The Optimal Stopping Time for Detecting Changes in Discrete Time Markov Processes

Fugee Tsung

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

Abstract

In this paper we prove that Page's stopping time (CUSUM test) is optimal for detecting the changes in Markov processes that have invariant distribution.

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References

1954CONTINUOUS INSPECTION SCHEMES 1971Procedures for Reacting to a Change in Distribution 1986Optimal Stopping Times for Detecting Changes in Distributions 1985Optimal Detection of a Change in Distribution 1998Information bounds and quick detection of parameter changes in stochastic systems 1990Decision Theoretic Optimality of the Cusum Procedure 1986An algorithm for detecting a change in a stochastic process 1994Optimal detection of a change in distribution when the observations form a Markov chain with a finite state space

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