Estimation of the Change Point in the X¯ and S Control Charts

Abstract

The X¯ and S (or R) control charts are most commonly used in practice for monitoring the process mean and variance, respectively. A method for detecting changes in the process mean or variance is to obtain a stopping time at which the control charts issue a signal. The potential delay in generating a signal from the control charts calls for the change point estimation combined with control charts. In this paper, when X¯ and S control charts issue a signal, a maximum likelihood joint estimator of the change point is suggested considering simultaneous change in the process mean and variance. The use of the proposed estimator is illustrated with an example.

Key Words:

• Control charts
• Detecting changes
• Joint estimation of a change point

Acknowledgments

This work was partially supported by a grant (R01-2003-000-10220-0) from the Korea Science and Engineering Foundation. The authors would like to thank the Editor-in-Chief and an anonymous referee for their comments on an earlier version of this paper that led to an improved final version.