Control Charts: Keep It Simple

Myth, misunderstanding, and bad teaching have lead to the belief control charts are hard. They aren't.

Published: Tuesday, December 18, 2018 - 12:03

The control chart is at the heart of the very definition of quality. It is central to building, maintaining, and predicting quality into the future. However, control charts today, more often than not, are misused and misunderstood. The aim of this article is to show not only how control charts are misunderstood, but also how control charts, when properly understood, are easy to use by any employee.

A bit of history

Mass production dates back 2,200 years to China, but it wasn’t until the Industrial Revolution at the start of the 19th century that it became commonplace. Mass production brought with it the need for identical and interchangeable parts, along with control of manufacturing processes. For example, in the 1860s during the American Civil War, interchangeability was key in using the Minié ball in both the U.S. Springfield and British Enfield rifles. Interchangeability was also important in watchmaking and in sewing machines at this time. The need for interchangeability of parts made good quality essential.

In 1870 the concept of the defect fully emerged with the development of the go/no-go gauge. It was a step of great importance but quite lacking with regard to process improvement. An item was either good, or it was trashed. There was nothing in between. Variation was just on/off.

Shewhart introduces the control chart

By the beginning of the 20th century, statistical methods had been available for more than a century, although these were poorly suited to processes. In 1924 Walter Shewhart introduced the control chart. Shewhart talked much of economics, and thus, his control chart was an economic chart, not a probability chart: “This state of control appears to be, in general, a kind of limit to which we may expect to go economically in finding and removing causes of variability,” he wrote in Economic Control of Quality of Manufactured Product¹ (Martino Fine Books, 2015 reprint). Shewhart defined his control limits as “economic limits.”

He also added a key point “...in developing a control criterion we should make the most efficient use of the order of occurrences as a clue to the presence of assignable causes.”² This is not provided by classical statistics. The control chart is unique in its use of the element of time. Even more important, “statistical control [is] not mere application of statistics.... Classical statistics start with the assumption that a statistical universe exists, whereas [SPC] starts with the assumption that a statistical universe does not exist.” (1944).³ That is, control charts do not need to be aware of the nature of underlying data distributions.

The Shewhart chart was a radical step forward. But many prominent figures at the time, such as Joseph Juran, failed to understand it. Juran stated that it was “beyond the grasp of the unsophisticated user.”⁴ Even by the 1980s, Juran still didn’t understand and was still referring to control charts as a “test of statistical significance.” Juran continued to produce charts of defects more appropriate to a century before.

Six Sigma confuses the use of control charts

The Six Sigma approach has been responsible for a massive misuse of control charts. The creator of Six Sigma, Mikel Harry, was a psychologist and can be forgiven for not understanding control charts. He even said, “I am not an engineer. I have to admit I did not know what Bill [Smith] was talking about.”⁵ Harry failed to understand that control charts are not probability charts. His statement, “If we narrow the control limits: alpha risk increases...” (i.e., type I and II errors), illustrates his misunderstanding.⁶

Subsequent Six Sigma authors turned control charts into an even greater mess. Popular Six Sigma authors showed a lack of understanding of the fundamentals of Shewhart’s control charts. Hundreds of thousands of practitioners and clients have read these authors’ material and have been misled. It was inevitable that quality suffered.

Six Sigma is based on a muddled probability of producing a defect. Most Six Sigma authors incorrectly extend such probabilities to control charts. For instance, when discussing control charts, Six Sigma author Douglas Montgomery writes on page 308 of his book, Introduction to Statistical Quality Control⁷ (Wiley, 2012 reprint) that “the probability of a point plotting in control is 0.9973.” In another part of his book, he writes, “The probability of producing a product within these [three standard deviation] specifications is 0.9973.” This lack of understanding leads to a host of nonsense, from attempts to normalize data before control charting, to Montgomery’s claim that for 100 parts “about 23.7 percent will be defective.” He also fails to understand the difference between the control chart’s process behavior limits and the customer’s specification limits. If he applied his same probability calculations to an automobile with a typical 30,000 parts, he would find that 9.7 percent of Six Sigma autos would have from 1 to tens of thousands of defects! Such probabilities are inappropriate for the analytic methods required for processes.⁸

Montgomery claims that process means are “allowed” to shift 1.5 standard deviations. He fails to appreciate that if that happens, data will fall outside control limits. That is, the process will be “out of control.” An out of control process is unpredictable and may produce any amount of defects, no matter where specification limits are set.

Deming understood

While the lack of understanding of control charts was growing like warts on the back of a Queensland cane toad, fortunately some folks did understand Shewhart’s innovation. The key figure was Juran’s rival, W. Edwards Deming. It is clear that no love was lost between these men, despite polite appearances. Deming elaborated on Shewhart’s methods, defining them as “analytic” compared to traditional “enumerative” statistics. He wrote in 1942: “The only useful function of a statistician is to make predictions, and thus to provide a basis for action.”⁹ This is the primary purpose of the control chart.

Genichi Taguchi also understood Shewhart. Through the 1950s into the ’60s, he worked with both Deming and Shewhart, focusing on economics and variation, in developing his “loss function,” which forms the basis of the definition of quality today: on target with minimum variance.

