistics, some of the specialized tools developed for data mining, and we will look at some simple examples of data mining methods using MINITAB and R.


The Normal Distribution, Variable Transforms, and Processes with Time-Dependent Parameters, 6 April 2018, 7:30-9:00AM, Room T136.
At this month's meeting we'll talk about methods for testing data for normality, why they matter, and what to do if our data aren't normal.

We all cross our fingers and hope that our first look at the histogram for our newest sample data shows that beautiful bell-shaped normal curve. We're always relieved when it does, but when it doesn't all hope is not lost. There's still a chance that some mathematical sleight of hand will fix the problem. A simple variable transform often does the trick. When none of those work it might still be possible that the data follow some other well-behaved model such as the Weibull distribution. And if that doesn't work we start to get desperate. We can compromise the measurement scale by treating the data as ordinal instead of interval or ratio; however, that gives up much of the power associated with normal distribution methods. The last method left - accept that the distribution has parameters that vary with time and learn to manage the time dependencies.


Outliers, 9 March 2018, 7:30-9:00AM, Room T136.
Nothing ruins a beautiful data set as fast as an ugly outlier. We've all seen them. We've all got them. What to do? What to do?

At this month's meeting we'll discuss outliers: where they come from, how to spot them, what to do with them, and what not to do with them. Here's an outlier story with an unexpected ending to get you primed for the discussion:
Years ago I attended a seminar taught by the chemical engineer Fred Wood who was coauthor of the famous LinWood statistical modeling program. Fred told a story about consulting at a petroleum refinery where he discovered an outlier. On Christmas Eve someone recorded a high octane reading from a low octane process that was incapable of producing high octane fuel. Everyone wrote off the observation as a bad measurement caused by too much holiday egg nog. But not Fred. Upon investigation it turned out that someone had indeed screwed up. The process had been accidentally tweaked by an operator, the process reacted to the tweak, and the high octane reading was real! Fred got the associated patent on the process to produce high octane fuel from a low octane process - because he knew and practiced the correct way to manage outliers.

When Experiments Go Bad (Part 3), 2 February 2018, 7:30-9:00AM, Room T136.
The discussion topic for our last two meetings was When Experiments Go Bad. There are so many ways that can happen that we're not done with the topic yet so we'll take it up one more time. In our previous discussions I've mentioned the use of the correlation matrix of model terms (e.g. main effects, two-factor interactions, quadratic terms, ...) to confirm the validity of a good experiment design or the damage done in a bad one. This month we'll discuss how to build and interpret the correlation matrix and use it to diagnose problems in compromised and completely botched experiments. If you have a good example of a bad experiment that you're willing to talk about and share please send me its run matrix before we meet so we can analyze it together.


When Experiments Go Bad (Part 2), 1 December 2017, 7:30-9:00AM, Room T136.
Last month we had such a great turnout and discussion about experiments that have gone bad and what we can learn from them that the group decided to do a follow-up session this month. I told many of my own best stories at the last meeting so I'll be more dependent on you to offer up your own. I'll also be prepared with some examples of how to detect a flawed experiment, how to assess the damage, and potential remedial actions to recover as much information as possible.


When Experiments Go Bad (Part 1), 3 November 2017, 7:30-9:00AM, Room T136.
This week I had two different customers who had problems with experiments that they were running and they reminded me how you can learn more from a compromised or even failed experiment than one that goes exactly as planned. On that theme, let's share war stories and discuss the experiments that we've run that have gone bad, how to salvage the situation, and how we can prevent these problems from happening again in the future.


A Discussion of John Ioannidis's article Why Most Published Research Findings Are False, 6 October 2017, 7:30-9:00AM, Room T136.
When we do statistical analysis of data we usually use the p < 0.05 criterion to indicate a statistically significant result. That choice means that in those cases where there really is no significant effect we will commit a type 1 error, i.e. a false alarm will occur, about 1 time in 20. That criterion might be acceptable when an experiment is unique; however, when many people are investigating the same process it means that about 1 in 20 will find a significant effect where there is none.  Given the preference of scientific and technical journals to accept for publication articles that show statistical significance and reject articles that don't, many of these false alarms make their way into print as described by John Ioannidis in his now-famous 2005 paper Why Most Published Research Findings Are False. Early on there was significant push back from the science and engineering community about Ioannidis's claims; however, over time they've been proved to be largely true and some journals and organizations have begun to make changes in their processes to reduce the risk of publishing false claims. At this month's meeting we'll discuss how the procedure for performing statistical analyses led to this problem, its consequences, and what is being done to fix the problem. If you can't make it to the meeting or want to be better prepared for the discussion check out Derek Muller's Veritassium video on the topic posted here.


Software Cost Estimation, Stuart Kretch, 1 September 2017, 7:30-9:00AM, Room T136.
Software implementation has been problematic for decades.  In spite of enormous amounts of investment and work, it remains highly uncertain work with failure rates that are worse than all but the worst-rated junk bonds (and at times worse than them).  Something is going on.  This presentation considers software implementation from a theoretical perspective.  It identifies what fundamentals impact software implementation and their outcomes.  The presentation shows how software implementation violates our usual statistical expectations and how in fact, it yields counter-intuitive results.  As a result, we find that planning software implementation is not a problem that can be optimized in the usual way; instead, it’s a yield management problem.  There are reasons why and some of them have been known and ignored for years.  If we’re going to implement software more effectively, we’re going to have to do a better job of respecting mathematics.


Development of a Custom Corrosion Measurement System, Paul Mathews and Joe R., 4 August 2017, 7:30-9:00AM, T136.
Network member Joe R is working on a project to reduce corrosion of steel parts. He plans to build a series of designed experiments to investigate anti-corrosion treatment methods; however, he first has to develop his own method for measuring corrosion by visual inspection. To this end Joe has produced physical samples covering a wide range of corrosion. At this month's meeting we'll inspect Joe's samples. Then we'll review nominal, binary, ordinal, interval, and ratio measurement scales and discuss how to define a corrosion measurement scale that will meet the needs of Joe's experiments.


A Peek into MINITAB V18 and Definitive Screening Designs, 2 June 2017, 7:30-9:00AM, Room T136.
I have a beta version of MINITAB V18. There are some significant changes coming, among them a complete redesign of the way the Session window is managed. We'll take a quick look at some of the changes and additions in V18 and then we'll dig into one of the additions in detail: Definitive Screening Designs (DSD). DSDs address some of the weaknesses of the classic screening designs like the Plackett-Burman designs. We'll investigate the structure of the DSDs and then compare their performance to the classic designs.


Use Accelerated Testing to Reduce the Length of Life Tests, 5 May 2017, 7:30-9:00AM, Lakeland Community College, Room T136.
In an ordinary life test, where the response (such as the fraction of units surviving or the concentration of a chemical) changes with time, the units under test are operated at the same conditions as are expected in actual use until they reach a defined end-of-useful-life condition. The downside of this approach is that if the life of the product is expected to be very long then the duration of your life test will also need to be that long. And iterations of the design could result in several consecutive life test cycles that will surely exceed the limits of any manager's patience. Thankfully the duration of many life tests can be reduced by operating the units under test at a higher stress level than they would see in normal use, thereby accelerating the rate of change of the response. Common stress variables are temperature, pressure, and voltage. Through careful design of the life test experiment - with particular attention paid to resolving the effect of the accelerating variable - we can build a model for the life test response that allows us to make life predictions for normal operating conditions from the accelerated life test data. This approach can reduce the duration of a life test to just a fraction of the time it would take to perform the same test under unaccelerated conditions.


Guidelines for Setting Specification Limits on CTQ and non-CTQ Quality Characteristics, 7 April 2017, 7:30-9:00AM, Lakeland Community College, Room T136.
Quality characteristics that are critical to quality (CTQ) for your customer must have their specifications set to meet your customer’s requirements; however, the constraints for setting specifications on non-CTQ quality characteristics are less clear. These differences lead to different statistical methods for setting specifications on CTQ and non-CTQ quality characteristics. At this month's meeting we'll discuss how to use Voice of the Customer (VoC) analysis to determine spec limits on CTQs and how to drive those back to specification limits on their Key Process Input Variables (KPIV). We'll then look at the use of the nonparametric tolerance limit and normal tolerance limit methods for setting specifications on the non-CTQs.

Just in case you’re wondering if you slept through or missed the class in engineering school when these methods were taught, most such programs never or only weakly address these problems so come join us to finally learn how setting specification limits should really be done.


Estimations from Distribution Tails with Applications to Process Capability and Reliability, 3 March 2017, 7:30-9:00AM, Lakeland Community College, Room T136.
Most of our statistical analysis tasks are directed at estimating the simplest distribution parameters. For example, in statistical process control we use x-bar and R charts to keep track of the population mean and standard deviation. Likewise, in design of experiments we build ANOVA and regression models to estimate the mean or standard deviation of a process under variable process input conditions. But there are also common instances where the distribution characteristic of interest comes from a distribution's tail. Two very common examples come from process capability analysis and reliability analysis. In process capability we usually calculate statistics like cp and cpk which are just surrogates for what we're really after - the process's fraction defective relative to a specification limit. And in reliability analysis we're either trying to estimate the fraction of a population that will fail relative to a specified number of hours or cycles to failure or we're trying the estimate a percentile such as the time or number of cycles to reach some specified failure rate. In all such cases we can easily make point estimates for the percents and percentiles but reliable decisions require that we calculate and interpret their associated confidence intervals. So in this month's QMN meeting we'll discuss methods for estimating percents and percentiles from the tails of distributions. We'll start with the relatively easy discussion of methods for normal distributions and then generalize those methods to other distributions such as the Weibull.


Multivariate Control Charts, 3 February 2017, 7:30-9:00AM, Lakeland Community College, Room T136.
An X-bar and R chart is appropriate when we want to control one process characteristic but what if there are two or more process characteristics to control in a single process? In such cases we can keep separate control charts for each characteristic; however, that approach doesn't take into account correlations between the process variables. A more powerful method that resolves the problem of correlations consolidates the several process characteristics into a single statistic called Hotelling's T2 statistic which can be plotted on a single control chart known as a multivariate control chart. In a lame Lord of the Rings analogy the multivariate control chart is the one chart to rule them all. In addition to providing a much simpler way to monitor the process the multivariate control chart also reduces the type 1 (false alarm) error rate and is more sensitive to subtle changes in the process that would probably be overlooked in the many individual control charts. So this month we'll discuss Hotelling's T2 statistic and its application to one-sample tests, two-sample tests, and multivariate control charts.


Hard-To-Change Variables in Designed Experiments, 6 January 2017, 7:30-9:00AM, Lakeland Community College, Room T136.
Ideally all of the study variables in a designed experiment are easy to change so that the levels of the study variables can all be randomized in the run matrix; however, in some cases one or more of the variables in an experiment are very hard to change. In such cases, the only practical way to build the experiment is to use different randomization plans for the easy-to-change and hard-to-change variables. The resulting experiment, called a split plot design, can be thought of as a hybrid design consisting of a matrix of hard-to-change variables crossed with a matrix of easy-to-change variables. At this month's meeting we'll discuss the design and analysis of split plot experiments and the consequences of analyzing a split plot design incorrectly as a full factorial design.


Assessing the Health of your SPC System and Alternatives to SPC (Part 2), 2 December 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
Our November meeting was very lively and well-attended and because we didn't finish our discussion on the topic we'll pick it up again in December. We'll start with a review of the November discussion and then talk about choosing process control methods for processes for which SPC isn't appropriate. My presentation notes from November are posted here and my old (in desperate need of revision) SPC Audit Checklist is posted here.


Assessing the Health of your SPC System and Alternatives to SPC (Part 1), 4 November 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
The go-to method for putting a process under control (such as in the Control phase of a Six Sigma DMAIC project) used by  most organizations is statistical process control (SPC); however, how do you know if your SPC processes are healthy and what alternatives are there when SPC isn't appropriate? At this month's meeting we'll discuss the use of an SPC Audit Checklist to measure the health and effectiveness of your SPC processes and then we'll discuss alternatives to SPC including: short-run SPC, process pre-control, process and product audits, checklists, and other methods. It's likely that this topic will be too big to cover in one session so we'll probably do a follow-up session in December.


