Discrete, Continuous and Conditional Multiple Window Scan Statistics

Tung-Lung Wu · Joseph Glaz · James C. Fu

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Advanced Statistical Process Monitoring Probability and Statistical Research Point processes and geometric inequalities

Abstract

The distributions of discrete, continuous and conditional multiple window scan statistics are studied. The finite Markov chain imbedding technique has been applied to obtain the distributions of fixed window scan statistics defined from a sequence of Bernoulli trials. In this manuscript the technique is extended to compute the distributions of multiple window scan statistics and the exact powers for multiple pulse and Markov dependent alternatives. An application in blood component quality monitoring is provided. Numerical results are also given to illustrate our theoretical results.

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1992STATISTICS FOR SPATIAL DATA 2004Multiple Window Discrete Scan Statistics 1994Power of the Scan Statistic in Detecting a Changed Segment in a Bernoulli Sequence 2010Chi-square Control Charts with Runs Rules

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