Deming’s protégé, Donald Wheeler, not only understood Shewhart but validated Shewhart’s assumptions, at great length, by testing 1,143 different distributions.¹⁰ He extended control chart theory through his many books and in articles in Quality Digest and other trade journals. Today, Wheeler is perhaps one of the world’s most notable living process statisticians.

Control charts are economic charts that raise a flag as to when it is appropriate to investigate a cause. Drawing, using, and understanding control charts is easy for any employee, whether working on the factory floor, or in the office. So many authors’ lack of understanding of the control chart has served to obfuscate the simplicity of the chart’s application. If control charts are used correctly, no special software is ever needed to draw them. They can easily be created in the way Shewhart did, and in the way that he intended.

Two articles, “Predictable”⁸ and “Enumerative and Analytic Studies,”¹¹ discuss how control charts (analytic methods) are the only tool appropriate for studying processes. Hypothesis testing (enumerative methods) is fine for studying a static collection of a psychologists’ lab rats but inappropriate for process improvement. Hypothesis tests do not consider the element of time. An example was presented where a control chart identified an unpredictable process from a predictable one, which no hypothesis test on Earth could have identified.

Misconceptions about control charts

Normality
Perhaps the biggest misconception and the biggest culprit in making a complex mess out of something simple is the misconstrued need for normal distributions. Normal distributions are irrelevant. There is no need for any employee to understand normal distributions, nor any other type of data distribution. We can never know the distribution for a changing process. Normal distributions have no place in quality training. Normality plays no part whatsoever in control charts. Control charts work for any data distribution. Furthermore, you should never attempt to normalize data by pressing a button on unnecessary statistical software.

Certainly, there is a complicated statistical background to proving why control charts are so simple, but employees don’t need to know about it. Those who do wish to understand normal distributions and the elegant statistics behind the simplicity, should read Wheeler’s book on the topic.¹⁰

Control chart as ‘probability chart’
Even worse than the fixation on normal distributions is the belief that the control chart is a probability chart. There are thousands of references to claims that 99.73 percent of data lie within control limits. This is nonsense. Control charts do not indicate the probability of any event. Even more ridiculous are claims, such as Montgomery’s, about a “3-sigma” process vs. “4-, 5-, 6-sigma” processes. There is no such thing as a 3-, 4-, 5-, or 6-sigma process.

Central Limit Theorem
Some experts sagely suggest the need for the Central Limit Theorem. It is true that for bigger subgroups, the distribution of subgroup averages appears more normal. However, this again is totally irrelevant to control charts. If the Central Limit Theorem was required, range charts would not work.¹² The distribution of ranges is never normal. Control charts are not based on the Central Limit Theorem, and they do not need normality.

Control charts are a bit like run charts. They display variation in a process over time. The difference is that the control chart has a filter for the nag, nag, nag of common causes. It’s a bit like knowing when to ignore the nag: Turn it off, put your feet up with a beer and a newspaper, and when you actually need to heed the nag, go out into the garage and pull out your toolbox. It might go something like this: “You didn’t put the seat down, there’s drips, the whole thing needs a clean, the cistern is leaking and making a noise that is annoying at night, and the level keeps rising, and it looks like it’s going to flood.” Now, while your spouse may disagree, except for that last bit, you can put your feet up. That last bit needs action. Find the assignable cause!

Of course it cuts both ways. A nag such as this also needs filtering: “Make sure you avoid the toll road, book the car in for a service, look twice in all the mirrors before reversing, always signal at roundabouts, put it through the car wash—oh, and by the way, the fuel gauge shows empty.”

Rules?
The key to nag filtering is simply knowing when to take action. Shewhart said that we can estimate the nag by looking at the variation at each point. Measure the range. What could be more simple? Easy with a pencil and paper. Wheeler showed it was not only the simplest but also the best. Sadly, it didn’t help companies sell software, so companies found many ways to make it complex. Instead of a simple range, it was claimed that the standard deviation of groups of points was needed. People believed it needed to be complicated, and you needed to do three-week courses to try to understand the complex software doing complicated things under the covers, to make something simple, complex. You don’t.

Many have heard of the Western Electric rules for control charts. Just when you might have been thinking control charts were as easy as run charts, along come the eight rules to help you identify something more serious than a nag. Who could keep that lot in their head and use it at a moment’s notice? Surely computer software really is needed? Once again, Wheeler came to the rescue. He has shown that all you need is the control limits.¹³ The rest just increases false alarms. Keep it simple.

Charts for count data
Finally, we have charts for count data. The commonly used p, np, c, and u charts all assume a particular distribution for the data. There are four types of charts, two binomial and two Poisson distributions. Can anyone actually remember which is which? Surely knowledge of such distributions immediately puts count charts into the hands of the cognoscenti? However, if the data do not follow our assumption, we get incorrect answers. Wheeler suggests that a Ph.D. in statistics is needed to be sure we have made a correct assumption.¹⁴ Now surely that is about as far from keeping it simple as it gets. However, Wheeler shows that we have an easy and foolproof way out... the same XmR chart that we used for variable data! XmR for everything. What employee could not understand that?

