## 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 - 13:03

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 Product*^{1} (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 Control*^{7}^{} (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.

**References**

1. *Economic Control of Quality of Manufactured Product.*

2. *Statistical Method from the Viewpoint of Quality Control*.

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. * Practitioner’s Guide to Statistics and Lean Sigma. Wiley, 2010. *

7. Montgomery, Douglas C. *Introduction to Statistical Quality Control*.

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.

## Comments

## Control Charts Misnamed

Unfortunately, Shewhart set quality back a century by naming these charts "Control" charts. 100 years after Shewhart created control charts, they are rarely found outside of manufacturing factory floors. Yet 80% of American businesses are service industries where control chart usage is minimal to nonexistent.

Most people, especially Americans, do not respond well to word "control." Wheeler has been trying to rename them "process behavior charts" which is on the right track but perhaps too long and bland.

If we start calling them what they are,

Performance Charts, perhaps more people will take notice. Everyone seems to want to improve their performance while few want to improve their control or their process behavior.I disagree that you don't need software to do control charts, otherwise they would be in every business everywhere.

## Process Behaviour Charts

I prefer "process behaviour chart" but "control chart" gets 1,400 times more Google hits. It is what people know ... or think they know.

"Performance chart" can mean just about anything.

It is not lack of software that limits the use of process behaviour charts. There is ample free software available to draw them. The more expensive the charting software, the more likely people are to make a mess of them, such as by normalization.

If people kept process behavior charts simple as Dr Shewhart did, and if all employees were trained as Professor Deming advocated, we were see much more of this powerful tool that is fundamental to quality.

## misnamed control charts

I do not agree Dr. Shewhart misnamed his charts. Nobody was more careful with words I have read. There is however, no short name that will communicate all they will do. No perfect name. Why the name control?

Shewhart asks: How far can Man go in controlling his physical environment? How does this depend upon the human factor of intelligence and how upon the element of chance?

I do appreciate Dr. Wheeler attempting to use simpler language as well as Dr. Deming. In hindsight, maybe just one name is better.

Great article!

## Control Charts Misnamed

Unfortunately, Shewhart set quality back a century by naming these charts "Control" charts. 100 years after Shewhart created control charts, they are rarely found outside of manufacturing factory floors. Yet 80% of American businesses are service industries where control chart usage is minimal to nonexistent.

Most people, especially Americans, do not respond well to word "control." Wheeler has been trying to rename them "process behavior charts" which is on the right track but perhaps too long and bland.

If we start calling them what they are,

Performance Charts, perhaps more people will take notice. Everyone seems to want to improve their performance while few want to improve their control or their process behavior.I disagree that you don't need software to do control charts, otherwise they would be in every business everywhere.

## Control charts for count of jobs per day

Most count charts I see are proportion. What about for count if jobs completed per day

## Count data

Hi Jason,

Did you have a look at the interactive training exercise example, from Q-Skills3D? It should address your question. It shows the effectiveness of XmR with the 4 types of count data. View it on a PC (non IE).

You can also view it on a mobile by installing the full

Q-Skills3D, training in quality and Lean, from the Google Android and Apple app stores. Q-Skills3D is the only quality training on both mobiles and PC. Q-Skills3D builds on the success of Q-Skills, with over 500,000 users.## Thanks for the reply, i will

Thanks for the reply, i will check it out