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An exponential riddle

Published online by Cambridge University Press:  14 July 2016

Bhaskar Sengupta
Bhaskar Sengupta*
Affiliation:
Bell Laboratories
*
∗Postal address: Bell Laboratories, HP-1C319, Holmdel, NJ 07733, U.S.A.
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Abstract

We present a problem of finding the optimum inspection procedure for a system whose time to failure is an exponential random variable. We characterize a simple and surprising solution to the problem.

Keywords

INSPECTIONMARKOVIAN DECISION PROCESSESRELIABILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 737 - 740
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

This work was done while the author was at Columbia University, New York.

References

[1] Astrom, K. J. (1965) Optimal control of Markov processes with incomplete state information. J. Math. Anal. Appl. 10, 174–205.CrossRefGoogle Scholar
[2] Barlow, R. E., Proschan, F. and Hunter, L. C. (1963) Optimum checking procedures. SIAM 11, 1078–1095.Google Scholar
[3] Luss, H. (1976) Maintenance policies when deterioration can be observed by inspections. Operat. Res. 24, 359–366.Google Scholar
[4] Sengupta, B. (1976) Optimum Inspection Schedules. Doctoral Dissertation, Columbia University, New York.Google Scholar
[5] Sengupta, B. (1981) Control limit policies for the early detection of failure. European J. Operat. Res. 7, 257–264.Google Scholar
[6] Wang, R. C. (1977) Optimum replacement policy with unobservable states. J. Appl. Prob. 14, 340–348.Google Scholar
[7] White, C. C. (1977) A Markov quality control process subject to partial observation. Management Sci. 23, 843–852.Google Scholar