Control charts are easy

The big challenge is getting the message to every employee about what can be done with control charts and how easy they really are. Decades of nonsense need to be unlearned to get back to the basics of quality. There is a huge need for re-education.

I am passionate that fun is the way back to the fundamentals, to make control charts less “scary.” Learning is facilitated when employees are enjoying themselves. Our Q-Skills3D product, for instance, has dozens of interactive 3D games and exercises that teach quality, including a count data training module shown below. It teaches how to plot the four types of count data. It’s a fun game based on an old-style shooting gallery. Control limits are recalculated when there is a system change—the target speed in this case. Tap a switch to see each type of chart. You can preview this new module on your PC (using any browser except Internet Explorer). Click the “continue” button when loading finishes (10 seconds or so). For mobiles, you can view the Q-Skills3D demonstration in the app stores.

Every employee has a role to play in quality. Control charts are easy for every employee to use and understand, if they are taught correctly.

Control charts exercise for count data: Wait about 10 seconds for game to load. Click CONTINUE.
Follow instructions. Switches on lower right corner of game control which chart is shown.

References
1. Shewhart, Walter A. Economic Control of Quality of Manufactured Product. Martino Fine Books, 2015 reprint.
2. Shewhart, Walter A. Statistical Method from the Viewpoint of Quality Control. Dover Publications, 1986.
3. Shewhart, Walter A. “Statistical Control in Applied Science.” Transactions of the ASME, April 1943, pp. 222–225.
4. Juran on Shewhart. Notes. August 1967.
5. Mikel Harry website http://www.mikeljharry.com/media/1984_01.pdf
6. Harry, Mikel J., et al. Practitioner’s Guide to Statistics and Lean Sigma. Wiley, 2010.
7. Montgomery, Douglas C. Introduction to Statistical Quality Control. Wiley, 2008.
8. Burns, Anthony D. “Predictable.” Quality Digest. June 13, 2018.
9. Journal of the American Statistical Association. Quoted in W. A. Wallis’ The Statistical Research Group, 1942–1945. Vol. 75, No. 370, p. 321.
10. Wheeler, Donald J. Normality and the Process Behavior Chart. SPC Press, 2000.
11. Wheeler, Donald J. “Enumerative and Analytic Studies.” Quality Digest, July 16, 2018.
12. Wheeler, Donald J. Advanced Topics in Statistical Process Control. SPC Press, 2004.
13. Wheeler, Donald J. and Stauffer, Rip. “When Should We Use Extra Detection Rules?” Quality Digest, Oct. 9, 2017.
14. Wheeler, Donald J. “What About p-Charts?” Quality Digest, Sept. 30, 2011.

About The Authors

Anthony D. Burns

Anthony Burns, Ph.D., has a bachelor of engineering and a doctorate in chemical engineering from the University of New South Wales in Sydney, Australia. He has 36 years of experience and his company, MicroMultimedia Pty. Ltd., is responsible for the development of the e-learning quality product Q-Skills and its support tools.

Michael McLean

Michael W. McLean is the Managig Director of McLean Management Consultants (Established 1988), Senior Fellow Australian Graduate School of Leadership,,Fellow Australian Institute of Company Director; Academic Fellow-Certified Management Consultant ICMCI; Fellow Australian Organisation for Quality. Australian Industry Group (AiGroup) Delegate to Standards Australia QR-008 ISO QM & QA Mirror Committee Member to ISO TC176 and AUstralian Member on the ISO TC176 Chairs' Strategy Advisory Group; IMC Australia delegate to SF-001 OH&S ISO Mirror Committee. Past Convenor for ISO "Integrated use of management system standards (IUMSS)" 2018. ISO Co-convener for ISO 9001 Brand Integrity; Member for ISO 10009 Qality Tools and ISO 10014; 10019.

AOQ NSW Silver Annivessary Award (1993), AOQ Dr JM Juran Medallist (2008); AOQ Shilkin Prize (2012); ISO Secretary General Excellence Award (2018) for Convenorship of ISO IUMSS 2018 Handbook.

His consultancy is a Australian Defence Recognised Supplier. Department of Foreign Affairs and Trade (AusAID) ASEAN Automotive and Australian Maritime Safety Authority Technical Specialist for DFAT ASEAN Development Programs. 

Chairman of Certex International Certification Advisory Board and Goal Group Professional Services Defence Supply Chain and Australian Government Security Vetting Agency Clearance NV1 (Secret) .

Author of various books and academic peer reviewed articles on his research into automotive, mining and education sectors. Co-developer with Dr A Burns for 'Q-Skills' Multi Media Software sold worlwide and co-author of various Exceutive Briefings and Thought Leadership.

Qualifiied Fitter and Turner, production engineering and senior manager with Standard Telephones & Cables / International Telephone & Telegraph (Australia, ITT HQ USA, Bell Telephone Belgium); Tenneco Monroe Automotive Springs, Wrangler and WDScott Management Consultants prior to starting his firm MMC in 1988. Assignments in Asia Pacific, ASEAN, Europe, Japan, North America, Middle East, NZ, Pacific Islands, PNG, Scotland, UK and USA.