Summary: MINDCUMIN charts
Willem Albers and Wilbert C. M. Kallenberg
Department of Applied Mathematics
University of Twente
P.O. Box 217, 7500 AE Enschede
Abstract. 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.
Keywords and phrases: Statistical Process Control, Phase II control limits, order statistics,
2000 Mathematics Subject Classification: 62P30, 62G30, 62L10