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

The Quality Engineers Network (QEN) is sponsored by Geauga Growth Partnership. 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.


Which Analysis to Choose: Confidence Interval or Hypothesis Test?, 7:30-9:00AM, 8 November 2024 via Zoom
We know that point estimates like the sample mean and standard deviation are insufficient for making data-based decisions because they don't take estimation precision into account. Proper data-based decision making requires the use of an inferential statistics method - either a confidence interval or a hypothesis test. The choice between the two methods of analysis has been made for us for many common applications, e.g. SPC, DOE, etc.; however, the choice may not be so clear in other cases. At this month's QEN meeting we will discuss the factors that should be considered when trying to choose between a confidence interval and a hypothesis test for the analysis of a planned experiment.


Applications of Chat GPT to Quality Engineering Problems, 7:30-9:00AM, 11 October 2024, by Zoom
At our September QEN meeting Sergei Ivanov of FoundAItion AI described the basics of using of Chat GPT for general problem solving. (E-mail me for Sergei's contact information if you want to follow up with him.) I (Paul) have been experimenting with the use of Chat GPT in more specific quality engineering applications including SPC, acceptance sampling, formulation of hypothesis test statements, sample size calculations, etc. At this month's QEN meeting I will present some of my results. We should have time to consider other problems if you have something in mind that would be interesting.
Applications of Chat GPT in Manufacturing Quality Engineering, 13 September, 7:30-9:00AM, by Zoom
Join us for an engaging presentation that explores the transformative capabilities of Chat GPT in Manufacturing Quality Engineering. This session will cover the basics of prompt engineering and demonstrate practical applications of Chat GPT in solving common engineering problems. Attendees will learn how to use Chat GPT to diagnose quality control issues, generate technical reports, draft internal memos, plan projects, and assist in research and analysis. Through hands-on exercises, we will show how AI can enhance efficiency and accuracy  in manufacturing processes. Discover how to leverage Chat GPT to improve your workflow and achieve quality excellence.


Nonstandard SPC Charts, 9 August 2024, 7:30-9:00AM, by Zoom
At our last two QEN meetings we discussed the Shewhart family of SPC charts. At this month's meeting we will consider some nonstandard charts including
 This is a lot of material so we'll only have time to do superficial coverage of these methods. Most of them are supported in MINITAB.


Introduction to Statistical Process Control (SPC) Part 2, 12 July 2024, 7:30-9:00AM, by Zoom
At our June QEN meeting we discussed:
 We discussed the most common form of control charts, the Shewhart charts, including:

We also talked about how to configure these charts in MINITAB, how to specify the observations to use for calculating control limits, and how to set up and interpret run rules to detect out-of-control events.

At this month's QEN meeting we will continue our discussion of SPC charts including:



An Introduction to SPC with Implementation in MINITAB, 14 June 2024, 7:30-9:00AM, by Zoom
At the request of a local company we are going to discuss the basics of Statistical Process Control (SPC) at this month's QEN meeting. We will begin with a discussion of the different types of process variation (common cause, special/assignable cause, structural, and tampering) and the different strategies to manage them. Then we will move on to the use of SPC control chart methods to distinguish between common cause variation (which requires no action) and special/assignable cause variation (which requires action). We will discuss the design and operation of the most common Shewhart control charts including design strategies for choosing samples, the calculation of control limits, the use of run rules, the risks of using too many run rules or keeping too many charts, and the implementation of these charts using MINITAB.


The Kano Model for Classifying Process Output Variables, 10 May 2024, 7:30-9:00AM, by Zoom
You guys know that I like to use an Input-Process-Output (IPO) diagram to document all of a process's process input variables (PIV) and process output variables (POV). The next step in understanding the process is classifying its POVs as Critical to Quality (CTQ), Key Process Output Variables (KPOV), and ordinary Process Output Variables (POV). This classification scheme comes from Six Sigma and works very well; however, I think that the distinction between the CTQs and KPOVs can be a bit murky. I usually describe the CTQs as characteristics that the customer specifically requests and the KPOVs as other characteristics that they assume will be present but don't know to ask for. I took these definitions from the Kano Model, which I think does a better job of classifying the POVs than the Six Sigma method does. We'll look at the Kano Model at this month's QEN meeting.

Kano Model: https://en.wikipedia.org/wiki/Kano_model


Interpreting the Results of a Medical Diagnostic Test, 9 February 2024, 7:30-9:00AM, by Zoom
There is a famous biomedical statistics problem that I use in homework assignments that was originally published by Edler and then followed up by Gerd Gigerenzer. The problem involves a cancer diagnostic test and the counterintuitive implications of a positive test result. ("Positive" here means positive for cancer.) In Edler's original publication he showed that many doctors incorrectly interpreted the result of the test. Gigerenzer showed that doctors could be taught to use a simple analysis method for analyzing the problem. The formal analysis of the problem uses Bayes's Theorem; however, Gigerenzer's approach only requires the use of a simple Venn diagram. We'll look at this problem and its variations at this month's meeting. If you don't have time to join us you can watch the brilliant presentation of the problem by Grant Sanderson (3 Blue 1 Brown) on Youtube here.


Analysis of Means, 12 January 2024, 7:30-9:00AM, via Zoom
The go-to method for testing for differences between treatment groups means in one-way or multi-way classification designs is the Analysis of Variance (ANOVA) method. An alternative but lesser known family of methods is the Analysis of Means (ANOM). ANOM has the advantage of presenting its results in a graphical form very similar to a control chart which can be useful for presenting to a statistically naive audience. At this month's QEN meeting we will consider the ANOM methods for variables data, proportions, and counts and MINITAB's implementation of them in the Stat> ANOVA> Analysis of Means menu.


