The Run Length Distribution of a Cumulative Sum Control Chart

The average run length (ARL) of a control chart is often used as the sole measure of the performance of the chart. However, the run length distribution of a cumulative sum (CUSUM) chart can be quite different from a geometric distribution especially when the process is not in control. Thus, the ARL may not be sufficient as the sole measure of performance. The probability function of run length provides a comprehensive understanding of the working of a CUSUM chart. A computer program for computing the probability function and percentiles of the run length for a CUSUM chart is presented. The program also provides the ARL and plots of the probability function and the corresponding cumulative distribution function. An underlying normal distribution is assumed.