Who Won the Debate? An Application of McNemar's Test, 7 October 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
We're coming to the end of election season which means we're now suffering through presidential debates. Immediately after one of these debates both sides claim that they won; however, how would you go about separating spin from fact? That is, what experiment design and analysis would you use to determine who really won? One experiment design that's used for this situation is the test/retest design which is analyzed by McNemar's test for correlated proportions. In the test/retest experiment likely voters/subjects are asked which candidate they prefer both before and after the debate. McNemar's test ignores those subjects who don't change their minds (before/after = D/D and R/R). The only subjects whose answers are considered are those few who change their minds (D/R and R/D). If the debate result was really a tie, then of those subjects who changed their minds the direction of the changes would be evenly split (about 50% D/R and 50% R/D). However, if one of the candidates clearly won the debate then the majority of the changes would be in one direction. McNemar's method uses the one-sample test for a proportion (p) to test the hypotheses H0: p = 0.5 (the debate was a tie) versus HA: p > 0.5 (someone won the debate).

In addition to the test/retest experiment, we'll take a look at some of the many other applications of McNemar's test. For example:

What Do You See When You Look At a Boxplot?,  2 September 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
Boxplots are the preferred graphical presentation method for small data sets. Despite their simplicity, they can be used to perform many analyses, some being quite complex. At this month's meeting we'll discuss the use of boxplots for the interpretation of one-, two-, and many-sample data sets with respect to: the identification of outliers, distribution shape (such as bimodal, symmetric, asymmetric, platykurtic, and leptokurtic distributions), tests for differences between two or more means, and tests for differences between two or more standard deviations.


Continuous and Skip Lot Sampling Plans, 5 August 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
I've been working with a customer recently who has a supplier inspection procedure that operates much like a skip lot sampling plan. I haven't seen skip lot sampling used in a while and I thought that it might be interesting and useful to some QMN members.

Skip lot sampling plans (SkSP) are closely related to continuous sampling plans (CSP) and CSPs are easier to understand so I'll start by explaining them. A CSP is used, much like SPC or process precontrol, to monitor product quality coming from a continuous process. CSPs utilize two sampling modes: 100% inspection and sample inspection, with switching rules to transition between modes. A CSP starts up in 100% inspection mode, rejecting bad parts and accepting good ones, until a specified consecutive number of good parts - called the clearance number (i) - is found. After the clearance number is reached, the sampling mode switches to random sampling of a fraction of the parts called the sampling fraction (f). When a defective part is found in sampling mode the inspection mode switches back to 100% inspection.

Where CSPs are used to monitor parts coming from a continuous process, SkSPs are used to monitor lots coming from a continuous stream of lots. As an example, in an SkSP with clearance number i = 8 and sampling fraction f = 1/3, the SkSP would start by 100% inspecting all lots, rejecting bad ones and accepting good ones, until i = 8 consecutive good lots were obtained. Then the inspection operation would shift to sampling mode by randomly inspecting f = 1/3rd of the lots until a defective lot was found and the sampling mode reverts back to 100% inspection.

Both CSPs and SkSPs are characterized by their clearance numbers and sampling fractions. I've written a MINITAB macro to calculate and plot the performance curves for these plans as functions of those parameters so after discussing the basics we'll look at some examples, compare the performance of some plans, and then talk about some of the published CSPs and SkSPs that are available.


Experiment Protocol Documents (Part 2), 3 June 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
Last month's meeting on experiment protocols was very well attended so this month we're going to do a follow-up on the same topic. We'll start by reviewing the potential content of an experiment protocol. Then we'll discuss how to structure a formal experiment protocol document and how it might be adapted to meet specific needs. We'll also look at an example protocol document and an example report written for the experiment performed under that protocol.

I couldn't get my computer to talk to the projector at last month's meeting so we were recreating my presentation notes on the board. I'll bring my own projector next month in case we have trouble again. In the meantime, here are links to different versions of my experiment protocol design mind map:

Experiment Protocol Documents, 6 May 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
As a consultant I've seen a wide range of practices with respect to how organizations plan and execute their experimental work. Those that skimp on the early planning and preparation phases and rush to build their experiments tend to experience more failures that are discovered late in the process when the consequences of lost time, wasted resources, slipped schedules, and aggravated managers is the most traumatic. Other organizations, such as those that are highly regulated, tend to use highly structured formal procedures that include much more up-front planning. The key document that distinguishes the two groups, the document that the highly regulated group depends on and the skimpers lack, is often referred to as an experiment protocol. From what I've seen experiments run under protocol tend to go more smoothly and have better endings than those that aren't. So at this month's meeting we'll discuss the content of an experiment protocol document and develop a protocol template that we can all share for managing our own experimental processes.


Nonlinear Regression Models, 8 April 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
When a simple linear model (y = b0 + b1x) for data in a scatter plot doesn't fit the data we can often apply a variable transformation to the x and/or y values and linearize the relationship; however, when transformations are inadequate it may be necessary to employ other methods. For example, when the theoretical functional form of y = f(x) is known we can fit a model of that form with appropriate nonlinear regression software. When the theoretical form is unknown it may be necessary to resort to a higher order polynomial model. At this month's meeting we'll take a look at all of these and related issues with examples. If you have your own nonlinear regression problem that you'd like to share with the network members please forward the data to Paul before the meeting and come prepared to explain the data set.


Two-level Factorial Experiments with Binary (e.g. Pass/Fail) Responses, 11 March 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
Designed experiments are the preferred method for studying how a quantitative response depends on several independent variables; however, what if the response is not quantitative but is instead a binary pass/fail result? At this month's QMN meeting we'll discuss the design of two-level factorial experiments with a binary response, the use of binary logistic regression for the analysis, and how to calculate an appropriate sample size for the experiment.


Validation/Sampling Plan Design for a Complex Product, 5 February 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
In training and most shop floor discussions of sampling plan design (be it for a one-time validation study or a periodic inspection operation) the processes we're considering are usually relatively simple. For example, we may need an attribute sampling plan for a product or process with one pass/fail output and we want the sampling plan to demonstrate that the defective rate is less than some specified value or hasn't changed significantly from prior experience. These are relatively straight-forward, textbook, easy-to-solve problems.

At this month's QMN meeting we're going to look at a more complicated situation. A network member (Mike) is trying to design a one-time product validation study of a complete printed circuit board (PCB). The PCB could fail in many different ways including: damaged PCB, missing components, bad solder connections, solder bridges, failed components, missed electrical performance requirements (e.g. draws too much current, shorting, arcing, clock/timing errors), missed functional requirements (bad or failed firmware), etc. Mike will be on hand to explain the PCB's performance requirements and then we'll brainstorm a list of tests to perform and determine sample sizes and acceptance criteria for those tests. Even if you don't do PCBs this discussion will be relevant to any product or process that has multiple and complex performance requirements.


Automate Microsoft Word Reports Using ODBC and VBA Calls to MINITAB, 8 January 2016, 7:30-9:00AM, Lakeland Community College, Room T136.
At our last two QMN meetings we discussed how to use MINITAB EXEC and LOCAL macros to perform routine MINITAB analyses. At this month's meeting we'll discuss two more methods to improve your MINITAB productivity - the use of ODBC to import data from a database (e.g. Excel) into MINITAB and the use of VBA to run MINITAB analyses and import their results directly into a Word document. We'll put all of these methods together to build an example Word file that automatically updates MINITAB from an Excel file and generates a ready-to-publish Word document including integrated output from MINITAB.


Automate Routine Graphical and Statistical Analyses Using MINITAB Macros (Part 2), 4 December 2015, 7:30-9:00AM, Lakeland Community College, Room T136.
At last month's QMN meeting we discussed how to create and run a MINITAB EXEC macro by collecting the code that MINITAB creates from operations performed with the graphical user interface. We also discussed how to edit and customize that code in the NotePad text editor and how to save and run a macro from the File> Other Files> Run an EXEC menu and from the MINITAB command prompt.

This month we'll continue our discussion of MINITAB macros with consideration of the more general and powerful LOCAL macro type. LOCAL macros require a bit more administration than EXEC macros but in addition to all of the functionality available from the MINITAB graphical user interface (and EXEC  macros) LOCAL macros also provide general programming structures for  column, constant, and matrix variables, branching, looping, subroutines, graphical and text output, etc. As an example of a LOCAL macro we'll study the correlate macro which calculates and displays the correlation matrix for main effects, two-factor interactions, and quadratic terms for two-level and response surface experiment designs. We'll also study the fitfinder macro which creates a 6x6 matrix of y versus x scatterplots with five variable transformations (logarithm, square root, square, power, and reciprocal) applied to both the y and x variables.

At January's meeting we'll wrap up the topic of MINITAB macros  with a discussion of how to call MINITAB using Visual Basic for Applications (VBA) from within Microsoft Office products to automatically populate Word and PowerPoint reports with MINITAB output.


Automate Routine Graphical and Statistical Analyses Using MINITAB Macros (Part 1), 6 November 2015, 7:30-9:00AM, Lakeland Community College, Room L104.
Many of us have graphical or statistical analyses in MINITAB that we have to repeat periodically. For example, we may have to prepare a weekly or monthly quality report, update a collection of SPC charts, or update the analysis of a product life test as new data become available. Most people just repeat the same series of commands manually each time they have to update their analyses; however, MINITAB provides a simple way to save these commands as a macro that can be run as required. So in this month's QMN meeting we will discuss how to create and run MINITAB EXEC macros and we'll start a discussion of MINITAB LOCAL macros. In a follow-up meeting we'll look at LOCAL macros in more detail and, if there's sufficient interest, we'll discuss how to call MINITAB using Visual Basic for Applications (VBA) from within Microsoft Office products to automatically populate Word and PowerPoint reports with MINITAB output.


Short Run SPC with MINITAB's Z-MR Charts, 2 October 2015, 7:30-9:00AM, Lakeland Community College, Room T136.
I recently spent two days at a conference for consultants hosted by and at MINITAB. A good portion of our time was spent on training on special methods including one session on short run SPC. I've always used MINITAB's individual and moving range charts (Stat> Control Charts> Variables Charts for Individuals> I-MR) for short run SPC. That method works but it's rather painful; however, the MINITAB trainers showed us how short run SPC was intended to be performed using standardized control charts (Stat> Control Charts> Variables Charts for Individuals> Z-MR). So in this month's meeting we'll discuss the use of MINITAB's Z-MR charts for the following short run SPC situations:

A Menagerie of Reliability Problems (Part 3), 4 September 2015, 7:30-9:00AM, Lakeland Community College, Room T-136.
At last month's meeting we used MINITAB's Stat> Reliability/Survival> Test Plans> Demonstration and Test Plans> Estimation menus to design and analyze experiments to demonstrate reliability requirements and estimate reliability parameter values. We also discussed the use of Stat> Reliability/Survival> Regression with Life Data to analyze reliability responses from designed experiments.

At this month's meeting we'll continue the theme of reliability analysis by looking at accelerated test problems. In accelerated testing the experimental runs are performed by operating a stress variable like temperature, pressure, or voltage at larger than normal values causing failures to occur early. Then by studying and understanding the stress variable effect predictions can be made for reliability at normal operating conditions by extrapolation. We'll look at several accelerated stress example problems, use MINITAB's Stat> Reliability/Survival> Test Plans> Accelerated Life Test to design accelerated tests, and use Stat> Reliability/Survival> Accelerated Life Test to analyze accelerated life test data. If you have data from an accelerated life test that you are willing to share with the network members please e-mail the data to Paul (paul@mmbstatistical.com) before the meeting.


A Menagerie of Reliability Problems (Part 2), 7 August 2015, 7:30-9:00AM, Lakeland Community College, Room T-136.
At last month's meeting we used MINITAB to analyze seven of the most common quality engineering problems. This month we'll continue the theme of reliability analysis with MINITAB by considering the design and analysis of reliability demonstration tests, accelerated reliability tests, and the analysis of reliability data using linear regression, ANOVA, and DOE methods.


A Menagerie of Reliability Problems (Part 1), 5 June 2015, 7:30-9:00AM, Lakeland Community College, Room T-136.
At this month's QMN meeting we're going to work through as many example reliability problems as possible using MINITAB. We'll look at examples of the following types:
If you have a reliability data set that you would like to share with the network members please e-mail the data to Paul (paul@mmbstatistical.com) before the meeting.

This topic is large enough that it will probably require at least one follow-up meeting.


Equivalence, Superiority, and Non-inferiority Tests (Part 2), 1 May 2015, 7:30-9:00AM, Lakeland Community College, Room L-104.
We had a great turnout at last month's meeting so this month we will continue our discussion of equivalence, superiority, and noninferiority tests. We'll review the material that we discussed last month (this time with the presentation notes) and then we'll look at examples of each type of hypothesis test. If you have a data set you would like to share with the group for discussion please e-mail it to me with a short description of the situation.


