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Optimal stopping in a semi-Markov shock model

Published online by Cambridge University Press:  14 July 2016

Dror Zuckerman
Dror Zuckerman*
Affiliation:
The Hebrew University of Jerusalem
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Abstract

We examine a failure model for a system existing in a random environment. The system accumulates damage through a shock process and the failure time depends on the accumulated damage in the system. The cumulative damage process is assumed to be a semi-Markov process. Upon failure the system must be replaced by a new identical one and a failure cost is incurred. If the system is replaced before failure, a smaller cost is incurred. We allow a controller to replace the system at any stopping time before failure time. We consider the problem of specifying a replacement rule which minimizes the total long-run average cost per unit time.

Keywords

REPLACEMENT POLICYSEMI-MARKOV PROCESSSTOPPING TIMECONTROL LIMIT POLICYINFINITESIMAL OPERATORHAZARD RATE
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 629 - 634
Copyright
Copyright © Applied Probability Trust 1978 

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References

[1] Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
[2] Dynkin, E. B. (1965) Markov Processes 1. Academic Press, New York.Google Scholar
[3] Feldman, R. M. (1976) Optimal replacement with semi-Markov shock models. J. Appl. Prob. 13, 108–117.Google Scholar
[4] Kao, E. P. C. (1973) Optimal replacement rules when changes of state are semi-Markovian. Opns Res. 21, 1231–1249.CrossRefGoogle Scholar
[5] Taylor, H. M. (1975) Optimal replacement under additive damage and other failure models. Naval Res. Logist. Quart. 22, 1–18.Google Scholar