Detection and Diagnosis of Unknown Abrupt Changes Using CUSUM Multi-Chart Schemes

Abstract

A cumulative sum (CUSUM) multi-chart scheme that consists of multiple CUSUM control charts is studied for detecting and diagnosing an unknown abrupt change in a stochastic system on the basis of sequential observations. We prove that the CUSUM multi-chart not only has a high diagnostic capability but also possesses a better detection performance than individual CUSUM charts when the in-control average run length is large. We also present an optimal design of the CUSUM multi-chart and two illustrative examples involving the normal and exponential distributions. Moreover, numerical comparisons of the average run lengths are made via Monte Carlo simulation among the CUSUM, generalized likelihood ratio, exponentially weighted moving average (EWMA), multi-chart, and CUSUM multi-chart. The numerical results indicate that the CUSUM multi-chart has the best performance on the whole among the five schemes in detecting the unknown mean shift.

Keywords:

• Asymptotic optimality
• Kullback–Leibler information distances
• Online detection and diagnosis
• Sequential analysis

Subject Classifications:

• 62L10
• 62N10

ACKNOWLEDGMENTS

We thank the special issue guest editor and two referees for their valuable comments and suggestions, which have improved this work. We are especially grateful to a referee who pointed out a mistake in an earlier proof of Lemma 3.1. We also thank Yanting Li for her help in the numerical simulations. This work was supported by RGC Competitive Earmarked Research Grants HKUST6232/04E and HKUST6204/05E.

Notes

Recommended by W. Schmid