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Optimal replacement for self-repairing shock models by general failure rate

Published online by Cambridge University Press:  14 July 2016

Gary Gottlieb  and
Benny Levikson
Gary Gottlieb*
Affiliation:
New York University
Benny Levikson*
Affiliation:
University of Haifa
*
∗ Postal address: Graduate School of Business Administration, New York University, 100 Trinity Place, New York, NY 10006, U.S.A.
∗∗ Postal address: Department of Statistics, University of Haifa, Mount Carmel, Haifa 31 999, Israel.
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Abstract

A device is subject to a series of shocks which cause damage and eventually failure will occur at the time of arrival of one of the shocks. In between the shocks, the device is partially repaired as the cumulative damage decreases as some Markov process. The device must be replaced upon failure at some cost but it can also be replaced before failure at a lower cost. We consider the general case where the failure rate need not be increasing and replacement can be made at any time. The form of the optimal replacement policy is found and fairly general conditions are given for which a control limit policy is optimal.

Keywords

CONTROL LIMIT POLICY
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 108 - 119
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Research carried out while this author was visiting the Department of Statistics, University of Haifa.

References

Barlow, R. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Bergman, B. (1978) Optimal replacement under a general failure model. Adv. Appl. Prob. 10, 431–451.CrossRefGoogle Scholar
Feldman, R. M. (1976) Optimal replacement with semi-Markov shock models. J. Appl. Prob. 13, 108–117.CrossRefGoogle Scholar
Gottlieb, G. (1982) Optimal replacement for shock models with general failure rate. Operat. Res. 30, 82–92.CrossRefGoogle Scholar
Mine, H. and Osaki, S. (1970) Markovian Decision Processes. American Elsevier, New York.Google Scholar
Shiryayev, A. N. (1978) Optimal Stopping Rules. Springer-Verlag, New York.Google Scholar
Taylor, H. M. (1975) Optimal replacement under additive damage and other failure models. Naval Res. Logist. Quart. 22, 1–18.CrossRefGoogle Scholar
Zuckerman, D. (1978) Optimal stopping in a semi-Markov-shock model. J. Appl. Prob. 15, 629–634.CrossRefGoogle Scholar