Guaranteed Conditional Performance of the S2 Control Chart with Estimated Parameters

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 charts 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.