Variable Transforms, 10 November 2023, 7:30-9:00AM, by Zoom
Most statistical analysis methods that test a characteristic of a distribution (e.g. mean, standard deviation, or distribution shape) make assumptions about the behavior of the data. These assumptions must be tested before the results of the chosen analysis method can be accepted. When an assumption is violated, then the analysis method's results can't be trusted and a corrective action must be applied or a different analysis method must be used. Among the most effective corrective actions is the application of a variable transform. For example, a violation of the normality or homoscedasticity (i.e. equal standard deviations) assumption can often be resolved by taking the square root, square, reciprocal, or log of the original data. At this month's QEN meeting we will look at how to recognize when an assumption of a statistical analysis method is violated and how to resolve the problem using an appropriate variable transform.


Confession Time: Things I've Done That Will Send Me to Statistics Hell, 13 October 2023, 7:30-9:00AM, by Zoom
Whether it's happened out of naivite, laziness, or desperation, I'm sure that we've all compromised "best practice" in some aspect of our statistical work. It's confession time: Let's share some of the poor choices we made, how we came to or why we were forced to make them, and how we could do better. It's probably too late to keep you out of statistics hell but this may help you avoid moving further up in line.


Manipulating Data in MINITAB, 8 September 2023, 7:30-9:00AM, by Zoom
Most of us use MINITAB for our statistical analysis needs but often format our data for analysis in Excel and then copy the Excel worksheet over into MINITAB. MINITAB has its own rich tool set for data manipulation including many features missing from base Excel. At this month's QEN meeting we will look at MINITAB's many tools for data manipulation.


Specifying Success Criteria for Attribute GR&R Studies, 11 August 2023, 7:30-9:00AM, by Zoom
GR&R attribute studies require a completely different set of performance metrics from their variables data siblings because of the pass/fail nature of their inspection results. If you look at the output from MINITAB's analysis of an attribute R&R study there is a bewildering collection of statistics - some which might make some sense and others which are completely cryptic. At this month's QEN meeting we will talk about what these different performance metrics are used for and which of them present the best opportunities to define attribute R&R study success criteria.


Assessing Agreement Between Two Measurement Systems with the Bland-Altman Method, 9 June 2023, 7:30-9:00AM, by Zoom
Some measurement systems can be difficult to use, take too long to perform, or are too expensive. In such cases, it is natural that an measurement alternative system be considered that addresses these issues; however, how do we compare the old and new measurement systems to quantify their agreement? The first analysis method that comes to mind is a simple correlation analysis: Measure many units spanning a range of measurement values using both measurement systems and calculate the correlation coefficient between paired observations; however, the correlation coefficient can be made arbitrarily large even when the agreement between the two measurements is poor by choosing a very wide range of values. The preferred method of analysis is Tukey's mean-different plot which was popularized by Bland and Altman. The Bland-Altman method is superior to the correlation method because it addresses issues of bias and scaling in absolute terms.


Experiment Protocol Documents, 12 May 2023, 7:30-9:00AM, by Zoom
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.


Design and Operation of Variables Sampling Plans for Defectives, 7:30-9:00AM, Friday, 14 April 2023, by Zoom
At last month's QEN meeting we discussed the calculation of and application of normal tolerance intervals. A closely related and well known alternative method is variables sampling plans (VSP) for defectives. VSPs are defined in the same terms as attribute sampling plans: By acceptable quality level (AQL) and rejectable quality level (RQL) conditions where:
 In an attribute sampling plan we draw a sample of specified size n, inspect the sample and count the number of defectives (D), and then accept the lot if D is less than or equal to a critical acceptance number c. In a VSP the decision to accept or reject a lot is based on a measurement response that is assumed to be normally distributed. If the sample mean is far enough away from the specification limits then the lot will be accepted and if the sample mean is too close to a specification limit then the lot will be rejected. The VSP's sample size n and critical distance k are defined by the choice of AQL and RQL values. At this month's meeting we will discuss the design and operation of VSPs by manual means and using MINITAB.


Normal Tolerance Intervals for Two or More Treatment Groups, 7:30-9:00AM, 10 March 2023, by Zoom
Given measurement data from a sample, a normal tolerance interval can be used to calculate an interval that contains a specified proportion of a population with a specified confidence level. Common applications for normal tolerance intervals are:
 Normal tolerance intervals are calculated from a sample's mean (xbar) and standard deviation (s) and a factor (k1 or k2) that accounts for the distribution of the population and the estimation precision for the population mean and standard deviation. Normal tolerance intervals have the form:
 where the k1 and k2 factors are functions of the coverage (i.e. the desired fraction of the population in the interval), the confidence level, and the sample size. k1 and k2 values are available in published tables and they are built into MINITAB's Stat> Quality Tools> Tolerance Intervals (Normal Distribution) method.

Although the normal tolerance interval method is fantastically useful when dealing with a single population, it is very common to have data that come from multiple treatment groups with fixed levels. For example, a medical device might need to operate under diverse orientation and environmental conditions. In such cases, individual normal tolerance intervals can be calculated for each unique treatment group; however, when the device is expected to be robust to changes in its operating conditions then all of the treatment groups often have similar or related behavior so their information can be pooled. This approach presents the opportunity to reduce an experiment's overall sample size by combining the information from all of the treatment groups. Although this method of pooling information from two or more treatment groups for a normal tolerance interval analysis is discussed in the literature it is not well known and it is not implemented in MINITAB. So at this month's QEN meeting we will discuss how to construct normal tolerance intervals for two or more treatment groups by combining their information into a single analysis.


