My Question is: What statistical methods can be used to examine whether a selection of tolerance limits of data makes sense, i.e. validation of tolerance limits?
My solution: I would analyse how many outliers exist (data greater than the tolerance limit), how they are distributed (>>tolerance limit oder low deviation from the tolerance limit), comparison of mean, quantiles, standard deviation of data (which allow statements about curtosis,skewness etc.).
But I'm not sure in which cases one can say that a stated tolerance limit makes sense. There is no optimal tolerance limit.
So my Questions summarized:
(1) Which statistical methods exist to validate a stated tolerance limit?
(2) What should be the "desired goal/result" of these statistical tests of validation?