Equivalence, Superiority, and Non-inferiority Tests, 10 April 2015, 7:30-9:00AM, Lakeland Community College, Room E116. (The presentation notes are here.)
The hypothesis testing method that all of us learned first and use almost exclusively is the method of significance tests. The goal of significance testing is to reject the null hypothesis of no difference or no effect in favor of the alternate hypothesis that a difference or effect is present. As an example, suppose that the goal of an experiment is to demonstrate that the population mean for a new process (#2) is different from the population mean for the old process (#1). Then we would test the hypotheses H0: µ1 = µ2 versus HA: µ1  ≠ µ2 and reject H0 in favor of HA if µ1 and µ2 were statistically far apart. Under the strict rules of hypothesis testing there is no opportunity to accept H0. We can only reject it in favor of HA or else the test is inconclusive. This approach puts the burden of proof on the data. It forces us to honor Sagan's guidance that the extraordinary claim (HA) requires extraordinary evidence. But what if the goal of the experiment is to demonstrate that there is no difference between the two population means? To honor Sagan's requirement we must put the burden of proof on the data by inverting the original hypotheses, writing the new hypotheses as H0: µ1 ≠ µ2 versus HA: µ1 = µ2 with the intention of rejecting H0 in favor of HA. This test belongs to the family of equivalence tests. Slight modifications to these hypotheses give rise to related methods called superiority tests and non-inferiority tests. All of these testing methods: significance tests, equivalence tests, superiority tests, and non-inferiority tests, can be easily interpreted using simple confidence intervals. So if you've ever needed a test other than a significance test come join us at this month's meeting to discuss the use of these other testing methods.


Acceptance Sampling Plan Design for Variables Data, 6 March 2015, 7:30-9:00AM, Lakeland Community College, Room T136.
Last month's meeting on acceptance sampling using attribute data was well attended so this month we'll continue the discussion by considering acceptance sampling using variables (aka measurement) data. As with the attribute case, the purpose of acceptance sampling using variables data is to control the lot fraction defective; however, the decision to accept or reject the lot is based on variables rather than attribute data. The inputs required to determine a variables sampling plan are: AQL and RQL levels and their corresponding acceptance probabilities, an upper and/or lower specification limit, and an estimate of the population standard deviation. The outputs from the calculation are the sample size and the acceptance criterion. We'll look at some simple manual variable sampling plan calculation methods and the corresponding methods provided in MINITAB.


Acceptance Sampling Plan Design for Attribute Data, 6 February 2015, 7:30-9:00AM, Lakeland Community College, Room T221.
Acceptance sampling is a fundamental method of quality engineering. In attribute acceptance sampling a random sample is drawn from a production lot and the sample is inspected to determine the number of defective parts. If the number of defectives in the sample is sufficiently small then the entire production lot is accepted. However, if the number of defectives is too large then the entire lot is rejected. Rejected lots can be handled in different ways. In some cases rejected lots are scrapped or returned to the supplier and in other cases the entire lot may be inspected to cull the defective units. The latter method is called rectifying inspection.

Attribute sampling plan design is performed by choosing sampling plan parameters (usually the sample size and the maximum allowable number of defectives in the sample called the acceptance number) that satisfy an acceptable quality level (AQL) condition, a rejectable quality level (RQL) condition, or both the AQL and RQL conditions simultaneously. Production lots of AQL quality have sufficiently low fraction defective that they should be accepted by the sampling plan most of the time. Lots of RQL quality have high fraction defective and should be rejected by the sampling plan most of the time.

In this month's QMN meeting we will use a graphical tool, called a nomogram, to design attribute sampling plans that meet AQL and RQL requirements. We will also use that tool to construct the operating characteristic (OC) curves to compare the performance of different sampling plans and we will look at MINITAB's tools for designing attribute sampling plans. In our next meeting (March?) we will continue this conversation by considering acceptance sampling plans for measurement data.


Binary Logistic Regression Case Studies: A Toxicology Study and O-ring Failures Before the Space Shuttle Challenger Accident, 7 November 2014, 7:30-9:00AM, Lakeland Community College, Room T136.
Many experiments generate responses that are quantitative, but some experiments generate qualitative or attribute responses. There are three common families of attribute responses: binary responses, ordinal responses, and nominal responses. Two-state (e.g. pass/fail or go/no-go) responses fall into the binary response category, ordinal responses have three or more levels related by size, and nominal responses group observations into three or more qualitative categories. Specialized regression analysis methods are available to build models for all three types of attribute responses as functions of quantitative and qualitative predictors. Paul Mathews will demonstrate how to perform and interpret regression analysis for binary responses using data from two case studies: 1) a drug toxicology study and 2) the o-ring failure data that was available before the loss of the space shuttle Challenger.


Those Confusing Process Capability Statistics (Part 3), 3 October 2014, 7:30-9:00AM, Lakeland Community College, *** Room L104 ***.
Our last two meetings about process capability issues were both lively and well attended. At this month's meeting we'll continue the process capability discussion by considering the Wilson point estimate method. (See Don Wheeler's article on this method here.) We'll also start working up a comprehensive list of strategies for performing process capability analysis under diverse conditions such as normal and non-normal data, short and long term data, time dependent distribution parameter values, etc.


 Those Confusing Process Capability Statistics (Part 2), 5 September 2014, 7:30-9:00AM, Lakeland Community College, Room T136.
At our last meeting in June, which was lively and well attended, we discussed some of the many process capability statistics that are in use and how they are related to each other. We'll follow up on this topic at our next meeting by discussing other important issues in process capability analysis including: experiment design, data analysis, normal and non-normal data, sample size, and confidence intervals. A lot of these issues are difficult, confusing, and contentious so we should have another lively discussion.


Those Confusing Process Capability Statistics (Part 1), 6 June 2014, 7:30-9:00AM, Lakeland Community College, Room T136.
You've probably developed some degree of comfort working with process capability statistics; however, sooner or later you're going to run into another organization that uses a different set of statistics than you do. They're all related to each other, of course, but that just adds to the confusion. Here's a list of the most common statistics in use and it's likely that you're unfamiliar with at least some of them: Cp, Cpl, Cpu, Cpk, Pp, Ppu, Ppl, Ppk, Zst, Zlt, Zbench, Zshift, Cpm, Cpkm, p, DPM, DPU, PCR, and others. At this QMN meeting we'll review these process capability statistics and others that you might know. In a follow-up meeting we'll consider other process capability issues and applications that might include the following: calculation methods, normality, process control, confidence intervals, hypothesis tests, sample size calculations, and statistical terrorism.


Quality Engineering Principles Applied to Health and Safety, 2 May 2014, 7:30-9:00AM, Lakeland Community College, Room T136.
Network members: I need your help. I recently met Melissa, a now-new QMN member, who has taken on a new job collecting, analyzing, and reporting on company-wide health and safety issues. She has lots of data but is struggling to figure out how to analyze and interpret it. This topic is outside of or on the periphery of most of our responsibilities; however, data are data and we should be able to help her. Melissa will be at this month's meeting to describe her data so please join me to help brainstorm analysis methods that she might use. Even if you're not involved in or interested in health and safety issues you should come just to get practice thinking outside of your own box.


When Gage Error Studies Go Bad (Part 2), 7 March 2014, 7:30-9:00AM, Lakeland Community College, Room T136.
At the last well-attended QMN meeting (Feb 7) we discussed the analysis and interpretation of a GR&R study performed by one of the network members, Ron I.. During the discussion we drew attention to both good and bad practices (Ron's were all good) and we assigned follow-up homework to Ron to revisit his GR&R study. At this month's meeting we will go over his new results and we will brainstorm a complete list of potential problems that are encountered in GR&R studies.


When Gage Error Studies Go Bad I (Part 1), 7 February 2014, 7:30-9:00AM, Lakeland Community College, Room T136.
Despite our best intentions, there are so many ways that a gage error study can go bad that they often get the better of us. We'll use this meeting of the QMN to discuss some of our experiences, both good and bad, so that perhaps some of us might avoid a disaster in the future based on someone else's account of a bad study.


Methods for Analyzing Censored Data, 6 December 2013, 7:30-9:00AM, Lakeland Community College, Room T136.
In some data collection situations it is impossible or impractical to observe values less than or greater than a limiting value. For example:
All of these situations involve incomplete or censored data and proper statistical analyses must take the censored observations into account. At this meeting of the QMN we will discuss some methods for analyzing data with censored observations including:


Sample Size Calculations for Experiments with Binary Responses, 4 October 2013, 7:30-9:00AM, Lakeland Community College, Room T136.
At this month's QMN meeting and at the request of a network member we're going to discuss sample size calculations for experiments with binary (pass/fail) responses. We'll start by considering one of the simplest of such experiments - the experiment to compare two population proportions (for example, two defective rates) - and then we'll move on to more complicated experiment designs such as the two-level factorial designs. We'll also discuss the interesting analogous relationship that these experiment designs and their sample size calculations have with the two-sample t test and regression/ANOVA for two-level factorial designs with quantitative responses.


The Kano Model, 2 August 2013, 7:30-9:00AM, Lakeland Community College, Room T136.
An important step in voice of the customer (VOC) analysis is to correctly classify process output variables (POVs) with respect to their importance to the customer. At the simplest level of distinction there are three levels of POVs: critical to quality (CTQ) characteristics, key process output variables (KPOVs), and ordinary POVs. The Kano Model gives this classification system another level of detail by considering the relationship between how well a POV is implemented and the degree of customer satisfaction. These two dimensions give (at least) four categories of POVs: satisfiers, dissatisfiers, delighters, and indifferent. At this month's QMN meeting we will discuss the Kano model, how to use Present / Not Present analysis to determine the Kano classification of a POV, how POVs change over time with respect to their Kano classification, and some extensions of the original Kano model.


Free Software!, 7 June 2013, 7:30-9:00AM, Lakeland Community College, Room T136.
Many of us have reluctantly become the computer and software technical support services for our family and extended family. For example, without spending any money, we often have to find software to meet a specific need or a way to extend the life of a worn out computer. Luckily, there are many free software solutions available. Paul Mathews will describe some of the free software that he has found to be useful and will entertain recommendations and alternatives from the network members. A list of some of the software that he will discuss is presented here.


To be rescheduled: A Comparison of Practices Used to Manage Experimental Work, 7:30-9:00AM, ???, Room T136
As a consultant I see a wide range of practices in how organizations manage their experimental work. (By "experiment" I mean any activity that involves data collection, analysis, and interpretation for the purpose of managing a process.) Some organizations have very loose guidelines for how to run experiments. These organizations tend to run many smaller, less well-planned experiments. Other organizations, such as those regulated by the FDA and contract research labs, have highly structured formal procedures with much up front planning and many interim check points. These organizations tend to run fewer experiments that lead to their carefully defined predetermined end points. Both approaches can work but of course they have their advantages and disadvantages. This session of the QMN will be used to discuss, compare, and contrast the problems, management tools, and solutions associated with different approaches to managing experimental work.


Diagnostic Tests and ROC Curves, 7:30-9:00AM, 5 April 2013, Room T136.
At this month's QMN meeting Paul Mathews will introduce the fundamental concepts and issues of diagnostic tests with examples from medicine, engineering, manufacturing, and science.

A medical diagnostic test is used to distinguish two populations, for example, diseased and healthy subjects, using a quantitative measurement compared to a threshold value. Observations that fall on one side of the threshold are judged to have the disease and observations that fall on the other side of the threshold are judged to be healthy. Diagnostic tests are also common in engineering, manufacturing, and other non-medical situations.

When the distributions of diseased and healthy subjects overlap on the measurement scale, the diagnostic test will misclassify some of the subjects. For example, the test will produce some false positives (subjects who are healthy but whose test indicates that they have the disease) and false negatives (subjects who have the disease but whose test indicates that they are healthy). Both types of errors have associated costs that must be taken into account when choosing the threshold value.

The overall performance of a diagnostic test is evaluated in terms of its true negative rate or specificity (the fraction of healthy subjects who are classified correctly) and its true positive rate or sensitivity (the fraction of diseased subjects who are classified correctly). The trade-offs associated with different threshold values can be evaluated using a receiver operating characteristic (ROC) curve - a plot of the true positive rate or sensitivity versus the false positive rate or 1 - specificity. Presentation Notes


Use of ISight Software for Propagation of Error Analysis, Paul Mathews with Mike Plishka and Jim Soltisz of Dassault Systems, 1 February 2013, 7:30-9:00AM, Room T136.
At the last QMN meeting in November we talked about propagation of error - how variation in process input variables (PIV) causes variation in a critical-to-quality (CTQ) response. As a case study, we considered a pressure fitting sealed by an o-ring. The compression of the o-ring was a known geometrical function of seven component dimensions with known tolerances. We observed that under the worst case combination of component dimensions the fitting would leak; however, by the propagation of error method (both analytical and simulation methods) we were able to show that the fraction of fittings expected to leak was negligible. We were also able to identify the two component dimensions that are the primary contributors to variation in the response.
 
