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For SPC, adjust the sigma so that the false alarm rate (ARL0) remains fixed, say (1 in 370), no matter how many rules tests are selected.

The more rules that are tested against the higher the false alarm rate becomes unless the sigma value is increased to compensate for multiple simultaneous tests/comparisons.  Please have an option to have the sigma automatically adjust to maintain a specified false alarm rate (default is say, 1 in 370 --> 3 sigma in normally distributed data) given the number of rules/tests that are selected, then resize the zones so that zone 1 = 1*adj. sigma, zone 2 = 2 * adjusted sigma and zone 3 = 3 * adjusted sigma.  Similar to adjusting alpha level for multiple comparisons.

 

https://analyse-it.com/docs/user-guide/process-control/shewhart-control-chart-ruleshttp://www.wseas....

 

The assumption is that each rule or test in isolation should have a ~1 in 370 chance of returning a false positive, therefore if multiple rules/tests are selected then either show the expected false alarm rate or have the option to hold it fixed at some level by adjusting the sigma.

 

Thanks.