The Design of GLR Control Charts for Monitoring the Process Mean and Variance

Abstract

This paper investigates generalized likelihood ratio (GLR) control charts for the problem of monitoring the mean and variance of a normally distributed process variable when the objective is to effectively detect both small and large shifts in these parameters. It is shown that the GLR charts are generally as effective at detecting a wide range of shift sizes as other options, such as the traditional practice of using a combination of a control chart for the mean and a control chart for the variance. Using a combination of control charts requires that multiple control-chart design parameters be specified. Although multiple design parameters allow for the charts to be tuned to be more sensitive to certain shifts that may be of particular interest, they complicate the process of designing these charts. The GLR chart for detecting a change in the mean or an increase in the variance does not have any control-chart parameters that need to be specified other than the control limit. The GLR chart for the case in which decreases in the variance are also of interest has one design parameter in addition to the control limit. Tables of control limits corresponding to specified values of the in-control average number of observations to signal are provided, so it is very easy to design the GLR chart for use in applications.