This month we'll continue our discussion of propagation of error by looking at a commercial software package, Isight. Mike Plishka and Jim Soltisz, local representatives from Dassault Systems, will present an overview of Dassault Systems' products including Solid Works, Abaqus, and Draft Sight (a free, 2D-only alternative to AutoCad) and then go into some detail on the Isight package. The Isight software interfaces to a customer-supplied computer model of the system to be studied. Isight connects to the model's PIVs and one or more CTQs and can manipulate the PIVs to determine how they influence the CTQs. Constraints can be set on the PIVs and goals on the CTQs, then Isight can exercise the computer model to determine combinations of PIVs that simultaneously satisfy the constraints on the PIVs and the goals for the CTQs. (I have personal experience with the ancestor of Isight - a software package called Engineous developed at GE Corporate Research. I successfully used Engineous to study systems with 3-5 CTQs as functions of more than 50 PIVs. - Paul)


Stack-up Tolerance Analysis for O-ring Compression in a Mechanical Seal, 7 December 2012, 7:30-9:00AM, Room T136.
At the last QMN meeting in October we decided that in a future meeting we'd discuss electronic data collection methods using a communication interface (e.g. RS232, GPIB, ...) between a computer and a measurement instrument. I haven't forgotten that request but I haven't had time to put a demonstration together so I'm postponing that topic for a future meeting. In the meantime ...

I have a customer (not to be named) who recently needed help evaluating specification limits on the components of a mechanical seal that operates under high pressure. The seal is made using an o-ring and metal components that compress it. The minimum o-ring seal compression required to prevent leaks is known from experience but there are seven component dimensions that affect compression. My role in this problem was to help calculate the expected distribution of compression (i.e. its mean, standard deviation, and distribution shape) as a function of the known distributions of the seven components. I was able to do this using two methods: simulation, which was fast and easy, and analytical calculation, which was complicated but confirmed the results of the simulation and identified the component dimensions that had the most impact on compression. At this month's QMN meeting I'll review the calculation of o-ring compression from the geometry of the seal and how to evaluate the distribution of compression from the component distributions by the simulation and analytical methods.


Beyond Shewhart Charts, 5 October 2012, 7:30-9:00AM, Room T136.
In most circumstances the classical Shewhart charts, like the well-known x-bar and R chart, are sufficient for effective statistical process control; however, the Shewhart charts are less sensitive to small shifts in the process compared to some other charting methods. These other charts, which are outside of the Shewhart paradigm, are the moving average (MA), exponentially-weighted moving average (EWMA), and cumulative sum (CUSUM) charts. These charts are more demanding than Shewhart charts with respect to the calculations required so they are best done with software; however, when there are large costs associated with small shifts in the process they can be well worth the extra work. At this month's QMN meeting, Paul Mathews will describe how to construct and use MA, EWMA, and CUSUM charts and demonstrate by example how they perform compared to the Shewhart charts in the presence of small shifts.

  
Introduction to Lean Six Sigma, 3 August 2012, 7:30-10:00AM, Room T136.
Lean Six Sigma is the integration of the two famous, complementary business process improvement methodologies – Lean to reduce waste and Six Sigma for quality improvement. Students of this course will learn to:

Failure Modes and Effects Analysis, Louise Watson, 1 June 2012, 7:30-9:00AM, Room T136.
Failure Modes and Effects Analysis (FMEA) is a well known method of risk assessment and risk management.  Louise Watson will review the steps involved in FMEA including: initial review of the project, determining the depth of knowledge required of team members, how to choose team members, the organization and use of FMEA forms, executing the FMEA, task management, and how to bring an FMEA project to closure.  Louise will demonstrate the documentation of an FMEA project using an Excel-based solution and she will describe some of her FMEA experiences.

Louise Watson has a Bachelors Degree in Engineering from Ohio State University.  She has worked as an Environmental Health and Safety professional for over 35 years in many types of high risk manufacturing, remediation, and mining scenarios including: deep mine coal removal in the eastern US, munitions storage remediation for the Air National Guard, uranium contamination cleanup for the Department of Energy, underground storage tank removal, managing large quantities of flammable liquids being used in fast drying ovens, high concentrations of toxic acids, flammable and toxic gases in pressure vessels, and oxygen-free high temperature furnaces.


Upgrade Your Inspections By Replacing Attribute Criteria With Measurement Criteria, 4 May 2012, 7:30-9:00AM, Room T136.
The value of individual observations increases according to the measurement scale hierarchy: nominal (of which binary is a special case), ordinal, interval, and ratio. Understanding this hierarchy presents the opportunity to improve your data collection processes (e.g. acceptance sampling, SPC, process capability, and DOE) by replacing low-value quality characteristics with high-value quality characteristics. For example, a substantial sample size reduction can be realized by replacing an attribute quality characteristic observed on a binary (i.e. pass/fail) scale with a measurement or pseudo-measurement quality characteristic observed on an interval or ratio scale. At this month's meeting, we'll review the hierarchy of measurement scales and discuss the opportunities and benefits of replacing low-value observations with high-value observations.
 

Interpreting Gage R&R Study Results (Part 2), 2 March 2012, 7:30-9:00AM, Room T136.
At the well-attended February 3rd QMN meeting we had a lively conversation about the different methods of interpreting gage error study results; however, we ran out of time before we were able to reach a consensus. There were several issues that were left unresolved, perhaps the most important being the method of choosing parts for the gage error study. We identified at least three different part selection strategies: choose parts that are typical of the process, choose parts that span the full width of the part tolerance, and choose parts that are similar in general features but of wildly different sizes. Most organizations use just one of these strategies but as a group we were able to identify situations in which each of the three strategies would be appropriate. At this month's meeting we'll elaborate on those three and other part selection strategies and their consequences and try to identify appropriate methods for interpreting their gage error study results.


Baselines for Interpreting Gage R&R Study Results (Part 1), 3 February 2012, 7:30-9:00AM, Room T136.
The default baseline for interpreting the gage repeatability (EV) and reproducibility (AV) in gage R&R studies is the tolerance width (TOL). The usual acceptance criteria are that EV/TOL and AV/TOL must both be less than 10% for a "good" measurement system and less than 30% for a "marginal" measurement system. There are, however, many other methods for interpreting EV and AV including:
* relative to total variation (TV)
* relative to part variation (PV)
* relative to independent process capability study results
* number of distinct categories (NDC)
* intraclass correlation (ICC)
Several of these methods are also sensitive to how the sample parts are chosen for the study.

At this month's QMN meeting we will review the different methods for evaluating gage R&R study results and discuss their strengths and weaknesses.


Binary Logistic Regression Case Studies: A Toxicology Study and O-ring Failures Before the Space Shuttle Challenger Accident, 6 January 2012, 7:30-9:00AM, Lakeland Community College, Room T136.
Many experiments generate responses that are quantitative, but some experiments generate qualitative or attribute responses. There are three common families of attribute responses: binary responses, ordinal responses, and nominal responses. Two-state (e.g. pass/fail or go/no-go) responses fall into the binary response category, ordinal responses have three or more levels related by size, and nominal responses group observations into three or more qualitative categories. Specialized regression analysis methods are available to build models for all three types of attribute responses as functions of quantitative and qualitative predictors. Paul Mathews will demonstrate how to perform and interpret regression analysis for binary responses using data from two case studies: 1) a drug toxicology study and 2) the o-ring failure data that was available before the loss of the space shuttle Challenger.


Variable Transformations (Part III), 2 December 2011, 7:30-9:00AM, Room T136.
In the last two meetings on the topic of variable transformations we considered transformations that convert nonnormal data to at least approximate normality such as for the purpose of process capability analysis. This month we'll talk about another reason for using variable transformations - to stabilize the standard deviations of different populations. A good example of this situation is the case of Poisson count data; the standard deviation of the Poisson distribution is related to the distribution's mean but the standard deviation of square root transformed count data is approximately constant, independent of the mean. This trick can significantly simplify and improve the power and robustness of some otherwise painful analyses.


Variable Transformations for Nonnormal Data (Part II), 4 November 2011, 7:30-9:00AM, Room T136.
At the October 7th meeting we talked about different variable transformation methods for performing process capability analysis of nonnormal data. This month we'll continue that conversation by reviewing the available analysis methods and then attempting to analyze some real nonnormal process capability data. If you have nonnormal data that you're struggling to analyze and are willing to share with the network members, please e-mail your data to Paul at paul@mmbstatistical.com.


Variable Transformations for Nonnormal Data, 7 October 2011, 7:30-9:00AM, Room E116.
Many statistical methods, such as process capability analysis, depend on the assumption that the quality characteristic under consideration is normally distributed. When a nonnormal distribution is unimodal (that is, has a single mode or hump in its histogram), it can often be transformed to at least approximate normality using a variable transform. Some common transforms are logarithms, power functions, square roots, and reciprocals. When those transforms fail, a more complicated method like Pearson curves, Box-Cox transforms, or Johnson tranforms may do the trick. At this month's meeting, Paul Mathews will discuss the use of these variable transformations and describe their role in process capability analysis. If you have nonnormal data that you're struggling to analyze and are willing to share with the network members, please e-mail your data to Paul at paul@mmbstatistical.com.


Introduction to Six Sigma, 9 September 2011, 7:30-10:00AM, Room T136.
Paul Mathews will present a free overview of Six Sigma.


Measurement Validation, 5 August 2011, 7:30-9:00AM, Room T136.
One of the secondary benefits of Six Sigma, Lean, and ISO9000 is that they have helped to standardize the methods of measurement systems analysis (MSA) which includes calibration and gage error studies. While the basic concepts of MSA are certainly better understood today, at least by the quality engineering community, there is still substantial confusion regarding the moderate to advanced concepts of MSA. Two of the useful government/industry standards that consolidate these issues are the FDA's guidance documents VICH GL1 - Validation of Analytical Procedures: Definition and Terminology (PDF - 65KB) and  VICH GL2 - Validation of Analytical Procedures: Methodology: Final Guidance (PDF - 168KB). Even though these documents were written for FDA purposes, they are still very valuable references to anyone practicing MSA. At this month's QMN meeting, Paul Mathews will lead a discussion of these FDA guidance documents and other valuable sources for industry standards.


Variable Scope in Experiments (Part 3), 3 June 2011, 7:30-9:00AM, Room T136.
We had great attendance at last month's meeting and I received many comments and requests afterward by e-mail, so we're going to do a third session on the topic of variable scope in experiments.

At last month's meeting we discussed the similarities in experiment design, analysis, and interpretation of gage error studies and process capability studies. We also talked about how the standard design templates for these studies are often too restrictive and how more diverse designs can be analyzed using general linear model ANOVA with fixed, random, and nested variables. We'll continue the discussion this month by considering a gage error study and a process capability study that use non-standard designs and how to calculate and express the results using the standard language of the study types.


Scope Management Decisions in Experiments (Part 2): Applications to Process Capability Studies, 6 May 2011, 7:30-9:00AM, Room T136. 
As a follow-up to last month's QMN meeting, we'll talk some more about issues of variable scope in experiments. Paul Mathews will present data and analysis from three different process capability studies:
* a study using a sample from a single homogenous population
* a study to quantify within and between subgroup variation (that is, data from a typical SPC x-bar and R chart)
* a study that incorporates several variables, including both fixed and random variables


Scope Management Decisions in Experiments, 8 April 2011, 7:30-9:00AM, Room T136. 
I recently had several customers who each needed to perform an experiment to study the effect of a single two-level variable. The simplest experiment design choices are the two independent samples and paired samples designs, however, in each case material lots and other unavoidable process variables were known to affect the response. The presence of secondary variables raises the question, should the experiment be built using one level or more than one level of each of the secondary variables? These two choices differ in:
* the complexity of the experiment design with associated consequences in the risk of execution and difficulties in statistical analysis.
* the opportunity to quantify the effects of the secondary variables.
* the ability to resolve interactions between variables.
* the scope of the claims that can be made about the effect of the primary variable.
* the sample size required to build the experiment.
* the likelihood of reaching an understanding of the process sufficient for successful long term process management.
At this month's QMN meeting we'll discuss this quite common situation, the consequences of the different approaches, and strategies for making decisions about scope in experiments.


Checking Model Assumptions in ANOVA and Regression, 7 January 2011, 7:30-9:00AM,  T136.
The statistician George Box said famously, "All models are wrong; some are useful." One of the important steps to determine if a model might be useful involves checking to see if the assumptions of the statistical analysis method are satisfied. The assumptions that have to be tested are: 1) the form of the model is correct, 2) the model residuals (i.e. the noise) have constant standard deviation, 3) the model residuals are independent, and 4) the distribution of model residuals is well-behaved. Paul Mathews will describe simple graphical methods to test these assumptions and suggest remedial actions to consider when they are violated.


