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This is a question question about why seven is used in the “seven run rule” for seven continuous controls points below or above the mean. I have researched a lot of QA databases and I haven’t been able to get an answer to this question. Any assistance will be greatly appreciated.
The issue of limiting values of runs on either side of the median of n cases and in particular the “rule” of 7 on one side is summarized in
Notes on Application of Runs to Quality Control Charts – Mosteller – Annals of Mathematical Statistics Vol XII (1941) p.232
If you want a general discussion without the proof but with some worked examples then you could read Quality Control and Industrial Statistics – Duncan – 4th Edition pp. 386 to 393 under the section The Theory of Runs in Random Data
It is a guideline not a rule. Minitab uses 9 as its default. Issue is what is the probability of consecutive points above or below a center line. The probability of one point is .5. Two points in a row about be .5 x .5. Seven in a row would be .5 to the 7th power. Those probabilities as random events is small so possibly you can assume some special cause and then investigate. Practically you might want to react at 5 or 6 or maybe 9 or 10. Depends on the process and your tolerance for risk.
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