A Robust-Likelihood Cumulative Sum Chart

Steven N. MacEachern · Youlan Rao · Chunjie Wu

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

Abstract

In practice, the cumulative sum (CUSUM) control chart is often used to detect small shifts in the mean of a normally distributed process, but it performs poorly for thick-tailed processes and for large shifts. This article provides a robust-likelihood cumulative sum (RLCUSUM) chart that discounts outliers and yet has the ability to detect large shifts quickly. The new chart is motivated by the likelihood underpinnings of the CUSUM. It is based on the likelihood of a variate constructed to ensure robust performance of the resulting chart. The new chart is compared with the conventional CUSUM in terms of average run length, with the finding that the RLCUSUM is much better than the conventional CUSUM, especially for large shifts. For small shifts, the two charts are essentially equivalent. We study the properties of the conditional limiting distribution. A final application of the RLCUSUM in assessing livestock disease shows that the method is applicable in process control.

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References

1954CONTINUOUS INSPECTION SCHEMES 1932Economic Control of Quality of Manufactured Product.1972An Approach to the Probability Distribution of Cusum Run Length 1998Cumulative Sum Charts and Charting for Quality Improvement 1982Combined Shewhart-CUSUM Quality Control Schemes 2000The State of Statistical Process Control as We Proceed into the 21st Century 2006A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison 1969Cumulative Sum Tests: Theory and Practice

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2023A robust adaptive exponentially weighted moving average control chart with a distribution-free design strategy 2015CUSUM chart for detecting range shifts when monotonicity of likelihood ratio is invalid 2017Properties and enhancements of robust likelihood CUSUM control chart

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