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I am aware that, in SPC, one can theoretically chose different control limits based on the number of standard deviations one wishes to use.

If one uses a control chart with control limits with fewer than three standard deviations - e.g. x-bar +- 2/1.128, do the corresponding Nelson rules - e.g. x number of observations below the mean, etc, change as well? The logical extension of reducing the control limits (and hence increasing the probability that rule 1 will be triggered), is that the sensitivity of the other rules should increase too. Is this the case?

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Decreasing the amount of standard deviations increases the probability that a point is outside of the control limits. Using only 2 standard deviations will give 1/20 points as false positive. The non-conformances are then no longer useful, as there are too many false positives.

To detect process shift, detecting only points outside 3 sigma is typically enough. The other Nelson rules provide significantly diminishing returns and increase the false positive rate.
Source: https://www.qualitydigest.com/inside/statistics-column/when-should-we-use-extra-detection-rules-100917.html

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