Outliers!, 7:30-9:00AM, 10 February 2023, by Zoom
I've been struggling recently to help a customer analyze his lab data. The analysis wouldn't be difficult except that there are occasional outliers in the data sets. Sometimes there are a few outliers that, together, look like they're from a long tail of the distribution. In other cases the outliers look very much like they come from a different population than the rest. At this month's QEN meeting we will discuss methods for detecting outliers, their possible causes, and the right and wrong way to handle them in our analyses.
The Effect of Part Choice on Gage R&R Study Results, 7:30-9:00AM, 13 January 2023, by Zoom
The classic gage R&R study experiment design uses three operators who each measure ten parts twice. In previous meetings we've discussed why three operators isn't enough and why measuring twice is sufficient. Modern guidance recommends at least seven operators (Burdick, Borror, and Montgomery: Design and Analysis of Gage R&R Studies). And while ten parts is often sufficient, how parts are chosen for the study can have a large effect on the results. The most common methods for choosing parts for a gage R&R study are 1) Choose parts typical of the process and 2) Choose parts that span the range of the tolerance but these choices can give very different results. We'll take a look at these choices and other possibilities at this month's meeting.


Analysis of Censored Data, 7:30-9:00AM, 9 December 2022, by Zoom
In most inspection or measurement operations we collect complete data; that is, we collect an observation from each unit in a sample and we use well known methods for analyzing the complete data. However, there are situations in which it may be impossible or impractical to collect an observation on some units in a sample. Data of this type are said to be incomplete or censored and require special analysis methods.

A customer recently asked me to help him analyze a data set. He was performing a tensile test of the force required to pull a drug vial from its mating adapter; however, sometimes during testing the adapter got pulled out of the tensile tester's chuck instead. This is an example of censored data: The drug vial/adapter interface was stronger than the adapter/chuck interface so the vial/adapter force is not known but the adapter/chuck force provides a lower limit for its value. Proper analysis of these data requires simultaneous analysis of all observations, including those observations that have measured vial/adapter forces AND those observations that were censored by the adapter/chuck force. At this month's QEN meeting we'll talk about how to analyze incomplete/censored data like this, how to get MINITAB to do the work, and how to interpret the results.


Statistical Quick Tests, 7:30-9:00AM, 11 November 2022, by Zoom
We all know that most statistical tests involve some manual calculation or require special software. The calculations aren't too difficult to perform but they do take some time, resources, perhaps a table or critical values, and of course remembering how to perform the analysis. Alternatively, there are some well known statistical "quick tests" that can be performed by a quick inspection of an appropriate table or graph. These methods aren't as powerful as others, but they have the benefit of being fast and so easy that you can't prevent yourself from applying them given the opportunity. This month we'll look at Tukey's Quick Test and the Boxplot Slippage Tests for the two-sample location problem, some other quick test methods, and some other closely related methods.


Case Study: Analysis of Very Noisy Serial Data, 7:30-9:00AM, 14 October 2022, by Zoom
I was recently helping network member Ralph L analyze some interesting lab data. His experiment involves two treatment groups - a test group and a control group - and he is trying to determine if there is a difference between the means of the two groups. The first complication is that the data are very noisy, covering a very wide range of response values - about 4 orders of magnitude! That problem is quickly dealt with using a log transform. The next complication is that Ralph has serial data, i.e. he has collected many observations periodically on the same samples and over a considerable period of time. Serial data tend to be strongly correlated so it would be incorrect to treat the observations as if they were independent. That problem is dealt with by some simple pre-processing of the data prior to performing the ultimate two-sample test for a difference between the two treatment group means. Ralph has volunteered to let us use his anonymized experimental data for this discussion. If you want to get a jump on understanding the analysis method check out this classic paper on the topic https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1662443/.


Editing Graphs in MINITAB, 7:30-9:00AM, 9 September 2022, by Zoom
In addition to its broad scope and depth in the statistical methods topics, MINITAB software provides an equally broad and deep set of graphical methods. MINITAB's default graphs are satisfactory for most purposes, but when a MINITAB graph must be modified to extract or highlight every piece of important information MINITAB also provides fantastic graph editing and customization tools. At this month's QEN meeting we will review the graph design features that MINITAB exposes in its normal menus and then we'll look at how to double click and right click your way through customizing your MINITAB-produced graphs to make the perfect graphs that you need.


Use Expectation Value to Evaluate and Compare Business Process Models, 7:30-9:00AM, 12 August 2022, by Zoom.
The method of expectation values is introduced in statistics courses to determine the parameters of a distribution; however, that's just the starting point for this valuable method. Expectation values are a form of weighted mean where the weighting factor can take on many different forms - most often money - so the method finds many important applications in quality cost and business cost analysis including:
 In addition to using the expectation value method to characterize a single process, the results from expectation value calculations can be used to compare variations on a process. For example, a manufacturing process may include a rework operation, but how do you know if the rework operation is worth the cost? The expectation value method can provide the answer. So at this month's QEN meeting we will review the method of expectation value, consider its application in some simple games and business problems, and then look at other applications of the method in quality cost analysis.
 

