A Fast Accurate Approximation for Average Run Lengths of CUSUM Control Charts

Abstract

Cumulative sum (CUSUM) control charts are very effective in detecting special causes. In designing a CUSUM chart, it is important to know the average run lengths (ARL's) corresponding to various possible choices of the mask parameters. This paper provides a relatively simple yet very accurate (typically within 3%) approximation for the ARL of a CUSUM chart, both when the process is in control and when it is out of control. Examples are given showing how the approximation can be used to evaluate the ARL for specific parameter values, to find values that give a desired ARL, and to evaluate the out-of-control ARL's of location and scale CUSUM charts.

• Approximation
• Average Run Length
• Cumulative Sum Control Charts
• Fast Initial Response

Additional information

Notes on contributors

Douglas M. Hawkins

Dr. Hawkins is a Professor in the Department of Applied Statistics. He is a Senior Member of ASQC.