A Binomial GLR Control Chart for Monitoring a Proportion

Wandi Huang · Marion R. Reynolds · Sai Wang

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

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.

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References

1971Procedures for Reacting to a Change in Distribution 1995Sequential Changepoint Detection in Quality Control and Dynamical Systems 1982Combined Shewhart-CUSUM Quality Control Schemes 1998Information bounds and quick detection of parameter changes in stochastic systems 2003The Changepoint Model for Statistical Process Control 1995Using the Generalized Likelihood Ratio Statistic for Sequential Detection of a Change-Point 1997Control Charts Based on Attribute Data: Bibliography and Review 1999A CUSUM Chart for Monitoring a Proportion When Inspecting Continuously

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2012A Generalized Likelihood Ratio Chart for Monitoring Bernoulli Processes 2016A control scheme for autocorrelated bivariate binomial data 2016Rank-based process control for mixed-type data 2017A GLR control chart for monitoring a multinomial process

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