Control Charts - Keep it Simple

Dr Tony Burns

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 are more often than not, misused and misunderstood.?The aim of this paper is not only to show how control charts became so corrupted but how, when properly understood, are easy to use by any employee.

Mass production dates back 2200 years to China, but it wasn’t till the Industrial Revolution at the start of the 19th Century that it because common place.?Mass production brought with it, the need for identical and interchangeable parts, along with control of manufacturing processes.?For example, in 1860’s in the American Civil War, interchangeability was key in using the Minié ball in both the US Springfield and British Enfield rifles.?Interchangeability was important in watch making 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. Quality was measured by counting defects.

While statistical methods had been available for over a century, these were poorly suited to processes[1, 2].?In 1924 Dr Shewhart introduced the control chart.?Dr Shewhart talked much of economics.?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”.??Dr Shewhart defined his control limits as “economic limits”.

Dr Shewhart 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” (1931). This is not provided by classical statistics.?The control chart is unique in its use of the element of time.?Even more importantly “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). [24] 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.?Many prominent figures at the time, such as Dr Juran, failed to understand it.?Dr Juran stated that it was “beyond the grasp of the unsophisticated user”.[24]?Even by the 1980’s Dr Juran still didn’t understand and was still referring to control charts as a 'test of statistical significance.’??Dr Juran continued to produce charts of defects more appropriate to a century before.?It is hardly surprising that when Six Sigma? arrived, he said he saw it as nothing different.?At 93 years of age he was swallowed by Six Sigma?.

The Six Sigma? approach has been responsible for a massive misuse of control charts.?The creator of Six Sigma?, Dr M Harry, was a psychologist and can be forgiven for not understanding control charts.?He said “I am not an engineer.?I have to admit I did not know what Bill [Smith] was talking about”. [8] He even admitted that even the fundamentals of Six Sigma? were nonsense "opponents of the shift factor are absolutely correct" [26]. Dr Harry, failed to understand that control charts are not probability charts: “If we narrow the control limits: alpha risk increases … (ie types I and II errors)” [25]

Subsequent Six Sigma??authors turned control charts into an even greater mess.?Every popular Six Sigma? author examined: Mr Pyzdek [14], Mr Breyfogle [17], Mr Kubiak [18], Mr Monro [19], Mr Shankar [20], Mr Martin [21], Mr P Gupta [22] and Professor D Montgomery[13] shows a lack of understanding of the fundamentals of Dr 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. “Of the 58 large companies announced Six Sigma? programs, 91 percent have trailed the S&P 500 since.”?[15]?Six Sigma? companies such as GE, Motorola, GM, Nortel, Honeywell, Home Depot, Target, Whirlpool lead the decline. [16]

If we consider for example, the popular author Professor D Montgomery [13], not only does he suggest that control charts are probability charts but he confuses specification and control limits. He throws in the nonsense term “three sigma performance”: “Now it turns out that in this situation the probability of producing a product within these specifications is 0.9973. … This is referred to as three-sigma quality performance."?There is no such thing as “three sigma performance”.?The performance of a process is determined by its stability, that is, whether or not assignable causes are present. Defects relate to the specification.

Montgomery’s failure to understand the nature of control charts leads him to the ridiculous claim that that for 100 parts: "… about 23.7% of the products produced under three-sigma quality will be defective."?He fails to understand that the control chart is the voice of the process.?An in control process is predictable but an out of control process makes no prediction whatsoever about the number of defects that may be produced.?The 23.7% figure is laughable.

Professor Montgomery suggests that at “six-sigma quality level … the process mean can shift by as much as 1.5 standard deviations off target … to produce about 3.4 ppm defective”.?We might apply his probability approach to an automobile, with a typical 30,000 parts.?Suppose each of these parts were built to his Six Sigma? claim of “excellence”, at 3.4 dpmo.?This would give a (1 - 0.9999966^30000 )?chance of having a defect.?In other words, every automobile manufactured would have a 9.7% chance of being a lemon.?That is, 9.7% of all cars would contain from 1 to many thousands of defects!?Clearly, the Six Sigma? approach to defects and probabilities gives?very silly results.

Montgomery suggests that to improve things, we should let the mean float around a bit.?Now who would have thunk of that?: "If the mean is drifting around, and ends up as much as 1.5 standard deviations off target, a prediction of 3.4 ppm defective may not be very reliable, because the mean might shift by more than the “allowed” 1.5 standard deviations."?It is not clear whether he realizes his shifting 1.5 is ludicrously based on the height of Dr Harry's stack of discs! [9].??He clearly fails to understand that if the mean is shifting 1.5 sigma, special causes are present. The process is out of control, and may produce any amount of defects no matter where specification limits are set.

