Optimal Designs Of Two-Sided CUSUM Schemes

Abstract

An optimal CUSUM chart is commonly defined as one with a fixed in control average run length (ARL) and the smallest ARL for a specified shift Άin the mean. As the run length distribution is usually positively skewed, median run length (MRL) is a more reasonable measure of location than the mean given by ARL. As such it is more reasonable to define the optimal CUSUM in terms of MRL. The optimal CUSUM schemes in terms of ARL and MRL are obtained in the case when the observations have a normal or exponential distribution. It is found that the parameter (k, h) of the optimal CUSUM in terms of ARL and that of the optimal CUSUM in terms of MRL are fairly different