CUSUM Charts with Controlled Conditional Performance Under Estimated Parameters

We study the effect of the Phase I estimation error on the cumulative sum (CUSUM) chart. Impractically large amounts of Phase I data are needed to sufficiently reduce the variation in the in-control average run lengths (ARL) between practitioners. To reduce the effect of estimation error on the chart's performance we design the CUSUM chart such that the in-control ARL exceeds a desired value with a specified probability. This is achieved by adjusting the control limits using a bootstrap-based design technique. Such approach does affect the out-of-control performance of the chart; however, we find that this effect is relatively small.