Mind Mapping Your ISO9000 Documentation with FreeMind, 3 December 2010, 7:30-9:00AM,  T136.
At the November 5th meeting we discussed the use of the FreeMind mind-mapping software (http://freemind.sourceforge.net/) for organizing information, such as for an input-process-output (IPO) diagram, the information collected during a brainstorming session, and the files on your computer's hard drive. At the December 3rd meeting we'll review mind maps, look at some more examples, and then use FreeMind to construct a mind map of the complete documentation for an ISO9000 quality management system. We'll also discuss how to add hyperlinks in FreeMind to create a single document containing links to all of your ISO9000 documentation.


Mind Maps, 5 November 2010, 7:30-9:00AM,  T136.
A mind map is a diagram with a radial branching tree-like structure used to organize information, especially information collected in a brainstorming session. Mind maps have general uses but in quality engineering they are closely related to and can be used to supplement cause and effect diagrams, affinity diagrams, input-process-output diagrams, and failure modes and effects analysis. Paul Mathews will show some examples of mind maps he has constructed and demonstrate the use of the FreeMind mind mapping software package (free from http://freemind.sourceforge.net/) to document a brainstorming activity.


Management of Circular Normal Quality Characteristics, 1 October 2010, 7:30-9:00AM, T136.
The normal distribution is the best known model for characterizing measurement data but when measurements are of radial deviations in a plane from a reference point then the two dimensional version of the normal distribution, called the circular normal distribution, may be required. (Imagine rotating the bell curve about its mean.) Examples of the circular normal distribution are: the run-out of a lathe-turned part, the radial deviation of a feature on a plane from its target position, and the distribution of positions reported by a fixed global positioning system (GPS) receiver. Paul Mathews will talk about these and other cases in which circular normal data appear, how to confirm that data are circular normal, how to calculate fractions defective and set specifications for circular normal data, and how to perform SPC and process capability calculations for circular normal data.


Use, Abuse, and Alternatives to the Correlation Coefficient, 10 September 2010, 7:30-9:00AM, T136.
The most popular summary statistic following any regression analysis or ANOVA is the coefficient of determination (R-squared) or its square root, called the correlation coefficient (R). The popularity of R-squared comes from its apparent ease of calculation and interpretation but in the majority of cases R-squared is inappropriate and/or misused.
Paul Mathews will discuss correct and incorrect uses of R-squared and alternative methods to R-squared when that method is inappropriate.


Managing Missing Values in Designed Experiments, 6 August 2010, 7:30-9:00AM, T136.
Designed experiments, such as the well known factorial designs, offer an efficient and low risk method for quantifying a response as a function of two more process variables, however, the analysis of these experiments becomes complicated when some of the experimental runs are lost. Paul Mathews will discuss mean substitution, hot and cold deck procedures, and statistical imputation methods for managing missing values in designed experiments.

Practical 5S Applications, Stephanie Demyan, 9 July 2010, 7:30-9:00AM, Lakeland Community College, Room T136.
Stephanie Demyan will present practical applications of 5S that will deliver improvements to your company's bottom line. After sharing common definitions of 5S, Stephanie will demonstrate a practical 5S application that can used in nearly all businesses including service industries. Feel free to submit 5S questions in advance to SDemyan@kikcorp.com.

Stephanie Demyan is a senior member of ASQ and Director of Quality, Technical & Regulatory for KIK Custom Products. KIK Custom Products is the leading aerosol contract filler in North America filling personal, household, and pharmaceutical products. Stephanie has a Chemical Engineering degree from Tri-State University and an MBA from Kent State. She is a CQA and CQIA and has over 25 years in the quality field with extensive auditing and continuous improvement experience.

Experiments with Two or More Responses, 4 June 2010, 7:30-9:00AM, Lakeland Community College, Room T136.
The goal of most designed experiments is to learn to manage a single response as a function of the input variables. Special analysis methods must be used when an experiment has two or more responses that are of comparable importance. Paul Mathews will describe several of these methods and demonstrate them using data from examples and computer simulated processes. If you've got relevant data of your own that you'd like to share at the meeting, please forward it to Paul at paul@mmbstatistical.com.


Carl Sagan's Baloney Detection Kit, 7 May 2010, 7:30-9:00AM, Lakeland Community College, Room T136.
Carl Sagan's many books are filled with important guidance for those of us who have to interpret data (which really means everyone). Among my favorites are his simple explanation of the role of data in hypothesis testing: "Extraordinary claims require extraordinary evidence," (Sagan and Druyan, Billions and Billions: Thoughts on Life and Death at the Brink of the Millennium, Ballantine, 1997) and his baloney detection kit (Sagan, The Demon-Haunted World: Science as a Candle in the Dark, Random House, 1996). At this month's QMN meeting we'll discuss these and other topics from Sagan. If you want to prepare for the meeting, start with a short summary of Sagan's baloney detection kit at http://www.xenu.net/archive/baloney_detection.html.


GM, Toyota, and NUMMI: GM's Failure to Learn Toyota's Lean Manufacturing Lessons at NUMMI, 9 April 2010, 7:30-9:00AM, Lakeland Community College, Room T136.
One of my all time favorite quality mis-management case studies is Chapter 2: The NUMMI Commandos, from Ingrassia and White's book Comeback: The Fall and Rise of the American Automobile Industry (Simon and Schuster, 1994). (Ingrassia and White won a Pulitzer Prize for this book and Ingrassia is highly sought-after as an expert since the bankruptcies of GM and Chrysler.) In the mid 1980s, GM entered a joint venture with Toyota to build cars at GM's NUMMI plant (New United Motor Manufacturing Inc.) in Fremont, California with GM providing the labor and Toyota providing the management. NUMMI made some of the best cars to ever come out of a GM plant, but upper management at GM didn't understand why NUMMI worked and shut the project down. Many of the GM middle managers trained at NUMMI were so frustrated by GM's decision that they left the company and went to work for Toyota and other competitors. GM is closing NUMMI at the end of March. The site may be used for a new stadium for the Oakland Athletics.

At 11:00AM this Saturday, the radio program This American Life (TAL) is broadcasting a story about what happened at NUMMI. You can listen to the program on WCPN (90.3 FM) and after the program airs, you can listen to the program on line. There's a bit more information available at http://www.thisamericanlife.org/radio-archives/episode/403/nummi.

I thought that we'd take this opportunity to talk about GM, Toyota, and NUMMI at the next QMN meeting. I'll bring my notes from Comeback as talking points and I'll see if we can listen to the (TAL) radio story together. (TAL's stories are usually about 20 minutes long.)


Free Software!, 5 March 2009, 7:30-9:00AM, Lakeland Community College, Room T136.
Many of us have reluctantly become the computer and software technical support services for our family and extended family. For example, without spending any money, we often have to find software to meet a specific need or a way to extend the life of a worn out computer. Luckily, there are many free software solutions available. Paul Mathews will describe some of the free software that he has found to be useful and will entertain recommendations and alternatives from the network members. A list of some of the software that he will discuss is presented here.


The Eight (8) Disciplines to Problem Solving, Paul Gundersen, 5 February 2010, 7:30-9:00AM, Lakeland Community College, Room T136.
Many companies and their quality assurance professionals initiate corrective actions only to have the symptoms recur.  The 8 Disciplines method provides a structured, permanent approach to problem solving. In some cases a corrective and preventive action (CAPA) or corrective and preventive action report (CPAR) might suffice, but for large-scale permanent action, the, 8D, the Global 8D, or Team Oriented Problem Solving (TOPS) methods are necessary.

Paul Gundersen will present an introduction to 8D methods. Paul is a quality control professional.  He has saved $1,800,000 for his employers by managing Lean Six Sigma projects and he has improved customer satisfaction by 84% by reducing warranty claims.  He has worked for several large companies including Eaton, Raytheon, Ford Motor Company, General Electric, and Johnson & Johnson and he has worked for smaller firms such as Libra Industries, CAD Engineering, Hexagram, Keithley Instruments, and Bird Electronics. Paul has a B.S. degree in Electrical Engineering and CSSBB, CQE, and CQA certifications from ASQ. Presentation Notes


A Six Sigma Master Black Belt's Journey Through Six Sigma Training, Angela Lunato, 4 December 2009, 7:30-9:00AM, Lakeland Community College, Room T136.
Many organizations today have attempted Six Sigma initiatives.  These initiatives typically include mass training programs which require significant infrastructure to contain and track Six Sigma projects and their costs and benefits. Angela Lunato will discuss her journey through the Six Sigma Master Black Belt accreditation process, the issues with Six Sigma programs today, and what actions could be taken to improve Six Sigma in your organization.


Binary Regression II: The Challenger and Titanic Accidents, 6 November 2009, 7:30-9:00AM, Lakeland Community College, Room T136.
Last month we discussed binary logistic regression and analyzed the o-ring failure data that were available before the space shuttle Challenger accident. I didn't find my presentation notes on the topic until after we met, so we're going to go over those this month. We'll look at the Challenger data again and then, since the disaster theme was so popular last month, we're going to analyze fatality data from the Titanic accident.


Regression Analysis with a Binary Response: Was the Loss of the Space Shuttle Challenger An Accident?, 2 October 2009, 7:30-9:00AM, Lakeland Community College, Room T136.
Many experiments generate responses that are quantitative, but some experiments generate qualitative or attribute responses. There are three common families of attribute responses: binary responses, ordinal responses, and nominal responses. Two-state (e.g. pass/fail or go/no-go) responses fall into the binary response category, ordinal responses have three or more levels related by size, and nominal responses group observations into three or more qualitative categories. Specialized regression analysis methods are available to build models for all three types of attribute responses as functions of quantitative and qualitative predictors. Paul Mathews will demonstrate how to perform and interpret regression analysis for a binary response using the o-ring failure data that was available before the loss of the space shuttle Challenger. Click here for presentation notes.

Use Quality Cost Analysis to Compare Process Models, 7:30-9:00AM, 4 September 2009, Lakeland Community College, Room T136.
Most companies have invested the time and effort to create flow charts or process maps for their processes. When the costs associated with the steps in a process are known, a quality cost analysis can be used to calculate responses like net income and cost of poor quality (COPQ). These calculations are useful because they can be used to compare different process models, such as to determine whether a rework operation is cost-effective or not. Paul Mathews will demonstrate how to calculate and use quality cost responses to compare some simple process models.


Response Surface Designs, 7:30-9:00AM, 7 August 2009, Lakeland Community College, Room T136.
In designed experiments, response surface designs are used when the response is expected to be a curved function of one or more of the design variables. The common response surface designs, central composite and Box-Behnken designs, can resolve main effects, two-factor interactions, and quadratic terms. Paul Mathews will review those designs, then he will show how to design a small hybrid response surface design with eight variables starting from a resolution III Plackett-Burman screening design.


Discussion of Joseph Conklin's article, It's a Marathon, Not a Sprint, in the June issue of Quality Progress magazine, 7:30-9:00 AM, THURSDAY, 25 June 2009, Lakeland Community College, Room T136.
At this month's meeting, we're going discuss Joseph Conklin's article, It's a Marathon, Not a Sprint, in the June issue of Quality Progress magazine. In the article, Conklin analyzes an electroplating process to determine how metal thickness depends on five process variables. The analysis is tricky because a designed experiment wasn't used, so there's some undesirable structure in the data, and there's at least one two-variable interaction that has to be handled correctly or you'll get the wrong answers. Let me know by e-mail (paul@mmbstatistical.com) if you'd like the data set so that you can try to analyze it yourself before we meet.


Prioritizing Process Variation Reduction Activities Using a DOE Model, 7:30-9:00 AM, 29 May 2009, Lakeland Community College, Room T136.
It's well known that the model obtained from a designed experiment may be used to predict or set the response as a function of the input variables. It's not so well known that the same model may be used to calculate how variation in those input variables, such as from normal manufacturing variation, induces variation in the response. This method may be used to prioritize activities to reduce variation in input variables. Paul Mathews will describe how this method works and demonstrate it with a simple example.


Errors in Predictor Variables, 7:30-9:00 AM, 3 April 2009, Lakeland Community College, Room T136.
Least squares linear regression for the response y as a function of the predictor variable x (where both y and x are quantitative) assumes that the x values are known exactly. Errors in determining the x values induce errors in the regression slope and intercept giving incorrect predictions for y, however, the prediction equation for y may be corrected for errors in x using a method called errors-in-variables. Paul Mathews will demonstrate the consequences of errors in predictor variables and describe the use of the errors-in-variables method to correct the situation.