Functional Applications of Machine Learning presented by Keith Fritz, in person at ASM International (reservation required), or by Zoom, 7:30-9:00AM, 8 July 2022
Machine Learning (ML), Artificial Intelligence (AI), and Integrated Computational Materials Engineering (ICME) cover a broad ranges of topics and applications. This presentation will focus on the practical real-world applications where these tools have been applied. Topics include:
- Algorithms to validate test data
- Simulation of manufacturing conditions to investigate defects
- How is machine learning different from traditional six sigma?
- Using ICME to increase material performance
- Resources for further education

Keith Fritz is a Metallurgist from University of Wisconsin and a GE trained Six Sigma Black Belt. He has held multiple technical roles at PCC, General Motors, ASM International, and QuesTek Innovations. He has a passion for the application of Machine Learning, Data Science, and Integrated Computational Materials Engineering for solving real world engineering and quality problems.


The Life Cycle of an SPC Control Chart, 10 June 2022, 7:30-9:00AM, by Zoom
When Walter Shewhart invented control charts a century ago, they were constructed using rocks and sticks (aka pencils and paper). Today SPC software is ubiquitous; however, many people who practice SPC today don't realize that the time, effort, and cost limiting considerations that Shewhart intended for the SPC charts of his day are easily violated by improperly used SPC software. At this month's QEN meeting we will discuss the design and administration of SPC charts as intended by Shewhart and what revisions to his intentions are required today when SPC is implemented in software.


Taguchi's Loss Function and the S-Double-Bar ($) Chart, 7:30-9:00AM, 13 May 2022, by Zoom
Most of us were taught the goalpost model of interpreting specification limits: Any units that fall between the specification limits (aka the goalposts) are good and any units that fall outside of the specification limits are bad. Taguchi showed, with his loss function, that real processes aren't that simple and that a different model for interpreting lost value (i.e. the cost of units out-of-spec) is required. At this month's QEN meeting we will discuss Taguchi's Loss Function, its implications for process improvement using Statistical Process Control (SPC) and Design of Experiment (DOE) methods, and we will design a Loss Function-based S-Double-Bar ($) Chart that can be used to supplement the usual SPC X-bar and R charts.


Misuse of Two-Sample T Tests To Analyze Two-way and Multi-way Classification Designs, 8 April 2022, 7:30-9:00AM, by Zoom
I have recently seen a flurry of incidents when people have inappropriately used a two-sample t test to analyze data from a two-way or multi-way classification design. There is a close relationship between the two-sample t test, one-way ANOVA, and two-way or multi-way ANOVA analyses so the cause for such confusion about the choice of analysis method can be understood. In fact, under some special circumstances the two-sample t test may reproduce the results from those other analysis methods; however, there are circumstances under which the two-sample t test would be the wrong choice and one of the other methods is required. We'll talk about this relationship at this month's meeting and we will look at examples of when there is agreement and disagreement between the different analysis methods.


Use Operating Characteristic (OC) Curves to Interpret Sampling Plan Performance, 7:30-9:00AM, 11 March 2022, by Zoom
Acceptance sampling plans, of both the attribute and variable type, are workhorse methods in quality engineering. We often pick a plan to meet one or two stated requirements, but we may not look beyond the plan's sample size and acceptance criterion to see its detailed performance. The best way to do that, and to compare the performance of sampling plans to each other, is to construct their operating characteristic (OC) curves - a plot of the probability of accepting a lot as a function of its proportion defective. At this month's meeting we will discuss how to create the OC curves for attribute and variable sampling plans, how to interpret them, and how to use them to compare the performance of two or more competing sampling plans.


The Role of Two-level Factorial, Fractional Factorial, and Responses Surface Designs in a Program of Designed Experiments, 7:30-9:00AM, 11 February 2022, by Zoom
At our December 10th meeting we introduced the two-level factorial experiment designs and at our January 14th meeting we extended them to the fractional factorial and response surface designs. At the end of the January 14th meeting we mentioned the role that all three types of designs play in a product or process development program. It's unusual that we ever run a development program that involves only a single experiment. Usually a series of experiments are required, of different design types to match the specific learning needs of each stage in the development program. Now that we have some knowledge of the two-level factorials and their extended designs, let's use our next QEN meeting to discuss how those various designs are used through the stages of a development program and how they can put you ahead of schedule and under budget.


Extending the Two-Level Factorial Designs to Fractional Factorial and Response Surface Designs, 7:30-9:00AM, 14 January 2022, by Zoom
This session is a follow up to our last (December 10) session when we discussed the basics of the two-level factorial experiment designs. In those designs all of the study variables (i.e the independent variables), whether they are of attribute or variable type, appear at only two levels. For example, in the paper helicopter experiment that we considered, the 2^3 experiment design had three variables: blade length (short/long), blade width (narrow/wide), and paper clip (without/with). We used ANOVA (or regression - they do the same thing) to test for response differences between each variable's two levels. This simplicity makes these experiment designs tremendously useful - you could base a whole career on them. However, quite soon you will run into two of their limitations:
 These limitations can be overcome by simple modifications to the two-level factorial designs - by the fractional factorial designs in the first situation and by response surface designs in the second situation. We will look at these designs in this month's session.


An Introduction to Two-Level Factorial Experiment Designs, 7:30-9:00AM, 10 December 2021, by Zoom
Design of Experiments (DOE) is a very broad topic and textbooks and courses on the topic can be very intimidating; however, the most basic concepts of the design and analysis of designed experiments are embodied in the very simple two-level factorial designs. In these experiments all process input variables (PIV), whether they are of attribute or variable type, appear at only two levels. This greatly simplifies the DOE analysis and interpretation because both ANOVA and regression methods, whichever you prefer, may be used. At this month's QEN meeting we will consider these two-level factorial designs, we'll look at their application to a simple classroom exercise (paper helicopters), and we'll talk about their role at the core of the fractional factorial and response surface designs. This topic may be extended to more sessions if there is sufficient interest.