Any company that does happen to have an out of control Six Sigma? process thanks to a 1.5 sigma drift, has an even money chance of detecting it immediately on a control chart [Power Curves, 10].?Any delay in detection is due to it being disguised by common cause variation.?It will quickly reveal itself.?Rather than relaxing and considering the chaos from a 1.5 sigma drift being a normal part of a Six Sigma? pseudo-perfection, the out-of control event should be acted upon immediately. Those claiming: “We were just reviewing our own experience with shift and it pretty conclusively exists in our processes” ... are doomed [27]

It is absolutely staggering to think that quality practitioners have accepted such pernicious professorial poppy cock.?No wonder that an ex-Baldrige examiner said to me that people are turning away from quality because it is perceived as “too hard”.?It is not too hard. The trash simply needs to be thrown out, so that people can get back to an understanding of the fundamentals of quality.

While the lack of understanding of control charts was growing like warts on the back of a Queensland cane toad, fortunately, some folk did understand Dr Shewhart’s innovation.?The key figure was Dr Juran’s rival, Professor Deming.?It is clear that no love was lost between these men, despite polite appearances.?Professor Deming elaborated on Dr Shewhart’s methods, defining them as “analytic” compared to traditional “enumerative” statistics [1],[2].?He wrote in 1942: “the only useful function of a statistician is to make predictions, and thus to provide a basis for action.”?This is the primary purpose of the control chart.

Dr Taguchi also understood Dr Shewhart.?Through the 1950’s into the sixties, he worked with both Professor Deming and Dr Shewhart, focussing on economics and variation, in developing his “Loss Function”, that forms the basis of the definition of quality today : ‘on target with minimum variance’.

Professor Deming’s protégé, Dr Wheeler not only understood Dr Shewhart, but at great length, validated Dr Shewhart’s assumptions, by testing 1143 different distributions. [3] Dr Wheeler proved conclusively that normality is not required for effective control charts. You do not need expensive statistical software to test for normality. He extended control chart theory through his many wonderful books and papers in Quality Digest.?Dr Wheeler stands alone as the world’s greatest living process statistician.

Drawing, using and understanding Control charts is easy for any employee, whether working on the factory floor, or in the office.?Lack of understanding by so many authors has served to obfuscate the simplicity of Control Chart application.?If Control Charts are used correctly, no special software is ever needed to draw them.?They can easily be created in the way Dr Shewhart did, and in the way that he intended.

Control charts are economic charts that raise a flag as to when it is appropriate to investigate a cause.?

“Predictable” [1], and “Enumerative and Analytic Studies” [2], discussed 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 psychologist's lab rats but inappropriate for process improvement. Hypothesis tests do not consider the element of time.?An example was presented [1] where a control chart identified an unpredictable process from a predictable one, that no hypothesis test on Earth could separate.

Firstly, 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.?

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 Dr Wheeler’s book on the topic [3].

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% of data lie within control limits. This is nonsense. Control charts do not indicate the probability of any event.?Even more ridiculous are claims about a “3 sigma” process vs “4, 5, 6 sigma” processes.?There is no such thing as a “3 sigma process”.?“6 sigma processes” are a farce [4][5][6][7][8][9].

Some pseudo-experts sagely suggest the need for the Central Limit Theorem.?It is true that for bigger sub groups, the distribution of sub group 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 [10]. The distribution of ranges is never normal [1].??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 off and put your feet up with a beer and a newspaper and when you actually need to go out into the garage and pull out your toolbox.?For example, it might go something like this : “you didn’t put the seat up, there’s drips, the whole thing needs a clean, the cistern is leaking and making a noise that is annoying at night, and level keeps rising and it looks like it’s going to flood”.?Now 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 gauge is on empty.”

The key to nag filtering is simply knowing when to take action.?Dr 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.?Dr Wheeler showed it was not only the simplest but also the best [Ch4, 10].?Sadly, it didn’t help folk sell software, so folk 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 3 week courses to try to understand the complex software doing complicated things under the covers, to make something simple, complex.?You don’t.?

Most folk 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 8 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, Dr Wheeler comes to the rescue.?He has shown that all you need is the control limits [11]. In most situations, more rules just increases false alarms.?Keep it simple. The most important rule of all is to use your brain. THINK. If something looks peculiar, investigate.

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 4 types of charts, 2 Binomial and 2 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 does not follow our assumption, we get incorrect answers.?Dr Wheeler suggests that a PhD in statistics is needed to be sure we have made a correct assumption [12].?Now surely that is about as far from keeping it simple as it gets.?However Dr 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?

