An Evaluation of a GLR Control Chart for Monitoring the Process Mean

Abstract

This paper considers the problem of monitoring the mean of a normally distributed process variable when the objective is to effectively detect both small and large shifts in this mean. The performance of a generalized likelihood ratio (GLR) control chart is evaluated, where the likelihood ratio is based on a moving window of past observations. The performance of the GLR chart is compared with the performance of other options, such as combinations of Shewhart and cumulative sum (CUSUM) charts and an adaptive CUSUM chart, that have been proposed for detecting a wide range of shift sizes. Performance is evaluated for sustained shifts, transient shifts, and drifts in the mean. It is shown that the overall performance of the GLR chart is at least as good as these other options. These other options have multiple control-chart parameters that allow for the charts to be tuned to be more sensitive to certain shifts that may be of interest. However, the GLR chart does not require users to specify the values of any control-chart parameters other than the size of the window and the control limit. We recommend a specific window size and provide a table of control limits corresponding to specified values of the false-alarm rate, so it is very easy to design the GLR chart for use in applications. Simulating the performance of the GLR chart is time consuming, but approximating the GLR chart with a set of CUSUM charts provides a much faster way of evaluating the performance of the GLR chart for research purposes.