On 100 years of the Shewhart control chart

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To celebrate the 100th anniversary of the Shewhart control chart, we hosted the award-winning Professor Emeritus of Statistics at Virginia Tech, Bill Woodall, and JMP’s own Annie Dudley, Senior Research Statistical Developer, to reflect on the evolution of monitoring methods to enable better processes. The topic was so well-received, we had more questions than time to answer them. Bill and Annie shared a lot of wisdom, so we encourage you to watch the on-demand version. Keep reading for more of their expertise and insights in their answers to the remaining questions:

Do you know of any cases where the process being monitored had seasonality that needed to be addressed to avoid unnecessary alerts?

Regular seasonality in industrial applications could provide clues for process improvement. For example, if quality is consistently worse (or better) on Mondays, it would be important to find out why this is the case. Regular seasonality is unavoidable when monitoring the rate of contagious diseases in public health applications, however, so frequently a time series model is fit and one can monitor the one-step-ahead forecast errors over time.

How would you set up a control chart for continuous data? What are the things to consider?

I assume you are asking about control charts for continuous measurements such as length or weight. In this case, one first needs a baseline sample to understand the process. This is considered Phase I, as discussed in the following paper:

Jones-Farmer, L. A., Woodall W. H., Steiner, S. H., and Champ, C. W. (2014). “An Overview of Phase I Analysis for Process Improvement and Monitoring”. Journal of Quality Technology 46(3), 265-280.

What to do in Phase II (the ongoing monitoring part) would depend on what was discovered in Phase I. Often one uses XBar and R charts.

You may mean a variable such as temperature, which could be measured continuously over time. In this case, one often sees the use of engineering-based limits, not control charts.

When control charts are built, which standard deviation should be used? Within or overall? What are the pros and cons of using one or the other? Which is an appropriate measure of process performance: Cpk or Ppk?

One should use within sample variation in setting up the control chart. The use of the overall standard deviation could hide unusual variation indicating the presence of assignable causes. Both capability indices are useful. The index Cpk gives the potential capability of the process, while Ppk gives the achieved capability.

Do you really think it is a good idea to put specification limits on an XBar chart when the subgroup size is greater than 1? The specifications are for individual parts, not averages of groups of parts – averages vary less than individuals.

Specification limits should be plotted on a control chart only when one has individual observations.

What is the biggest change between Industry 3.0 and Industry 4.0 of the control chart since we have more computer power and are having a lot more data now?

There are too many changes to list. I suggest taking a look at the following paper:

Colosimo, B. M., Jones-Farmer, L. A., Megahed, F. M., Paynabar, K., Ranjan, C., and Woodall, W. H. (2024). “Statistical Process Monitoring from Industry 2.0 to Industry 4.0: Insights into Research and Practice.” To appear in Technometrics.

What is your take on non-normality and the impact on the false alarm rate of the individuals chart? Dr. Wheeler, and Shewhart himself, is less concerned with the underlying data distribution, whereas others recommend transforming the data.

Using a nonlinear transformation of the data in an attempt to achieve approximate normality is often ill-advised, especially in Phase I. Many of the issues are discussed in the following paper:

Khakifirooz, M., Tercero-Gómez, V. G. and Woodall, W. H. (2021). “The Role of the Normal Distribution in Statistical Process Monitoring”, Quality Engineering 33(3), 497–510.

With respect to the false alarm rate, the degree of non-normality is important, as well as the sample size.

Does the transition to Industry 4.0 also mean fewer univariate and more multivariate control charts, since more data is being produced from sensors?

Multivariate methods will be required in Industry 4.0. New multivariate methods will be needed.

What are control chart guidelines for qualitative (Pass/Fail) data?

One can use p-charts or charts based on the geometric distribution if failures are rare.

You suggested that a Shewhart control chart should always be over time. In Shewhart's 1931 book, he talked about rational subgrouping and gave examples (p. 310, 313, 331) of control charts that are not time focused. What is your thinking here?

Time order is a fundamental characteristic of control charting. The use of analysis of variance would seem more appropriate in these examples.

Does the transition to Industry 4.0 also mean more multivariate SPC and less univariate, e.g., PCA modeling of sensor data? Why does JMP not have alarm scripts for MDMCC?

While JMP does have Model Driven Multivariate Control Charts (MDMCC was added in JMP 15), JMP does not yet have alarm scripts available in that platform because we hadn’t thought of that. Great suggestion!

Can you recommend a paper/book/source providing a "glossary" with "definition(s)" of terms especially used for control charts?

The best book is the 8^th Edition of “Introduction to Statistical Quality Control” by Douglas C. Montgomery published by John Wiley & Sons. We don’t know the best glossary, although there are some available online.

In addition to the on-demand version of this episode of Statistically Speaking, the white paper Bill authored, On 100 Years of the Shewhart Control Chart, is highly recommended. Bill has kindly offered to share the papers he mentioned. Request them by emailing bwoodall@vt.edu. Thank you, Bill and Annie, for sharing so much useful expertise! We invite your comments to help us celebrate the 100^th anniversary of the Shewhart control chart. Here's to continuous improvement!