A Binomial GLR Control Chart for Monitoring a Proportion

This paper considers a control chart for monitoring a process proportion based on a generalized likelihood ratio (GLR) statistic. The objective is to effectively detect a wide range of shift sizes. The GLR statistic is obtained from a moving window of past sample statistics that follow a binomial distribution. The Phase II performance of this chart is evaluated using the steady state average number of observations to signal (SSANOS) for detecting sustained increases in the proportion. Comparisons of the binomial GLR chart to the Shewhart np-chart, the individual binomial cumulative sum (CUSUM) chart, and combinations of multiple binomial CUSUM charts show that the overall performance of the binomial GLR chart is at least as good as these other options. Moreover, unlike the other charts, the binomial GLR chart has an advantage that it does not require users to specify multiple charting parameters that may be difficult to obtain, and this makes it easier for the GLR chart to be designed for practical applications.