Design of SPC Chart Run Rules, 7:30-9:00AM, 12 November 2021, by Zoom
In many circumstances, Walter Shewhart's Western Electric Rules for out-of-control patterns on SPC charts are safe and sufficient; however, Shewhart didn't anticipate that SPC charts could become automated. SPC automation presents the potentially serious problem of excessive Type 1 errors (false alarms) if too many run rules are used, especially when too many charts are kept. This risk can be managed by proper run rule design that takes into account the number of rules and the number of charts. At this month's QEN meeting we will discuss Shewhart's design criteria for run rules, their performance in the context of Shewhart's era, and how the rules can be modified to be save in the modern context of automated SPC charts.


The SPC Between/Within Subgroups Chart, 7:30-9:00AM, 8 October 2021, by Zoom
At this month's QEN meeting will will discuss SPC Between/Within Subgroups Charts and the associated process capability analysis.

The traditional SPC x-bar and R charts track changes in the mean on the x-bar chart and changes in the within-subgroup variation on the R chart. The x-bar chart's control limits are determined from R-bar from the R chart. The x-bar and R charts are very effective when out-of-control events on the x-bar chart are limited to spurious special causes; however, they can fail when the within-subgroup variation indicated on the R chart does not correctly capture the range of variation seen on the x-bar chart. Some common situations in which this problem occurs is when the subgroups come from different lots with no production continuity between them or the subgroups means are slowly drifting. This problem is addressed in an alternative SPC chart called a Between/Within chart. Three charts are maintained in the Between/Within chart method: the x-bar chart with modified control limits, a moving range chart of subgroup means, and the original R chart. This three-chart set allows the between-subgroup variation that appears on the standard x-bar chart to be partitioned into two components: a between-subgroups long term component and a between-subgroups short term component. The benefit of this approach is that it provides a more useful set of control charts that correctly account for the different types of variation in the process and it can be used to calculate a more accurate set of process capability statistics that indicate the true capability of the process.

MINITAB's Graph Builder Tool, 7:30-9:00AM, 10 September 2021, by Zoom
Finding the right graphical presentation method for a data set can be crucial to conveying the correct interpretation of the data to your audience; however, finding that perfect graph can be a challenge. For example, given a single sample of measurement values we could construct a dotplot, boxplot, histogram, stem-and-leaf plot, normal plot, run chart, individual value plot, interval plot, and I'm sure there are others. The magnitude of the problem grows when we add classifying variables or dependent (e.g. y(x)) variables. To help us along on our searches for these perfect graphs MINITAB's new release (V. 20.3) includes a new Graph Builder tool in the Graphs menu. The Graph Builder tool provides a quick way of constructing many different graphs from the same data set so that we can inspect them to choose our favorite. We'll take a look at the MINITAB Graph Builder tool at this month's QEN meeting.


Using Jitter to Address a Coarse Measurement Scale When Assessing Normality, 7:30-9:00AM, 13 August 2021 by Zoom
One of the most common assumptions we check in the many different statistical analyses that we perform is the assumption of normality. Normality tests appear in ordinary confidence intervals and hypothesis tests, acceptance sampling for variables, SPC, process capability, gage R&R studies, DOE, reliability, and many other areas. The two most commonly used normality test methods are the normal probability plot and the Anderson-Darling Test. The subjective and quantitative nature of the two methods, respectively, complement each other nicely, but the Anderson-Darling test can be susceptible to some errors that can be easy to identify and mitigate if you're paying attention. One of these error situations is when the measurement data are collected on a coarse measurement scale - especially when all of the observations fall into only a few measurement value bins. In many cases the compromised validity of the Anderson-Darling test can be salvaged by the use of jittering the original data. At this month's meeting we'll discuss this case, when the use of jitter is appropriate, how to implement jitter, and how to report the results.


Crafting Hypotheses, 7:30-9:00AM, 11 June 2021 by Zoom
The issues surrounding statistical methods can present a bewildering array of choices to statistical novices. One of the most crucial topics - and the among the most difficult to learn - is how to craft the hypotheses for a hypothesis test. If you do this step incorrectly you can get into all kinds of trouble and the only way to learn it is either by making lots of mistakes (and getting caught) or by careful study. The careful study route is a lot less traumatic, so this month we will talk about the many issues that have to be considered when crafting hypotheses including:

Improving the Quality of Your Graphical Presentations, 7:30-9:00AM, 14 May 2021, by Zoom
I recently suffered through a presentation that included a series of horrendous graphs. Axis labels were missing, measurement units were missing, the font size of numbers on the axis scales were too small to read, legends were missing or made no sense, and the charts were filled with clutter and special effects that were distracting and added no value. I learned long ago (it was beaten into me) to make my graphs complete and as lean as possible but no leaner than necessary. (I have a great story for you on this theme.) Where do you learn what distinguishes good and bad graphical displays? It comes with experience but if you want to learn faster the authority of graphical data presentation best practices is Edward Tufte who published a famous and beautiful collection of books on the topic (https://www.edwardtufte.com/tufte/books_vdqi). We'll discuss some of these best and worst practices in this month's meeting.


Gage R&R Studies With More Variables Than Operator and Part, 7:30-9:00AM, 9 April 2021, by Zoom
At last month's QEN meeting we talked about MINITAB's Type 1 Gage Study and Gage Linearity and Bias Study in relation to the classic Gage R&R Study operator by part crossed design. It came up in the conversation that it's possible to have more variables in a gage R&R study than just operator and part. For example, you might also consider:
And many other study variables are possible. MINITAB provides support for these modified GR&R study designs in its Stat> Quality Tools> Gage Study> Gage R&R Study (Expanded) menu but the analysis can also be done using Stat> ANOVA> General Linear Model. We'll look at some of these more complicated experiment designs and analysis tools at this month's meeting.


