Guaranteed conditional performance of the<i>S</i>²control chart with estimated parameters

Abstract

We evaluate the in-control performance of the S2 control chart with estimated parameters conditional on the Phase I sample. Simulation results indicate no realistic amount of Phase I data is enough to have confidence that the in-control average run length (ARL) obtained will be near the desired value. To overcome this problem, we adjust the S2 chart’s control limits such that the in-control ARL is guaranteed to be above a specified value with a certain specified probability. The required adjustment does not have too much of an adverse effect on the out-of-control performance of the chart.