ARLs and Higher-Order Run-Length Moments for the Poisson CUSUM

摘要

We present a Microsoft QuickBASIC program which uses the Markov chain approach to calculate average run length (ARL) values for a Poisson CUSUM control scheme. Using a recursive formula, the program can also calculate higher-order moments such as skewness and kurtosis. The program my be used to obtain any Poisson CUSUM ARL for either the increasing or decreasing rate case, under any shift in the process mean, at both the zero starting point and the fast initial response starting point.