Comparing MINITAB's Three Gage Study Methods: Type 1 Study, Linearity and Bias Study, and GR&R Study, 7:30-9:00AM, 12 March 2021, by Zoom
The gage R&R study operator-by-part crossed design, implemented in MINITAB's Stat> Quality Tools> Gage Study> Gage R&R Study (Crossed) method, is by far the most-used gage study method; however, MINITAB also provides two other gage study methods: the Type 1 Gage Study and the Gage Linearity and Bias Study. The capabilities of these three methods have some overlap but they each have some unique features. At this month's QEN meeting we will compare these three gage study methods and discuss what conditions would indicate a preference for one method over the others.


Part Selection for Gage R&R Studies, 7:30-9:00AM, 12 February 2021, by Zoom
Many people give little thought to part selection for their GR&R studies; however, the choice of parts can have a huge impact on the results and usefulness for these studies. As one example: the choice of parts for a study must be matched to the measurement intent. Suppose that a process produces parts that have a much tighter distribution than the spec limits allow (i.e. the process capability is excellent). If the purpose of the intended measurement is to support process capability claims then drawing a random sample of parts from that process would be appropriate; however, if the purpose of the measurement is to check parts against the spec limits then a random sample of parts from the process probably won't span the entire range of the spec and parts with more variability would be appropriate. There are many other situations that must be considered when choosing parts for a gage study. We'll talk about them at this month's meeting.


ASQ Certification, 7:30-9:00AM, 15 January 2021, by Zoom
Within your own company your managers and peers probably have a good idea of your quality engineering skill set but if you want to reinforce their opinions or obtain a credential that is known and valued outside of your company then you should consider obtaining one of the American Society for Quality's (ASQ) certifications. ASQ offers 18 different certifications in the quality field (https://asq.org/cert/catalog). Some of the certifications that will be of interest to the QMN and QEN audience are:
At this month's QEN meeting we will talk about the types of certifications that ASQ offers, their technical scope, the requirements for applying for certification, how to prepare for the exam, and the general value of holding these certifications.


Free Software!, 7:30-9:00AM, Friday, 11 December 2020, by Zoom
Everybody loves free stuff! This is a topic that we do periodically that's always a lot of fun and everyone leaves finding something that they need or at least want to try out. I've posted my four page list of free software that you can check out here (Warning: it hasn't been updated in a while) but plan to come with your own suggestions.


Tests for Proportions or Fractions Defective, 7:30-9:00AM, 13 November 2020, by Zoom
I was in a meeting recently with a customer where the topic of discussion was the possibility of a difference between the defective rates of two product assembly processes. When both processes were running well they were expected to have similar defective rates but one of the processes was more sensitive to environmental conditions and could go bad more easily. Recent experience suggested that the defective rates of the two processes had diverged so a simple experiment was performed by collecting 20 random units from each process and inspecting them for defective units. There were no defectives found in the sample from the robust process and there were three defectives found in the sample from the weaker process. At first glance this result feels conclusive - there must be a difference in the defective rates between the two processes; however, a formal statistical test (Fisher's Exact test) indicates that there is a high probability that the observed result could have been obtained by random chance. This case is an example of a statistical test for two proportions. At this week's QEN meeting we will discuss this and similar situations:

Two Types of Missing Values in Data Sets: Data Truncation and Data Censoring, 7:30-9:00AM, 9 October 2020, by Zoom
At last month's QEN meeting we discussed the use of mathematical transformations to convert nonnormal responses to normal so that classical statistical tests and analysis methods can be used. During that discussion we mentioned the possibility of encountering incomplete data sets; that is, data sets that have some observations that are missing. We're not talking about the common case of observations missing-at-random (MAR) here. We're talking about observations that are missing-with-cause (MWC). There are several kinds of MWC situations but this month we'll discuss two of the most common ones:

Variable Transformations for Nonnormal Data, 7:30-9:00AM, 11 September 2020, by Zoom
I recently heard from a customer who was struggling to analyze and present data which had a number of outliers with large values in the data set. She was trying to make the case that those observations were different from the others so that they could be omitted from the analysis; however, after omitting them and reanalyzing the data there were even more observations that looked like outliers. This turned out to be the classic case of the need for a variable transform - specifically a log transform. This is a common occurrence in statistical analysis - that a response requires a transformation - so the method is used everywhere including inferential methods, gage studies, process capability studies, designed experiments, statistical process control, and many other situations. With some practice and experience you can even learn to recognize when a transformation will be required and which transformation will do the job given the fundamental first principles of the process that produced the response.


Use An Input-Process-Output Diagram to Document the Variables in Your Process, 7:30-9:00AM, 14 August 2020, by Zoom
We all use the well known Cause and Effect Diagram (aka Fishbone or Ishikawa diagram) for documenting the factors that affect a process. Recall that in the absence of specific categories for organizing the bones on the fishbone diagram we use the default ones: Manpower, Methods, Machine, Materials, and Environment. The IPO diagram's structure is taken from the fishbone diagram; the process name is identified in the middle of the diagram, the process inputs are presented in fishbone structure to the left, and the process outputs are presented in fishbone structure to the right. I (Paul) have found the IPO diagram to be invaluable for quickly communicating the process input and output variables to a new team member or to a manager who underestimates the complexity of the system. There are many ways to build a fishbone diagram. Note cards on a bulletin board work great, but we will use the free software package FreeMind to study the construction of and some examples of IPO diagrams.