Good and Bad Practices in Process Capability Analysis, 7:30-9:00 AM, 6 March 2009, Lakeland Community College, Room T136.
By the end of last month's well-attended meeting on the source of the 1.5σ shift in process capability analysis our discussion had turned to common mistakes and misunderstandings in the calculation and interpretation of process capability statistics. We'll continue that conversation this month with considerations of the effect of sample size and deviations from normality on the usefulness of process capability statistics. We'll also consider how to calculate and report process capability indices for non-normal and censored data.


Six Sigma's 1.5σ Process Capability Shift, 7:30-9:00 AM, 6 February 2009, Lakeland Community College, Room T136.
Motorola introduced the practice of allowing a 1.5σ shift in the mean of a process when setting tolerances and process capability requirements, however, the motivation for this practice is not well understood. Paul Mathews will present his interpretation of where the 1.5σ shift comes from and why it's necessary.


Rectifying Inspection Using the Dodge-Romig Method, 7:30-9:00 AM, 9 January 2009, Room T136.
At our last meetings we've discussed the attributes sampling standard ANSI/ASQ Z1.4 (formerly MIL-STD-105) and the variables sampling standard ANSI/ASQ Z1.9 (formerly MIL-STD-414). At the January 9th meeting as continuation of this topic we'll discuss the Dodge-Romig rectifying inspection method. In rectifying inspection a lot that is rejected in sample inspection is 100% inspected and all of the defective parts are replaced with good ones. Where the Z1.4 and Z1.9 standards are designed to have a high probability of passing lots with specified acceptable quality level (AQL), the Dodge-Romig plans are designed specifically to control the post-inspection rejectable quality level (RQL).


The ANSI/ASQ Z1.9 Acceptance Sampling Standard for Variables Data, 7:30-9:00AM, 5 December 2008, Room T136.
At last month's meeting we discussed the use and performance of two well known attribute acceptance sampling standards: ANSI/ASQ Z1.4 (formerly MIL-STD-105) and Squeglia's Zero Acceptance Number Sampling Plans. This month we'll extend the discussion to the lesser known and unfortunately under-used ANSI/ASQ Z1.9 variables sampling standard.


Evaluating Sampling Plans from ANSI/ASQ Z1.4 (Formerly MIL-STD-105) Using Operating Characteristic Curves, 7:30-9:00AM, 31 October 2008, Room E116.
ANSI/ASQ Z1.4 is the best known and most popular sampling standard for attributes. Paul Mathews will review the use of the standard including the switching rules between normal, tightened, and reduced inspection and he will discuss the use of operating characteristic (OC) curves to evaluate and compare sampling plans.

Paul Mathews will be teaching his new course Sample Size Calculations for Process Improvement at Lakeland from 8:00AM to 12:00PM on November 7, 14, 21, and December 5 in Room T136. The cost will be $399 (textbook included). Details for this course are here. Contact Paul at paul@mmbstatistical.com if you have any questions.


Comparing the Sample Sizes Required for Attribute and Variables Inspections, 7:30-9:00AM, 3 October 2008, Room T136.
A common mistake that quality technicians and engineers often make is to use an attribute (i.e. pass/fail) inspection when a suitable variables or measurements inspection is available. While the individual attribute inspections might be very fast to perform (such as with a snap gage), the number of observations required is usually prohibitively large compared to what a variables plan requires. Paul Mathews will show how to evaluate the trade off between the attribute and variables inspection methods using a simple calculation for the ratio of the two plans' sample sizes.

The next Quality Managers Network meeting will be held on 31 October 2008 in Room E116. (Note the room change!) Paul Mathews will discuss the use of operating characteristic (OC) curves to compare attribute inspection sampling plans and then use OC curves to evaluate plans from the ANSI/ASQ Z1.4 (formerly MIL-STD-105) sampling standard.

Paul Mathews will be teaching his new course Sample Size Calculations for Process Improvement at Lakeland from 8:00AM to 12:00PM on November 7, 14, 21, and December 5 in Room T136. The cost will be $399 (textbook included). Details for this course are here. Contact Paul at paul@mmbstatistical.com if you have any questions.


An Introduction to Sample Size Calculations II, 29 August 2008, 7:30-9:00AM, T136.
At the last meeting we discussed sample size calculations for confidence intervals and we looked at several examples including the sample sizes required to estimate: a small proportion (e.g. a small fraction defective), a moderate proportion (e.g. the fraction of the votes that a candidate will receive), a population mean, and the cpk process capability parameter. In this second session on the topic, Paul Mathews will show how to calculate sample sizes for hypothesis tests for simple one- and two-sample tests for proportions and means. He'll also demonstrate the use of Russ Lenth's free power and sample size calculation program called piface (http://www.stat.uiowa.edu/~rlenth/Power/).

Paul will be teaching his new course Sample Size Calculations for Process Improvement at Lakeland beginning some time in September. The class will meet for four four-hour sessions (16 hours total) and the cost will be $399 (textbook included). Details for this course are here. Class dates have yet to be determined, but if you have a preference please let Paul know at paul@mmbstatistical.com.


An Introduction to Sample Size Calculations I, 1 August 2008, 7:30-9:00AM, T136.
Every opportunity to collect data raises the issue of how much data are necessary. Collecting too few data might cause you to miss an important opportunity and collecting too many data wastes time and resources. Paul Mathews will explain how to right-size your data collection activities by calculating sample sizes that are consistent with the goals of those activities.


Managing Missing Data in Experiments, 27 June 2008, 7:30-9:00AM, T136.
When each level of a variable in an experiment has the same number of observations, the experiment is said to be balanced. Balanced experiments have desireable properties but when an experiment becomes unbalanced because of missing observations these properties are compromised - sometimes seriously. Paul Mathews will describe the consequences of unbalanced designs and suggest some strategies for managing missing data.


Arc Lamp Dose Development Using Mixture Designs, Tom Coffey, 30 May 2008, 7:30-9:00AM, T136.
Mixture designs are a special family of designed experiments used to determine the correct proportions of the components in a multi-component blend. Tom Coffey will describe the use of a mixture design by GE Lighting to determine the dose composition for a ceramic metal halide (CMH) arc lamp. CMH lamps offer high efficiency, excellent color, and long life and are becoming increasingly important as pressure grows to decrease commercial and residential energy consumption.


A Tour of a Dimensional Metrology Calibration Lab, Keith Kokal, 25 April 2008, 8:00-9:30AM, at Micro Laboratories, Inc., 7158 Industrial Park Blvd., Mentor, OH.
At our March meeting we discussed calibration uncertainty statements so it seems fitting that this month we should go see how calibrations are done. Keith Kokal is President of Micro Laboratories, Inc. located in Mentor, Ohio. Micro Laboratories is an ISO 17025 A2LA-accredited dimensional metrology calibration supplier. They can also do torque calibrations and are expanding their services to provide calibrations for pressure gages and electrical instruments. Keith and his staff will give us a tour of their lab which uses instruments and procedures similar to those used by NIST. Some of the lab areas have very tight heat and humidity tolerances so this tour is limited to 15 people and will be necessarily broken into small groups. If you'd like to come please RSVP by e-mail to Paul at paul@mmbstatistical.com. Note that this tour starts at 8:00AM and please park on the side of the building. Coffee and pastry will be provided.


Measurement Uncertainty in Calibration, 28 March 2008, 7:30-9:00AM, T136.
Measurement accuracy is established by calibration, but even the best calibration still contains errors (hopefully small ones) from many different sources. The combined effect of these potential calibration errors is called the measurement uncertainty. Paul Mathews will present an introduction to measurement uncertainty analysis as defined in ISO's Guide to Uncertainty in Measurement (GUM) and describe how measurement uncertainty analysis relates to measurement systems analysis (MSA) and gage error (GR&R) studies.


Resampling Statistics III, 29 February 2008, 7:30-9:00AM, T136.
Paul Mathews will continue with the demonstration of the free resampling software Statistics101 (www.statistics101.net) which reproduces many of the features of the commercial package Resampling Stats. In this presentation Paul will show how to construct bias-corrected confidence intervals for highly skewed (i.e. non-normal) data sets.


Resampling Statistics II, 25 January 2008, 7:30-9:00AM, T136.
At the last QMN meeting in November Paul Mathews presented an introduction to resampling statistics methods which provide distribution-free methods for constructing confidence intervals and performing hypothesis tests using sample data. At this second meeting on the same topic, Paul will present more detail on resampling methods and demonstrate John Grosberg's free resampling software Statistics101 (www.statistics101.net) which reproduces many of the features of the commercial package Resampling Stats.


Resampling Statistics I,  30 November 2007, 7:30-9:00AM, T136.
Classical inferential statistical methods make assumptions about the distributions of test statistics in order to calculate confidence intervals and hypothesis tests. For example, the classical methods assume normal or Student t distributions for sample means, chi-square distributions for sample variances, and F distributions for the ratios of two sample variances. When the conditions that justify these assumed distributions aren't satisfied, the classical inferential methods may fail. As a distribution-free alternative, resampling methods which rely heavily on the computer to build the sampling distributions have been developed. These methods are particularly useful for small or badly-behaved samples when the validity of the classical distributions cannot be assumed or tested. Paul Mathews will present an overview of resampling methods for constructing confidence intervals and performing hypothesis tests.


Quality management of half-normal and circular-normal distribution data, 26 October 2007, 7:30-9:00AM, T136.
In engineering and manufacturing there are two special “relatives” of the normal distribution that appear frequently but are not usually recognized. These are the half-normal and circular-normal distributions.

In the half-normal case, deviations from the distribution mean are measured but the direction of these deviations is unknown so only positive values are observed. Such data result in a normal bell-shaped distribution that’s folded over about the mean, giving a double-amplitude normal curve for positive values and a completely truncated left tail for the negative values.

In the circular-normal case, the location of a feature moves about on a plane giving a two-dimensional normal distribution surface. (Picture a bell-shaped curve rotated about its mean.) Sometimes the feature’s deviations from the target location can be determined independently in the two dimensions, but in many cases only the radial distance between the observed and target locations can be determined. In the latter case, the distribution of the radial deviation data often follows a circular-normal distribution.

Paul Mathews will describe some situations that produce half-normal and circular-normal data and the corresponding methods for testing for these distributions, setting specifications, determining process yields, and setting statistical process control limits.


 Are Your Data Normal?, 28 Sept 2007, 7:30-9:00AM, T136
Many statistical analysis methods (e.g. SPC, acceptance sampling, GR&R studies, process capability studies, tolerancing) require that the distribution of measurement values under consideration follow the normal or bell-shaped curve. When these data don't follow the normal curve the usual methods of analysis may be incorrect. In many cases the problem can be resolved by applying a mathematical transformation (e.g. a square or square root operation) to the original measurement values but more difficult problems require special analyses. In the first part of a two-part presentation, Paul Mathews will demonstrate how to use normal probability plots and quantitative tests for normality to determine if data follow the normal distribution. He will also describe some common situations in which you can expect to use transformations. In the second installment of the two-part presentation, Paul will describe some special non-normal distributions that show up frequently in real life situations.

An Introduction to and Some Examples of Failure Mode and Effect Analysis (FMEA), Haans Petruschke, 27 July 2007, 7:30-9:00 AM, Room T136
Haans Petruscke is a Deming-trained quality engineer currently employed at Libra Industries in Mentor. At this meeting Haans will present a novice-level introduction to failure modes and effects analysis (FMEA) and several FMEA case studies. (A comment from Paul: I've seen Haans do this FMEA presentation and thought that he was a great speaker and VERY knowledgeable on this topic, among many others. Even if you're already an FMEA  expert, I think that you'll enjoy Haans' presentation and the lively discussion that I think will follow.)

Attribute GR&R Studies (III),  29 June 2007, 7:30-9:00 AM, Room T136.
At the last two network meetings Paul Mathews presented an overview of gage error studies (GR&R studies) for measurement and attribute data and methods of analyzing GR&R study data. At the last meeting the attendees took data for three GR&R studies: a measurement response study, a binary (pass/fail) response study, and an ordinal (severity index) response study. We ran out of time to analyze these data in detail, so at this month's meeting we will review the experiments that were run and analyze the data more carefully. If you have your own GR&R attribute response data that you'd like to share with the network, please forward your data to Paul at paul@mmbstatistical.com.


Attribute GR&R Studies (II), 1 June 2007, 7:30-9:00 AM, Room T136.
At the last network meeting (27 April 2007) we discussed different types of attribute gage error studies, their design, and analysis. At the next meeting (1 June 2007) we will design, collect the data for, and analyze three GR&R studies:
    1) A traditional gage error long study on a measurement response.
    2) An attribute gage error study on a binary (pass/fail) response.
    3) An attribute gage error study on an ordinal (defect severity) response.
The experimental GR&R study data will be analyzed using MINITAB.

