A Generalized Likelihood Ratio Control Chart for Monitoring the Process Mean Subject to Linear Drifts

Abstract

This article considers the problem of monitoring a normally distributed process variable when a special cause may produce a time‐varying linear drift in the mean. The design and application of a generalized likelihood ratio (GLR) control chart for drift detection are evaluated. The GLR drift chart does not require specification of any tuning parameters by the practitioner and has the advantage that, at the time of the signal, estimates of both the change point and the drift size are immediately available. An equation to accurately approximate the control limit is provided. The performance of the GLR drift chart is compared with that of other control charts such as a standard cumulative sum chart and a cumulative score chart designed for drift detection. We also compare the GLR chart designed for drift detection with the GLR chart designed for sustained shift detection because both of them require only a control limit to be specified. In terms of the expected time for detection and in terms of the bias and mean squared error of the change‐point estimators, the GLR drift chart has better performance for a wide range of drift rates relative to the GLR shift chart when the out‐of‐control process is truly a linear drift. Copyright © 2012 John Wiley & Sons, Ltd.