Exact Average Run Lengths for Monitoring Poisson Counts

Abstract

Control charts are widely employed in public health surveillance. One use is as an aid in monitoring rare health events. A chart is designed to exhibit acceptable average run lengths both when the process is in and out of control. Thus, the chart provides a real-time assessment of the situation. This paper considers the average run lengths of general control charts associated with the Poisson distribution. The Shewhart, cumulative sum, and exponentially weighted moving average charts are special cases of the general chart considered here. An exact solution for the average run length is found for a chart with integer parameters. An approximate solution is obtained for a chart with non integer parameters. If desired, this solution can be iterated to provide an accurate full description of the average run length distribution.Short Control charts are widely employed in public health surveillance. A chart is designed to exhibit acceptable average run lengths both when the process is in and out of control. Thus, the chart provides a real-time assessment of the situation. This paper considers the average run lengths of general control charts associated with the Poisson distribution. An exact solution for the average run length is found for a chart with integer parameters. An approximate solution is obtained for a chart with non integer parameters. If desired, this solution can be iterated to provide the exact average run length distribution.