Which Interval Do I Need: Confidence, Prediction, or Tolerance?, 7:30-9:00AM, 10 July 2020, by Zoom
Statistical software like MINITAB can be an amazing tool but it can also present a bewildering collection of methods that look so much alike that it can be difficult to determine which ones are interchangeable and which ones are different. One such collection of methods is statistical intervals including confidence intervals, prediction intervals, and tolerance intervals. At this month's QEN meeting we'll discuss the calculation, use, and interpretation of each type of statistical interval. If you have any examples or data you would like to share for the discussion, please send them to me (Paul) with a short description of what you're trying to do.


Improve the Quality of Your Inspection Results by Upgrading the Measurement Scale, 7:30-9:00AM, 12 June 2020, by Zoom
I've seen a recent flurry of customers who were struggling to define methods to characterize somewhat subjective quality characteristics in their experiments:
In each case their first thoughts were to use a binary (pass or fail) inspection criterion - and that method would work except that binary responses typically demand very large sample sizes that may not be practical or possible due to time and resource constraints. In each case we solved the problem by upgrading the measurement scale that was used to record the observations to a scale of higher value/information content resulting in significantly reduced sample sizes.

The value of individual observations increases according to the following 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 observations with observations of higher value. The higher value observations carry more information than the lower values ones so sample sizes can be smaller - in some cases smaller by a factor of 10 to 30. At this month's meeting, we'll review the hierarchy of measurement scales, discuss the opportunities and benefits of replacing low-value observations with high-value observations, and the possibilities for reducing experimental sample size.


Errors, Mistakes, and Failures of Measurement Instruments, 8 May 2020, 7:30-9:00AM, by Zoom
At last month's QEN meeting we discussed considerations in choosing a measurement instrument to match the requirements of a measurement task. We discussed the usual issues: range, discrimination, linearity, repeatability, reproducibility, and measurement goal - whether the measurement's intent is to determine if parts meet specification limits or to determine process capability. Carefully choosing a measurement instrument should always happen at the beginning of the life cycle of a measurement process but during that life cycle measurement instruments can fail. Let's spend this session talking about our experiences with failed measurement instruments including the conditions that caused the failure, the impact on the instrument, the time elapsed between when an instrument failed and when the failure was detected, and the associated consequences to the business.


Considerations in Choosing a Measurement Instrument, 10 April 2020, 7:30-9:00AM.
Join the on-line meeting using Zoom here or from your web browser using meeting ID: 421 185 186 and password: 022 990.
We had a request at our last meeting to discuss how to choose an appropriate measurement instrument for an inspection operation. This question isn't as simple as it sounds. The usual first thought is to identify candidate instruments by their measurement range and then to choose the specific instrument using the rule of 10; i.e. that the measurement instrument's resolution/graduations must be less then or equal to 1/10th of the part tolerance. That algorithm provides a starting point; however, it is also necessary to consider the gage R&R capability of the instrument, its measurement uncertainty (in the accuracy sense), the part's process capability, and whether the purpose of the inspection operation is to collect data to be used to determine process capability or just to provide pass/fail results relative to specification limits. We'll discuss all of these issues at our April 10th meeting.


Quality Audit Checklists with Examples, 13 March 2020, 7:30-9:00AM, at GGP
Quality audit checklists are a crucial quality management tool for processes that are complex and difficult to quantify. At this month's meeting we will discuss the design, construction, and use of audit checklists and we'll look at some obscure examples including 1) a checklist for evaluating the use of SPC within an organization, 2) a health and safety checklist, and 3) a checklist for evaluating quality culture within an organization at the upper management, middle management, and worker levels. The results from the quality culture audits are especially fascinating - they provide very clear indications of healthy and disfunctional quality cultures.


Process Precontrol, 14 February 2020, 7:30-9:00AM, at GGP
At this month's meeting we're going to discuss an alternative to Statistical Process Control (SPC) called Process Precontrol.

We spent our last two sessions talking about the design and operation of SPC charts. SPC works best when we have long production runs of a single product. SPC can still be used for short production runs using special Short Run SPC methods but those methods can be complicated and require a knowledgeable and experienced SPC practitioner. A simple alternative method to Short Run SPC that can also be used for long runs is Process Precontrol. Process Precontrol works by starting in a 100% inspection mode until there is sufficient evidence that the process is stable and then shifting to a sampling mode. After entering sampling mode, we draw periodic samples to assess the current state of the process and either stay in sampling mode when the data look good or switch back to 100% inspection mode when the data indicates that the process has gone out of control.

Statistical Process Control, Part 2, 17 January 2020, 7:30-9:00AM, at GGP
At last month's QEN meeting we started a discussion about the basics of statistical process control (SPC) including the design and operation of IMR and x-bar and R charts. This month we'll continue our discussion of SPC by considering more types of charts and go into the design and operation of them in more detail. We'll also talk about sample size, sampling frequency, the risks of using too many charts at one time, and the life cycle of a control chart.


An Introduction to SPC and Control Charts, 13 December 2019, 7:30-9:00AM, at GGP
Perhaps the single, most effective and ubiquitous process improvement method in existence is statistical process control (SPC). SPC is a foundational tool in the quality engineering tool set and deserves at least some attention from anyone who deals with any type of process data and substantial attention from experts within the organization. At this month's QEN meeting we will look at some of the motivations and philosophy behind SPC, its role in quality costs, and the simplest of the control charts - the individual and moving range (IMR) charts and xbar and R charts. We can discuss other types of charts and advanced methods in future meetings.