If you have your own attribute GR&R study data that you'd like to share with the network members, please e-mail your data and a description of the situation to Paul Mathews at paul@mmbstatistical.com.


Attribute Gage Error Studies (I),  27 April 2007, 7:30 - 9:00 AM, Room T136.
Most of us are familiar with gage repeatability and reproducibility (GR&R) studies for measurement data, however, eventually everyone encounters an attribute inspection operation that must be validated with a gage error study. The design of attribute gage error studies isn't any different from the design of studies for measurement data, however, attribute GR&R studies are analyzed using different statistics and have different acceptance criteria. Paul Mathews will describe the calculation and interpretation of two common statistics used for analyzing attribute gage error studies: kappa and intraclass correlation. Then he will present examples of capable and incapable attribute gaging systems.


Interference Fit and Stack-Up Tolerancing, 30 March 2007, 7:30 - 9:00 AM, Room T136.
Paul Mathews will discuss tolerance calculations for interference fit and stack-up tolerancing problems, including methods for both normal and non-normal distributions. He will also demonstrate the use of simulation methods to analyze fictional stack-up assemblies using data from relatively small samples.


Excel Pivot Tables, Ray Tison, 2 March 2007, 7:30-9:00 AM, T136.
Pivot tables in Excel provide a powerful tool to subset and stratify your data. Ray Tison will demonstrate how to create a pivot table in Excel and how to use the pivot table to identify patterns in the data and extract summary statistics. Ray will also demonstrate how to use pivot tables in Access when your data set becomes too big for Excel.


An Introduction to Data Analysis Using R, 26 January 2007, 7:30-9:00 AM, T136.
R is free software used for graphical and statistical data analysis that can be downloaded from the Internet. Because R code is written and shared by many people around the world, it has a tremendous range of capabilities. Consequently, most graphical and statistical methods that have been implemented in any commercially-available statistical software package have been implemented in R.

Paul Mathews will present an introduction to data analysis using R including:
   * How to obtain and install R and R packages.
   * How to access limited  R functions from the R Commander GUI package.
   * How to enter your data into R.
   * How to graph your data.
   * How to perform basic statistical analyses.
   * How to analyze designed experiments.
   * How to save your work.
   * How to learn more about R.


Too Many Experiment Designs? (Part II), 1 December 2006, 7:30-9:00 AM, T136.
We had such good turnout at the 27 October meeting (about 20 people), and we didn't finish our discussion of the topic (Too Many Experiment Designs?), so we're going hold a second session on the same topic.

At the 27 October meeting, Paul Mathews described the various methods available for analyzing experiments with qualitative and quantitative responses. At the 1 December meeting, he'll review this topic by presenting examples of these methods. Then we'll procede in our discussion of types of experiment designs including qualitative and quantitative variables; crossed and nested variables; and full factorial, fractional factorial, response surface, and Taguchi orthogonal designs.


Too Many Experiment Designs?, 27 October 2006, 7:30-9:00 AM, T136.
There are so many different kinds of experiment designs available that it can be difficult to choose the right one for a particular situation. Paul Mathews will present a review of types experiment designs and their capabilities including designs from classical DOE, Taguchi, and Shainin methods. Then he will lead an exercise to develop a flow chart for experiment design selection.


Component Swap II, 29 September 2006, 7:30-9:00 AM, T136.
At this second session on the component swap method, Paul Mathews will discuss the use of ANOVA to analyze component swap data and severl network members will present their component swap case studies.


Component Swap I, 1 September 2006, 7:30-9:00 AM, T136.
When an assembly has several separable components and there is excess variability that causes some of the assemblies to be good and others to be bad, the component swap method introduced by Dorian Shainin may be used to identify the component, components, or component interactions that cause that excess variability. Paul Mathews will describe the component swap method and demonstrate how to perform both Shainin's simplified analysis and a formal statistical analysis of component swap data. If you have a component swap case study that you'd like to share, please contact Paul before the meeting at paul@mmbstatistical.com.


Quality Management Jeopardy, 23 June 2006, 7:30-9:00 AM, T136.
Paul Mathews will host three rounds of quality management Jeopardy! Bring your co-workers and test your knowledge of quality management, Six Sigma, and Lean against other network members. Attendees will be given access to these Jeopardy rounds and Paul will explain how to populate the Jeopardy program with your own questions. Go here to get your own copy of our Jeopardy Excel/VB interface so you can re-play these three rounds of Quality Management Jeopardy and create your own rounds.


Design and Analysis of Accelerated Life Tests, 2 June 2006, 7:30-9:00 AM, T136.
When a life test run under normal operating conditions would take more time than is available and when there is a known stress factor (temperature, voltage, load, ...) that decreases life in a predictable way, an accelerated life test can be performed to reduce test time. Paul Mathews will present some of the considerations in the design of accelerated life tests and then he will use MINITAB to analyze a stepped-stress experiment.


Reliability Demonstration Tests, 31 March 2006, 7:30 - 9:00 AM, T136
Common goals of reliability experiments are to: demonstrate that the mean life exceeds a minimum value; demonstrate that the reliability at a specified time exceeds a minimum value; and demonstrate that the percentile (time or number of cycles) associated with a specified reliability exceeds a minimum value. All of these goals can be achieved using a special family of tests called reliability demonstration tests. Paul Mathews will discuss the basic concepts and methods of reliability demonstration tests for exponential, normal, and Weibull reliability distributions and he will demonstrate how to design such tests using the new tools available in MINITAB V14.


Analysis of Experiments with Nested Variables, 24 February 2006, 7:30 - 9:00 AM, T136
Experiments that include all possible combinations of levels of two or more variables are called factorial experiments, however, sometimes the levels of an experimental variable are unique to the levels of another experimental variable. In this case we say that the levels of one variable are nested within the levels of another. For example, an operation with three shifts may have four operators on each shift, but obviously not the same four operators on all shifts, so operators are nested within shifts. In more complicated cases, there may be several levels of nesting.

Paul Mathews will demonstrate the statistical analysis and interpretation of experiments with nested variables using two examples. The first example will consider a gage R&R study where each operator measures different parts. The second example will consider the variation in concentration of the active ingredient in a dry powdered blended product which is subdivided into a series of smaller and smaller nested units. If you have data from your own nested experiment that you would like to share with the network members, please forward them to Paul at paul@mmbstatistical.com.


Validating Your Process Capability Statistics, 27 January 2006, 7:30-9:00AM, Location T136
With the popularity and growth of Six Sigma, the use of process capability and performance statistics has exploded, but few people recognize how sensitive these statistics are to underlying assumptions that usually go unchecked. Paul Mathews will use example data sets to demonstrate the importance of population normality, process stability, the presence of outliers, and sample size in the evaluation of process capability and present a procedure for validating process capability statistics.


Process Capability Analysis For Non-Normal Populations, 2 December 2005, 7:30-9:00AM, T136
The popular process capability statistics like cp and cpk are only meaningful if the population being studied is normally distributed. When the population is known or suspected to be non-normal, alternative analysis methods should be used instead.

Paul Mathews will desmonstrate how the process fraction defective can be calculated directly from a cp/cpk pair and the consequences of a non-normal population. Then he will describe some appropriate alternative methods for analyzing and reporting process capability for non-normal populations.


Time-Weighted SPC Charts, 23 September 2005, 7:30-9:00AM, T136
The most common control charts (e.g. x-bar and R, IMR, p, np, c, and u charts) plot statistics determined from the most recent process data. These charts are referred to as Shewhart charts because they follow the control chart principles developed by Walter Shewhart. A disadvantage of Shewhart charts is that they are relatively insensitive to small shifts in location. Even with the use of run or sensitizing rules (e.g. the Western Electric rules), Shewhart charts remain relatively weak to small shifts in location. This weakness is reduced by time-weighted control charts which plot statistics derived from the time-series of process data. Examples of time-weighted charts - which differ in the weights they apply to the time-series data - are cumulative sum (CUSUM) charts, exponentially-weighted moving average (EWMA) charts, and moving average (MA) charts. Paul Mathews will present an overview of time-weighted control charts, discuss some of their advantages and disadvantages, and analyze case study data using CUSUM, EWMA,  and MA methods.


Analysis Methods for Autocorrelated SPC Data, 26 August 2005, 7:30-9:00AM, T136
 Time-series data frequently display autocorrelation, that is, observations are not independent of each other but are serially correlated. For example, the temperature of a furnace, the dimension of a part feature manufactured with a wearing tool, and the sales of a seasonal product all frequently exhibit autocorrelation. When SPC charts are constructed for autocorrelated data, the control limits calculated by the usual methods are inappropriate and impractical, however, these difficulties can be resolved using the appropriate analysis.

Paul Mathews will demonstrate how to detect autocorrelation in time-series data, how to extract the necessary statistics from the data to account for autocorrelation, and how to construct an appropriate control chart with meaningful control limits for such data.

If you think that you have time series data that suffer from autocorrelation and are willing to share your data with the network members, please forward your data to Paul in Excel or MINITAB format at paul@mmbstatistical.com.


Experiments with Attribute Responses - Binary Responses III, Paul Mathews, Ray Tison, and Bob Anastos (22 July 2005, 7:30-9:00AM, T136)
At our last two meetings we discussed experiments that involved binary (e.g. pass/fail) responses. Now that we know how to fit and interpret binary logistic regression models and validate those models using lack of fit and residuals analyses, it's time to look at some more case studies. Ray Tison from Dominion Gas Company will present a collections study; he needs to develop a model from historical data that will allow Dominion to predict whether a customer will pay their past-due gas bill or not. Bob Anastos will present data from a Plain Dealer article about the performance (number of educational goals met) of about 100 Cleveand area public schools as a function of number of students, median household income, spending per student, teacher pay, and other predictors. If you have your own binary response data set that you'd like to share with the group, please send it in advance to Paul Mathews at paul@mmbstatistical.com.


Experiments with Attribute Responses - Binary Responses II, 24 June 2005, 7:30-9:00AM, T136
At the last meeting (27 May 2005), Paul Mathews presented some basic concepts in the analysis of binary (pass/fail) responses and we analyzed a factorial experiment performed at Bescast to study the effect of three two-level process variables on a pair of binary responses. At the 24 June 2005 meeting, Paul will describe some of the diagnostic tools available to validate a binary logistic regression model and demonstrate them using the data from the Bescast case study. We will also discuss experimental design issues associated with binary response experiments and analyze data from several other experiments.


 Experiments with Attribute Responses - Binary Responses I, 27 May 2005, 7:30-9:00AM, T136
While many experiments generate responses that are quantitative, some experiments generate qualitative or attribute responses. There are three common familes of attribute responses: binary responses, ordinal responses, and nominal responses. Two-state (e.g. pass/fail or go/no-go) responses fall into the binary response category, ordinal responses have three or more levels related by size, and nominal responses group observations into three or more qualitative categories.
At this first in a series of sessions on analysis of attribute responses, Paul Mathews will present an overview of attribute response types with examples of each type. Then he will describe the analysis of binary response data and demonstrate these methods using the results from a factorial experiment performed on an investment casting process at Bescast. Subsequent meetings will consider other examples of binary response experiments and the other types of attribute responses.

Multiple-Stream Processes II, 22 April 2005, 7:30-9:00AM, T136
At our last meeting, Paul Mathews described some of the quality control methods available for multiple stream processes. In this second installment on the same topic, Paul will present examples of multiple stream processes that demonstrate the strengths and weaknesses of the various methods. If you have data from a multiple stream process that you wish to share with the group, please forward them to Paul at paul@mmbstatistical.com.


Multiple-Stream Processes, 24 March 2005, 7:30-9:00AM, T136
Multiple-stream processes have two or more parallel paths along which parts or material passes. Ideally all of the paths operate identically, so that there are no differences between the product from the different process streams, but in practice this rarely happens. Examples of multiple-stream processes are multi-cavity molding operations, multi-head machining operations, and multiple service providers (e.g. cashiers in a grocery store, help desk operators, etc.). Although each stream of a multiple-stream process could be evaluated for process control and capability, the amount of data and work required makes this approach impractical. Paul Mathews will discuss multiple-stream processes and the special methods available for process control (SPC) and process capability evaluation for these situations. If you have data from a multiple-stream process that you would like to share with the network members, please bring it in an Excel or MINITAB formatted file or e-mail the data to Paul before the meeting.


