An Adaptive CUSUM Procedure for Signaling Process Variance Changes of Unknown Sizes

Lianjie Shu · Hang-Fai Yeung · Wei Jiang

27 citations0/0 files storedJournal of Quality Technology

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

Abstract

Similar to the CUSUM location chart, the traditional CUSUM dispersion chart can be designed to optimize the detection of specified variance changes. However, this optimality property requires that the magnitude of the out-of-control variance is known exactly a priori. To get away from this requirement, this paper suggests an adaptive CUSUM procedure for signaling changes in the process variance of unknown sizes. The basic idea is to first estimate the current process variance and then dynamically adjust the CUSUM chart to match the variance estimate. A two-dimensional Markov chain model is developed to analyze the chart performance. The comparison results with the traditional CUSUM dispersion chart and other competitive procedures favor the proposed one.

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References

1992Introduction to Statistical Quality Control 1954CONTINUOUS INSPECTION SCHEMES 1986Optimal Stopping Times for Detecting Changes in Distributions 2005Introduction to Statistical Quality Control 1972An Approach to the Probability Distribution of Cusum Run Length 1998Cumulative Sum Charts and Charting for Quality Improvement 1985Sequential Analysis 2003The Changepoint Model for Statistical Process Control

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