The Run Length Distribution of the CUSUM Chart with Estimated Parameters

Authors

Allison L. Jones-Farmer, Auburn UniversityFollow
Charles W. Champ, Georgia Southern UniversityFollow
Steven E. Rigdon, Southern Illinois University EdwardsvilleFollow

Document Type

Article

Publication Date

1-2004

Publication Title

Journal of Quality Technology

DOI

10.1080/00224065.2004.11980254

ISSN

0022-4065

Abstract

The CUSUM control chart is a popular method used to monitor the performance of production processes. The performance of the CUSUM is generally evaluated with the assumption that the process parameters are known. In practice, the parameters are rarely known and are frequently replaced with estimates from an in-control reference sample. We discuss the run length distribution of the CUSUM with estimated parameters and provide a method for approximating this distribution and moments. We evaluate the performance of the CUSUM with estimated parameters in a variety of practical situations.

Recommended Citation

Jones-Farmer, Allison L., Charles W. Champ, Steven E. Rigdon. 2004. "The Run Length Distribution of the CUSUM Chart with Estimated Parameters." Journal of Quality Technology, 36: 95-108. doi: 10.1080/00224065.2004.11980254
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/498