As you can see, when taught correctly, control charts are simple enough for a company's real experts, the operators, to understand, draw and use. The big challenge is getting the message to management that quality is easy if done correctly. There is no need to give up and move on to the next quality fad. However, decades of nonsense need to be un-learned in order to get back to the basics of quality.?There is a huge need for re-education.?

We feel fun is the way back to the fundamentals.?Learning is facilitated when employees are motivated and engaged.?We aim to give employees an experience to remember, in marked contrast to the boring talking head, text and clip art e-learning of the past.

We use interactive games, simulations and exercises to engage employees to help them learn. Our approach to teaching the fundamentals of quality has been validated by our 500,000 users across hundreds of clients such as Microsoft, GE, Toyota, Chrysler, Zurich, Delta Airlines. A client's 500 user survey showed that 96% of employees prefer our approach.

Our interactive approach makes learning fun and engaging.?Despite almost a decade’s work, we have broken away from the common trend of ridiculously expensive quality training.?We have kept the price low enough to make it affordable for every employee.?Search for Q-Skills3D in the Apple and Google app stores. Also on PC.

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.

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References

1)?????“Predictable” – Dr A Burns – Quality Digest https://www.qualitydigest.com/inside/six-sigma-article/predictable-061318.html

2)?????“Enumerative and Analytic Studies” – Dr D Wheeler – Quality Digest https://www.qualitydigest.com/inside/statistics-column/enumerative-and-analytic-studies-071618.html

3)?????“Normality and the Process Behavior Chart” – Dr D Wheeler

4)??????“Six Sigma – Lessons From Deming – Part 1” – Dr A Burns – Quality Digest https://www.qualitydigest.com/inside/six-sigma-article/six-sigma-lessons-deming-part-1

5)?????“Six Sigma – Lessons From Deming – Part 2” – Dr A Burns – Quality Digest https://www.qualitydigest.com/inside/six-sigma-article/six-sigma-lessons-deming-part-2

6)?????“Six Sigma Psychology – Part 1” – Dr A Burns – Quality Digest https://www.qualitydigest.com/inside/quality-insider-column/six-sigma-psychology.html

7)?????“Six Sigma Psychology – Part 2” – Dr A Burns - https://www.dhirubhai.net/pulse/six-sigma-psychology-part-2-tony-burns/

8)?????“Blame Mr Bill Smith?” – Dr A Burns -?https://www.dhirubhai.net/pulse/blame-mr-bill-smith-tony-burns/

9)?????“Sick Sigma” – Dr A Burns – Quality Digest - https://www.qualitydigest.com/inside/six-sigma-article/sick-sigma.html

10)??“Advanced Topics in Statistical Process Control” – Dr D Wheeler

11)??“When Should We Use Extra Detection Rules?” - Dr Wheeler – Quality Digest - https://www.qualitydigest.com/inside/statistics-column/when-should-we-use-extra-detection-rules-100917.html

12)??“What About p-Charts?” - Dr D Wheeler – Quality Digest - https://www.qualitydigest.com/inside/quality-insider-article/what-about-p-charts.html

13)??Introduction to Statistical Quality Control – Professor Douglas Montgomery (PhD Industrial Engineering) 2009

14)??The Six Sigma Handbook – Thomas Pyzdek 2010

15)??CNN Money https://money.cnn.com/sales/executive_resource_center/articles2/rule4.fortune/index.htm

16)??Six Sigma Failures?https://sixsigmafails.com/six-sigma-failures-1

17)???“Managing Six Sigma”??- Mr Breyfogle?https://www.kvimis.co.in/sites/kvimis.co.in/kumarfiles/ebook_attachments/Forrest%20W%20Breyfogle%20Managing%20six%20sigma.pdf

18)??‘The ASQ Pocket Guide for the Certified Six Sigma Black Belt’ - Mr T.M.Kubiak

19)??‘The Certified Six Sigma Green Belt Handbook’?- Mr R Munro

20)???“Process Improvement Using Six Sigma” - Mr R Shankar??

21)???“Lean Six Sigma For the Office” - Mr James W Martin

22)???“Three Sigma Barrier to Process Yield” - Mr Praveen Gupta

23)??“Statistical Control in Applied Science,” by Walter A. Shewhart

24)??Juran on Shewhart.?Aug 1967.?Notes.

25)??“Practitioner’s Guide to Statistics and Lean Sigma” – Dr Mikel Harry.

26) "The Shifty Business of Process Shifts" - Dr Mikel Harry

27) Six Sigma Gems - Dr Burns https://www.dhirubhai.net/pulse/six-sigma-gems-tony-burns/