Designing Control Charts Using an Empirical Reference Distribution

We address a problem of increasing practical interest: control charting in the absence of an assumed normal distribution. We analyze the sampling uncertainties inherent in selecting control limits from the empirical distribution of a large sample of whatever statistic is to be charted. We then relate the selections of the number of preliminary observations and control limits to on-target and off-target performance measures. The methodology is nonparametric, requiring only that the plotted statistics be independent and come from the same distribution.