Who Is Sir Francis Galton?

The control chart was developed by Walter Shewhart and Egon Pearson, in the 1920s. Simply stated, a control chart is a distribution spread out over time.

The Japanese management understood the importance of control charts. If any reader should decide to investigate control charts, I must recommend to you the wonderful video “The Japanese Control Chart”, produced by Dr. Wheeler. It lasts for only twenty minutes, but many of my students have said it is the best illustration of the power of the control chart they have seen. It is based on data from Tokai Rika, a company which made parts for Ford Motor Co. When Dr Deming visited this company, he found more than 200 control charts in use, with a management review of each chart every two months. Dr Deming also observed that control charts are being used in Japan more and more as time goes by.

Now I want to show you some real control charts, taken from my own experience. There are many examples of control charts for manufacturing available. The referenced Wheeler text has scores of them, so I will only present one. But we will look at some other types of control charts; from management, from “public” information, and even the stock market.

It has been estimated that the factory floor represents only 3% of the potential uses for control charts, yet in the US, it is a very rare occurrence to find a control chart anywhere else; for example, a manager using a control chart to analyse some characteristic such as sales, profit, delinquencies, or other key indicator. It is ironic that when statistical methods and tools for making significantly better decisions are available, the very persons whose decisions have the most impact, for better or worse, the managers, are not using these methods.

Let me preface our look at the management control chart, with the following background: our company began what was then a popular “Quality Improvement Program”. This started with the organisation of a steering committee (usually the same as the existing staff and executives), with the initial task of determining the “Cost of Quality”. This included such items as scrap, rework, inspection, and many lesser items.

Each month the total amount of these collected costs was placed on a simple chart, Figure 1; the chart was reviewed monthly by the steering committee.

Let’s take a look at this chart after several months. The idea is to reduce the Cost of Quality. What would you say is happening?

Now, as the Quality Director, I attended all the meetings related to this chart. The explanations given below represent the consensus of the staff.

The rationale for the end of:

The reader is invited to imagine the dialogue for the rest of the data, which oscillates above and below the average of all the data, but ends in August on a value higher than any except January’s.

What is really going on here? It’s time to ask the Magic Question. “Are things getting better or worse?” Well, we all want to think things are getting better (our jobs may depend on it), so it’s relatively easy to come up with a rationale which seems to explain the results from month to month. So it would seem that the Magic Question is easy to answer. But wait! The Magic Question is a two parter. The second part of the Magic Question is: “How do you know?” The answer can only be obtained by using the power of the control chart.

So let’s convert the run chart to a control chart. This is very easy to do. A pocket calculator will suffice, and Dr. Wheeler’s referenced text will explain exactly how to do this.

What we want to add to the chart are the average (or mean) value of all the data, an upper control limit, and a lower control limit. It must be emphasised strongly that these limits are not arbitrary, that is, not selected independently of the data, but are derived from the data itself. In effect, the process (or system) producing this cost as an output, is telling us that these are the natural limits of the distribution of its outputs.

In other words, we would not expect to see values of the output (quality cost) which exceed 23% (the upper control limit), or which are less than 11%, (the lower control limit), Figure 2. And since the data does exhibit symmetrical variation about the average, we can infer that the process is stable, which means (statistically) that its average behaviour is predictable, and is not changing with time!

Amazing! What we, the staff, have been trying to explain, month by month, is nothing more than the natural variation in the output of a stable system, and the month by month explanations themselves are meaningless, regardless of how appropriate they may have seemed at the time they were made.

So the conclusion in this case is perhaps painful. The activities put in place to reduce the quality cost have been ineffectual. But a good manager would surely want to know this, so as to take action to significantly change the system. The control chart will clearly show whether a statistically significant change has occurred.

Now let’s look at a factory floor situation. For a particular product, one of the incoming materials is being evaluated before use by a sample evaluation. Twenty sample devices are assembled from each lot of incoming material. Engineering has made the arbitrary yet reasonable decision to accept the lot of material if no more than 10% of the sample devices fail to meet specifications. A sample lot of 20 devices has been established by engineering. Therefore, if more than 2 out of 20 devices fail the test criteria, the material lot from which the sample devices are obtained will not be accepted for use. Each material lot may contain thousands of potential devices.

When I was made aware of this situation, I asked whether a control chart was being maintained, using the data from the sample evaluation tests. There was no control chart, but the sample test data had been retained, so I was able to construct the appropriate chart. This chart is shown in Figure 3.

This chart shows us what the process is capable of doing. We see that there are no values above the upper control limit, which means that, as long as this continues to be the case, the process can be considered stable. This in turn, means that the process output or distribution is constant with time. In other words, the process quality is the same whether a plotted value falls above or below the mean value. The variations observed are due to the small sample sizes.

So, let’s repeat. This chart shows that the process output varies in a repeatable manner (is statistically stable) over time; therefore each lot is as good as the next. But the sample inspection method being used rejected half the lots, because half of the sample values are above the mean value. That is, greater than the two defective unit specification for the sample lots established by engineering.

At this time, because of this material shortage, production was behind schedule, and orders were delinquent.

Fortunately, most of the rejected material had been put on the shelf, and I suggested that some of it be evaluated in a production lot large enough to avoid a sampling error.

Engineering, having created the faulty inspection method, were reluctant, but because of the urgent need, could hardly refuse.

The results were as predicted, the material shortage was eliminated, and hundreds of thousands of dollars were saved in the first year.

Reference: Wheeler, Donald J and Chambers, David S, Understanding Statistical Process Control, ISBN 0-945320-01-9