On Statistical Design of the<i>S</i>²Control Chart

Abstract

ABSTRACT The usual S 2 chart is constructed with equal false alarm probabilities for the lower and upper control limits. An alternative is the ARL-unbiased S 2 chart, where the ARL (average run length) curve attains its maximum when the common-cause variance is at its in-control value. We examine the ARL properties of these S 2 charts, and show that neither the usual S 2 chart nor the ARL-unbiased S 2 chart is optimal in a natural sense. We propose two criteria, under which optimal S 2 charts can be constructed. The effects of parameter estimation on our designs are also discussed, and suggestions are made regarding practical implementation.