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A lower bound on the ARL to detection of a change with a probability constraint on false alarm. (English) Zbl 0853.62063

Summary: An inequality that relates the probability of false alarm of a change-point detection policy to its average run length to detection is proved. By means of this inequality, a lower bound on the rate of detection, when the change occurs after a long delay, is derived.

MSC:

62L10 Sequential statistical analysis
62P30 Applications of statistics in engineering and industry; control charts
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References:

[1] KESTEN, H. 1973. Random difference equations and renewal theory for products of random matrices. Acta Math. 131 207 248. · Zbl 0291.60029 · doi:10.1007/BF02392040
[2] POLLAK, M. and SIEGMUND, D. 1975. Approximations to the expected sample size of certain sequential tests. Ann. Statist. 3 1267 1282. · Zbl 0347.62063 · doi:10.1214/aos/1176343284
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