Testing Data for Normality and What to Do When They're Not, 8 November 2019, 7:30-9:00AM, at GGP
In our last two meetings on process capability we saw that it was very important to test process capability data for normality. Normality testing also has a huge role in many other statistical methodologies including SPC, acceptance sampling, GR&R studies, Design of Experiments, reliability, and many more. At this month's meeting we'll look at some of the most popular methods for testing data for normality starting with normal probability plots and the Anderson-Darling test. We'll also look at the use of variable transforms (such as square roots and logarithms) to transform data from non-normal to normal and we'll look at related methods for fitting other distributions that aren't inherently normal.


Process Capability, 11 October 2019, 7:30-9:00AM, at GGP
At this month's QEN meeting we will continue our discussion of process capability. We'll review the basic process capability statistics Cp, Cpk, Pp, and Ppk and their confidence intervals and how to interpret them. We'll use those observations to develop sample size guidelines for process capability studies. We'll also look at methods of assessing distribution shape (the common process capability statistics require a normal distribution) and the use of transformations to convert non-normal distributions back to normal distributions.


Process Capability, 13 September 2019, 7:30-9:00AM, at GGP
At this month's QEN meeting we will take up a discussion of process capability. We'll review the basic process capability statistics Cp, Cpk, Pp, and Ppk and then discuss their use, interpretation, and the conditions required for their validity. We'll start a more advanced discussion of how to do process capability under complicated conditions, such as for non-normal distributions, and we'll take up that topic again at the October meeting.


Design and Analysis of Gage R&R Studies (Part 2), 9 August 2019, 7:30-9:00AM, at GGP
At last month's QEN meeting we started a discussion of the design and analysis of gage R&R studies. We'll take up the topic again this month by going into more details of the classic operator by part crossed experiment, paying particular attention to the number of and selection of operators, parts, and trials for the study. We'll also discuss extensions of the classic design including nested designs, designs with additional study variables (i.e. "expanded" designs), and studies with attribute responses. We may pick up one or more of these advanced topics in a third session.


Design and Analysis of Gage R&R Studies (Part 1), 12 July 2019, 7:30-9:00AM, at GGP
Measurement reliability is determined by measurement accuracy which is established by calibration and measurement precision which is quantified in a gage repeatability and reproducibility or GR&R study. If a measurement is both accurate and precise then it may be appropriate for its intended purpose.

The best known GR&R study design is the classic operator by part crossed design with 3 operators, 10 parts, and 2 trials. Most references don't give any guidance about why those numbers are used but good guidance is presented in books like Design and Analysis of Gauge R&R Studies by Burdick, Borror, and Montgomery. At this month's QEN meeting we will 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. If we have time, we'll start talking about the analysis and interpretation of GR&R studies but we'll resume that discussion in more detail at the next meeting.


A Quality Cost Interpretation for Acceptance Sampling Plans, 14 June 2019, 7:30-9:00AM, at GGP
At last month's QEN meeting we discussed how to design attribute and variable sampling plans to control defective rates relative to specification limits. The design of these plans required us to specify AQL (acceptable quality level) and RQL (rejectable quality level) conditions that lead to a unique sample size and acceptance criterion. Although these methods are well known and easily understood by quality engineers, the AQL and RQL concepts can be too abstract for others (especially managers) so an alternate, easier to understand approach is desired. The solution comes by applying quality cost methods to the acceptance sampling problem. By specifying the necessary cost inputs (material and labor cost, inspection cost, and external failure cost) we can express the performance of a sampling plan in terms of its net income and cost of poor quality (COPQ). This approach also allows for easy-to-understand comparisons between different sampling plans such as the special cases of no inspection and 100% inspection. Even when the cost information isn't available for a specific process, understanding the general behavior of quality cost in acceptance sampling can provide significant insight into the benefits and risks of the method.


An Introduction to Acceptance Sampling for Attributes and Variables, 10 May 2019, 7:30-9:00AM, at GGP
Acceptance sampling in quality control is a huge topic but the simplest acceptance sampling methods are pretty easy to understand. In a classic acceptance sampling for attributes (i.e. for pass/fail inspection) application a single random sample is drawn from a lot and inspected for defectives. If the number of defectives in the sample is less than or equal to a critical value, called the acceptance number, the lot is accepted. If the number of defectives in the sample is greater than the acceptance number then the lot is rejected. A similar strategy is used for measurement responses by comparing the mean of a random sample to a critical acceptance value.

Attributes and variables sampling plans are usually designed to meet two input criteria which may be:
1) Provide a high probability of accepting good product and a low probability of accepting bad product
2) Provide a high probability of accepting good product with a zero acceptance number sampling plan
3) Provide a low probability of accepting bad product with a zero acceptance number sampling plan

These plans provide different protections for the manufacturer and for the consumer so it is crucial to understand what you're getting when you choose a sampling plan. At this month's QEN meeting we will discuss the design of simple attributes and variables sampling plans and we'll talk about some of the issues in setting up and operating them.


Inaugural Meeting: A Survey of Quality Engineering Methods, 12 April 2019, 7:30-9:00AM, at GGP
The first QEN meeting will be held on Friday, April 12th, from 7:30-9:00 AM at GGP's location in Newbury Business Park when Paul Mathews and Rick Ales will present a survey of quality engineering methods for the purpose of assessing the interests and needs of participants. Learn about the program and facilitators Paul Mathews and Rick Ales here. To attend email info@geaugagrowth.com or register here.

The topics to be discussed are but are not limited to:




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