The Deming Forum

Understanding variation – the springboard for process improvement

By Dr. Henry R. Neave

Edited and abridged by Mitch Beedie

There are four components, the main article: "Understanding Variation" and three linked expansions on the article.

"Six processes"

Two sets of six control charts (Figures A1 to F1 and A2 to F2) help to illustrate the difference between common and special causes. The six quantities are plotted over 24 points, which is ample to start drawing solid conclusions (less can be used, particularly when you are starting with weekly or monthly charts, and can’t afford to wait). The quantities vary around their average value (the central line), and are comfortably contained within the control limits in Figures A1 to F1, but not in Figures A2 to F2.

Figures A1 to F1 are pretty boring. Why “boring”? Because nothing happens in any of them, other than what may be interpreted as “chance” fluctuations. They are all “much of a muchness”. Who would dream that in fact they are from six very different sources? The processes are all in statistical control, stable, “within limits”: their general behaviour is predictable. “Boring” is nice! The prediction is that, unless the process changes, future data will also lie between these limits. We can therefore extend these limits into the future to help us recognize changes if and when they do occur.

Control charts of stable processes all look pretty much the same, wherever they’re from. These are (A1) the sum of four dice thrown 24 times; (B1) the number of heads from 25 coins tossed 24 times; (C1) the number of “defective products” recorded by inspectors in a “Red Beads” experiment used by Deming to demonstrate how futile it is to blame workers for common-cause variations; (D1) the author's pulse rate taken at breakfast time over 24 days; (E1) the dimensions of a cigarette-lighter socket from 24 samples in a Japanese case study (see References); and (F1) the monthly US trade deficits in billions of dollars over two successive years. We said these processes were very different from each other!

Things get more interesting (but usually therefore more problematic) when the processes go out of control, as in the second six graphs, which show what happened to the six processes later on.

Why are graphs A2 to F2 “interesting”? Because, in each case, something has happened – indicated in particular by one or more points lying outside the control limits. These points show real changes, caused by something different from the routine factors which were all that were previously influencing the process. We should now look for something unusual – something either improving results or (more usually) degrading them.

Actually, with all but one of these processes, we know what changed: (A2) only two dice were used for throws 7 to 12, and then six dice for the rest; (B2) the number of coins was increased by two each time from point 15 onwards; (C2) another “Red Beads” experiment but with the inspectors’ final six measurements mistakenly being added rather than averaged; (D2) the author's pulse rate over a later 24 days, with the final four days showing the effects of a newly-prescribed beta-blocker; (E2) a further 24 samples from the Japanese case study, when a fault developed and was rectified; (F2) the monthly US trade deficits for the following two years – it would be an exercise for economics experts to explain what happened here.

The control chart hence picks out those features that can be distinguished from random background variation. Many people find the analogy between “noise” (common-cause variation) and “signals” (special-cause variation) helpful. The variation in control charts A1 to F1 is indistinguishable from “noise” – but that in A2 to F2 is not. It is the changed behaviour – “signals” – that makes A2 to F2 “interesting”, but also unpredictable unless we can identify the special causes.

There is an important lesson to learn from all this. Everybody would surely agree that it is pointless when throwing dice or tossing coins to try to explain the fine detail of the results obtained. So what if now and again we get a rather larger number of heads than normal – or an unusually low score on the dice? Of course we do: that’s just a feature of the randomness – there’s nothing “special” about it. However, having already observed that we cannot distinguish between the statistical behaviour of any of the six processes A1 to F1, why should we be any more justified in trying to explain the fine detail of these or any other stable processes?

So, in summary, as long as the process remains stable, there is nothing worth learning from the occasional relatively high or low pulse rate, or high or low trade (or sales) figure. Except for an occasional repeat figure, each current figure must be higher or lower than the previous one! This is not opinion, or even theory – it is simple statistical fact. It is only when a process becomes unstable that it is worth your while to go looking for the cause.

How much time and money are wasted in our companies through ignoring these simple facts?

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