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On a quickest detection problem with variable monitoring

Published online by Cambridge University Press:  14 July 2016

D. W. Balmer
D. W. Balmer*
Affiliation:
London School of Economics and Political Science
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Abstract

The problem of detecting the arrival of a ‘disorder' in a process observed through a monitoring facility which may operate in ‘slow’ or ‘fast’ mode, is formulated as an optimal stopping problem. It is shown that in all circumstances where there may exist an optimal policy specifying the mode of observation and the time of stopping there is a unique policy satisfying certain necessary conditions of optimality; the various circumstances and control policies are specified.

Keywords

QUICKEST DETECTIONOPTIMAL STOPPINGCOSTLY INFORMATIONCOSTLY SURVEILLANCECONTROLFREE BOUNDARY PROBLEM
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 760 - 767
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Balmer, D. W. (1975) On a quickest detection problem with costly information. J. Appl. Prob. 12, 87–97.CrossRefGoogle Scholar
[2] Bather, J. A. (1967) On a quickest detection problem. Ann. Math. Statist. 38, 711–724.Google Scholar
[3] Bather, J.A. (1973) Free boundary problems in the design of control charts. Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Academia, Prague, 89–106.Google Scholar
[4] Bather, J. A. (1973) An optimal stopping problem with costly information. Bull. I.S.I. 45 (3), 9–24.Google Scholar
[5] Shiryaev, A. N. (1963) On optimum methods in quickest detection problems. Theor. Prob. Appl. 8, 22–46.CrossRefGoogle Scholar