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This question relates to the Nelson rules for statistical process control.

Does rule 2 - nine points in a row on the same side of the mean - apply if one or two of those points are very narrowly on that side of the mean?

I have a series where there are nine points below the mean, but two of them are below by very small amounts. Does this count as evidence of special-cause variation?

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  • $\begingroup$ How quantitative, definite, or rigorous do you suppose "below by very small amounts" might be as a criterion? This sounds a bit like the defendant pleading before a judge "please don't send me to jail because I offended nine times--in two of those cases, I stole only a small amount." $\endgroup$ – whuber Jul 14 '17 at 15:15
  • $\begingroup$ Fair point, but I was looking for a general answer. $\endgroup$ – Statsanalyst Jul 14 '17 at 15:20
  • $\begingroup$ @Scortchi thanks for adding the tag - there isn't one for SPC and couldn't find one sufficiently similar...perhaps there should be an SPC tag? $\endgroup$ – Statsanalyst Jul 14 '17 at 15:20
  • $\begingroup$ @Statsanalyst I think that what whuber means is that the answer is "yes". $\endgroup$ – Kodiologist Jul 14 '17 at 15:53
  • $\begingroup$ @whuber add your comment as an answer & I'll mark it as answered. $\endgroup$ – Statsanalyst Jul 14 '17 at 17:41
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The probability calculations involved in producing those rules would be based on the stated criterion as is.

That is the calculations that led to deciding on 9 in the rule "nine points in a row on the same side of the mean" would be based not on how far they were on that side, just on them being on that side at all.

So - as arbitrary as it may seem - if you want the rules to retain their supposed properties (both the false alarm rate and the chances of detecting something when it's actually happening), you would use them as stated. If you want to vary the criterion, you would also vary the number of points so that they retained the properties they were designed to have (or to deal with the consequences of changing those properties).

If you modify it so that you need 9 points beyond some point further beyond the mean, you'd reduce the false alarm rate and the power to detect problems at the same time; that's not automatically a problem but (i) it would be best to be very aware of exactly how much you're impacting both those things, and (ii) people aware of Nelson's rules might look askance at the modification without a good justification for it.

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