MINDCUMIN charts

A serious drawback of classical control charts is their high sensitivity to deviations from normality. By now, many alternative procedures, often of a nonparametric nature, have been proposed. A danger with these competitors is that unrealistically large Phase I samples might be needed. This can be avoided by using groups of, rather than individual (IND), observations during Phase II. A recently introduced successful example is the CUMIN chart: a signal occurs as soon as m consecutive observations all exceed some suitably chosen upper limit. An interesting question is how m should be chosen in this cumulative minimum. If large (small) shifts are likely to occur, m should be small (large). As often the magnitude of possible shifts is unclear, it is attractive to be flexible w.r.t. the choice of m. In the present paper, a procedure is developed which achieves this goal by combining an IND and a CUMIN procedure. As input minima of small blocks (e.g. pairs or triples) of observations should be used to avoid recurrence of the problem of the need for unrealistically large Phase I samples. The nice performance of the proposed MINDCUMIN chart and its straightforward implementation make it very useful for application in practice.