Computing the Run Length Probability Distribution for CUSUM Charts

It is widely recognized that the run length probability distribution of a cumulative sum (CUSUM) chart may be rather different from a geometric distribution. This is generally true for the left tail of the distribution, but, when the decision interval is large, it can apply to the whole distribution whether the process is in control or out of control. This paper provides a computer implementation of a fast and accurate algorithm to compute the run length probability distribution for CUSUM charts to monitor the process mean. The program may be used not only under the usual normality assumption but also for nonsymmetric and long-tailed continuous distributions.