A Trebuchet Experiment (Session 2): Documenting the Experiment, 25 Feb 2005, 7:30-9:00AM, T136
 At our last meeting (February 4) we designed and ran a screening experiment to study the launch distance of a trebuchet. We ran into some problems though, or rather the projectile did, like the wall in front of the trebuchet, the wall behind it, and even the ceiling. (There's right and left censored data, but ceiling censored???) Although the response was compromised by these problems, the experiment was still sensitive enough to identify the key variables that affect the trebuchet. At this week's joint meeting between the Tools and Techniques and the ISO/QS subgroups, Paul Mathews will use the trebuchet experiment as an example to demonstrate three different forms of documentation for a designed experiment. Specifically, he will discuss the documentation components of: 1) the complete DOE project, 2) a Powerpoint presentation, and 3) a formal report. Click here for presentation notes.


Design of Experiments: A Trebuchet Experiment (Session 1) and How to Document and Report It (Session 2), 4 Feb and 25 Feb 2005, 7:30-9:00AM, T136
The next two sessions (February 4 and Feruary 25) of the Tools and Techniques subgroup will consider design of experiments (DOE) topics. At the February 4 meeting, we will run an experiment to characterize the performance of a trebuchet. (Trebuchet's are a form of catapult that were developed during the middle ages as siege weapons. The trebuchet that we'll use won't be so big, so if we storm any castles, they're going to be real small.) The experimental program will be structured using Mathews' 11-step procedure: 1) Perform the input/process/output (IPO) analysis, 2) Document the process, 3) Construct the problem statement, 4) Perform preliminary experiments, 5) Select the experimental variables, their levels, and the experiment design, 6) Determine the randomization and blocking plans, 7) Execute the experiment, 8) Analyze the data, 9) Interpret the results, 10) Run a confirmation experiment, and 11) Report the results.

At the February 25 meeting, which will be a joint session between the Tools and Techniques and the ISO/QS subgroups, we will talk about the documentation associated with designed experiments. We will use the information collected from the February 4 trebuchet experiment as an example to: 1) show what documentation should be kept by the DOE project team leader, 2) prepare a plan for writing a formal report, and 3) outline the Powerpoint slides required for a presentation to a management leadership team.

If you're planning to come to these presentations, especially the first one, please be sure to RSVP. If there are a lot of people coming, we'll try to have more than one trebuchet available.


Degrees of Freedom, 3 Dec 2004, 7:30-9:00AM, T136
In response to a recent query from one of the network members, the next T&T session will be on degrees of freedom. The concept of degrees of freedom is fundamental to statistical methods, linear regression, ANOVA, and designed experiments, but a deep understanding of degrees of freedom takes some practice and study to achieve. In this session, Paul Mathews will present an overview of the calculation and interpretation of degrees of freedom in common statistical analyses. His presentation will start from the simplest of problems – the one-sample t test for location – and make the logical progression through two-sample t tests for location (Did you know that there are three different two-sample t tests, with different degrees of freedom?); one-way and two-way ANOVA; full-factorial and nested designs; linear, polynomial, and multiple regression; two-level factorial designs with and without center cells; and response surface designs. If you’re studying for the ASQ CQE or CSSBB certifications, or just anxious to understand this initially abstract topic, this session will be of significant value to you. Click here for presentation notes.


A Designed Experiment: The Bending of Beams, 2 Nov 2004, 7:30-9:00AM, T136
At the request of several network members, our next session will be on design of experiments (DOE). Classroom exercises in DOE and Six Sigma Black Belt courses usually involve paper helicopters and catapults. Another experiment that is easy to perform in a classroom setting is the study of the deflection of rectangular beams.

Paul Mathews will lead an experiment to study the deflection of simply supported rectangular beams as a function of beam height, width, span, and load. Paul will use a four variable Box-Behnken design to develop a response surface model for beam deflection. He will also show how to analyze the experimental data using a model derived from the mechanical analysis of beam bending. This case is of special interest because the two models, the first empirical and the second based on the first principles of mechanics, allow different interpretations and scopes of use.

If you plan to attend, please come promptly because the Box-Behnken design requires 27 experimental runs and we will have to work quickly to get through both the data collection and analysis steps.


Reliability IV, 24 Sept 2004, 7:30-9:00AM, T136
Based on the high degree of interest in the topic and the great attendance at the earlier sessions, we decided to hold another Tools and Techniques subgroup session on reliability. This time we'll talk about life studies that utilize accelerated testing. These tests employ an increased level of stress that decreases unit life, but the tests are performed in such a way that their results can be used to make life predictions under normal operating conditions. Some methods of accelerated testing are: running 120V appliances at 130V, running electrical components intended for use at room temperature at an elevated temperature, and running corrosion resistant components in higher-than-normal corrosive environments. Paul Mathews will provide an introduction to accelerated testing with some examples. If you have any data from an accelerated test that you would like to share, please forward the data to Paul at pmathews@apk.net or bring the data with you on a floppy disk in a MINITAB or Excel format.


Reliability III, Angela Lunato and Paul Mathews, 3 Sept 2004, 7:30-9:00AM, T136
In this third session on reliability, Angela Lunato will describe two recent experiments that she was involved in to study electric motor life and electrical cord strength.

She and Paul Mathews will present the analysis and the interpretation of the data using MINITAB. Paul will also demonstrate how to plan a life demonstration test and how to calculate the necessary sample size and acceptance requirements for the test. If you have any reliability study examples or case studies that you would like to share, please contact Paul at pmathews@apk.net.


Reliability II, 30 July 2004, 7:30-9:00AM, T136
At the last network meeting Paul Mathews presented an overview of reliability experiments, data, and analysis using exponential and Weibull reliability models. He also demonstrated how to construct confidence intervals, perform hypothesis tests, and calculate sample sizes for reliability problems. Since the examples that he used were chosen for their simplicity and good behavior, and now that you're all reliability experts, at this month's meeting he'll present some less well-behaved examples. If you have data that you'd like to share with the group please forward it to Paul at pmathews@apk.net.


Reliability I, 25 June 2004, 7:30-9:00AM, T136
In our next three meetings (June, July, and August) Paul Mathews will give presentations on the design and analysis of experiments to study reliability. In the first meeting (June 25, 2004) Paul will provide an introduction to reliability and describe the analysis of experiments that produce complete failure data, repairable systems data, and right censored data.  Examples from both life and strength testing situations will be presented and data will be analyzed using the Stat> Reliability/Survival tools in Minitab. Tentative plans for the second and third meetings are reliability demonstration tests and accelerated tests, however, suggestions for other reliability topics will be considered. If you have an interesting reliability problem that you think would be of general interest and would like to share with the Network members please contact Paul at pmathews@apk.net.


Management of Circular Normal Quality Characteristics, 21 May 2004, 7:30-9:00AM, T136
The normal distribution model is the one usually invoked to characterize measurement data, however, in some cases the normal model isn’t appropriate. One such case is common in manufacturing operations; if a position characteristic can vary in two perpendicular directions then the appropriate distribution model is possibly the two-dimensional normal or /circular normal/ distribution. Examples of the circular normal distribution are: the run-out of a lathe-turned part, the radial deviation of a feature on a plane from its target position, and the distribution of positions reported by a fixed global positioning system (GPS) receiver. Paul Mathews will talk about these and other cases in which circular normal data appear, how to confirm that data are circular normal, how to calculate fractions defective and set specifications for circular normal data, and how to perform SPC and process capability calculations for circular normal data. If you have data that you think might be circular normal please bring them to class in an Excel or Minitab file or forward them to Paul at pmathews@apk.net.


 Acceptance Sampling and Quality Cost, 23 April 2004, 7:30-9:00AM, T136
Although quality engineers frequently use the ANSI/ASQ Z1.4 standard (formerly Mil-Std-105) to design sampling plans for pass/fail inspection, Z1.4 does not explicitly take into account the costs associated with inspection and external failures. Paul Mathews will present an Excel spreadsheet demonstration that calculates and graphs the performance and quality costs associated with various sampling plans as a function of the sampling plan design, material/labor cost, inspection cost, and external failure cost. Each specified sampling plan is contrasted to the no-inspection and 100% inspection cases as benchmarks.

 If you have a case that you would like Paul to discuss in his presentation please forward him your sampling plan design and cost information at pmathews@apk.net.


 How to Use Statistical Methods to Analyze Investments, Paul Mathews and George Braidich, 26 March 2004, 7:30-9:00AM, T136
Statistics are an extremely powerful and reliable tool in determining an investment’s short-term performance. Still today they are not widely talked about. This presentation will illustrate how to use basic statistics to determine if an investment is a winner, loser, or just plain too risky.

In the first half of this presentation, Paul Mathews will review some basic statistical concepts. In the second half George Braidich will illustrate how to apply these concepts to evaluate financial investments.


 How to Read a Financial Statement - An Overview for Non-Financial Managers, George Braidich, 20 Feb 2004, 7:30-9:00AM, T136
Financial statements are the instrument panel of a business enterprise. They constitute a report on current managerial performance and flash warning signals of future impending difficulties. To read a complex instrument panel, one must understand its gages and their calibration to make sense of the data they convey. Various ratios and other mathematical techniques are used in a financial analysis. George will discuss these ratios and what each ratio attempts to measure. He will also discuss the “Quality of Earnings” in a business entity.


 The Use of Gage Error Studies to Guide An Instrument Purchasing Decision, 23 Jan 2004, 7:30-9:00AM, L104
Prior to making a large purchase of new large diameter bore gages, a network member ran a series of gage error studies of gages from four different manufacturers. The purpose of the study was to determine if there were differences in the repeatability and reproducibility of the different gages (there were!) and to use these observations to help guide the purchasing decision. Even if you’re not interested in large diameter bore gages, this case study effectively demonstrates the use of gage error studies to guide an important business decision – one that you’ll probably have to live with for years after the purchasing decision is made.


 Are Your Data Normal?, 20 Nov 2003, 7:30-9:00AM, T136
Most QC methods for products and processes assume that the distribution of errors follows the normal or bell-shaped curve. When this assumption is violated those methods can give erroneous results that frustrate quality managers and customers. One common example of this problem appears in manufacturing situations that involve positional deviations in two dimensions, such as run-out from an axis of rotation in a turning operation or the deviation of a feature from a target position on a two-dimensional surface. In these cases the normal distribution model underestimates the severity of positional problems and provides inadequate QC tools, however, there are appropriate QC tools available to manage this kind of data. Paul Mathews will demonstrate how to calculate specification limits, construct control charts, and evaluate process capability for such responses. If you have responses that you think might behave in the manner described please bring it on a floppy disk in Excel or Minitab format to share with the network members.


 Are Your Data Normal?, 23 Sept and 23 Oct, 2003, 7:30-9:00AM, T136
Many statistical analysis methods (e.g. SPC, acceptance sampling, GR&R studies, process capability studies, tolerancing) require that the distribution of measurement values under consideration follow the normal or bell-shaped curve. When these data don't follow the normal curve the usual methods of analysis may be incorrect. In many cases the problem can be resolved by applying a mathematical transformation (e.g. a square or square root operation) to the original measurement values but more difficult problems require special analyses. In the first part of a two-part presentation, Paul Mathews will demonstrate how to use normal probability plots and quantitative tests for normality to determine if data follow the normal distribution. He will also describe some common situations in which you can expect to use transformations. In the second installment of the two-part presentation, Paul will describe some special not-quite-normal distributions, specifically the half-normal and circular normal distributions, that show up frequently in real life situations.


 Methods of Setting Specifications, 25 July and 22 August, 2003, 7:30-9:00AM, T136
Quality characteristics that are critical to quality (CTQ) for your customer must have their specifications set to meet your customer’s requirements. However, the specifications for many other quality characteristics that are not critical to quality are often set by observation – if experience has shown that a certain range of values is acceptable then that range is taken to be the specification. Despite the lesser importance of these non-CTQ quality characteristics, valid methods of setting their specifications are very important because the non-CTQ quality characteristics greatly outnumber the CTQ quality characteristics.

In this two part presentation Paul Mathews will demonstrate statistically valid methods of setting specifications for quality characteristics that are not CTQ. In the first part (July 25) Paul will demonstrate a nonparametric or distribution-free method of setting specs that does not require the demonstration or assumption that the quality characteristic follows a normal or some other well behaved distribution. In the second part (August 22) Paul will demonstrate the tolerance limit method. This method is used when it is safe to assume that the quality characteristic is normally distributed – an assumption which must be carefully tested. Specifications determined from both methods, the nonparametric and tolerance limit methods, are determined from random samples drawn from the product or process being studied.

 Just in case you’re wondering if you slept through or missed the class in mechanical or manufacturing engineering school when these methods were taught, most such programs never or only weakly address these problems so come join us to finally learn how setting specifications should really be done.


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