A GLR Control Chart for Monitoring the Process Variance

Abstract

This paper considers the problem of monitoring the variance of a normally distributed process variable when the objective is to effectively detect both small and large increases in the variance. 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 to the performance of other options such as Shewhart charts, CUSUM charts, and combinations of two CUSUM charts. It is shown that the overall performance of the GLR chart is as good as or better than these other options. A CUSUM chart has a tuning parameter which allows for the chart to be tuned to be sensitive to a certain shift of interest. However, the GLR chart does not require users to specify the values of any tuning 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 in-control average number of samples to signal, so the GLR chart has the advantage that it can be easily designed for use in applications. Simulating the performance of the GLR chart is time consuming, but the GLR chart can be very well approximated with a set of CUSUM charts, and this provides a fast method for evaluating the performance of the GLR chart.

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