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The moving window detection procedure for discrete data is studied. Bounds for the probabilities and expected values of the waiting time for a detection are derived. The bounds are evaluated for independent identically distributed zero-one Bernoulli trials, binomial, and Poisson random variables, and also for the two-state stationary Markov chain. The results are applicable to the theory of radar detection, time sharing systems, and quality control.
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Joseph Glaz (1983) studied this question.
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