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Inspection and replacement policies

Published online by Cambridge University Press:  14 July 2016

Dror Zuckerman
Dror Zuckerman*
Affiliation:
The Hebrew University
*
∗Present address: Graduate School of Management, MEDS Department, Northwestern University, Evanston, Illinois 60201, U.S.A.
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Abstract

In this article we examine a breakdown model in which the system's status can be determined only by a test. Upon detection of failure the system must be replaced by a new identical one. The costs incurred include cost of inspection, operating costs, failure cost and a cost associated with planned replacements. Throughout the paper we restrict attention to replacement rules in which the time interval between two successive inspections is regarded as a fixed quantity. The decision variables include the inspection interval and the scheduling for preventive (planned) replacements. The problem is to specify a replacement rule which minimizes the long-run average cost per unit time. We show that under certain monotone conditions there is a natural candidate for an optimal replacement rule.

Keywords

REPLACEMENT POLICYOPTIMAL POLICYPLANNED REPLACEMENTSTOPPING TIMEINSPECTION POLICY
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 168 - 177
Copyright
Copyright © Applied Probability Trust 1980 

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References

[1] Abdel-Hameed, M. S. and Shimi, I. N. (1978) Optimal replacement of damaged devices. J. Appl. Prob. 15, 153–161.Google Scholar
[2] Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
[3] Bergman, B. (1978) Optimal replacement under a general failure model. Adv. Appl. Prob. 10, 431–451.Google Scholar
[4] Dynkin, E. B. (1965) Markov Processes 1. Academic Press, New York.Google Scholar
[5] Feldman, R. M. (1976) Optimal replacement with semi-Markov shock models. J. Appl. Prob. 13, 108–117.CrossRefGoogle Scholar
[6] Feldman, R. M. (1977) Optimal replacement for systems governed by Markov additive shock processes. Ann. Prob. 5, 413–429.CrossRefGoogle Scholar
[7] Kao, E. P. (1973) Optimal replacement rules when changes of state are semi-Markovian. Operat. Res. 21, 1231–1249.CrossRefGoogle Scholar
[8] Klein, M. (1962) Inspection — maintenance — replacement schedules under Markovian deterioration. Management. Sci. 9, 25–32.CrossRefGoogle Scholar
[9] Luss, H. (1976) Maintenance policies when deterioration can be observed by inspections. Operat. Res. 24, 359–366.CrossRefGoogle Scholar
[10] Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
[11] Taylor, H. M. (1975) Optimal replacement under additive damage and other failure models. Naval Res. Logist. Quart. 22, 1–18.CrossRefGoogle Scholar
[12] Zuckerman, D. (1978) Optimal stopping in a semi-Markov shock model. J. Appl. Prob. 15, 629–634.CrossRefGoogle Scholar
[13] Zuckerman, D. (1979) Optimal replacement policy for the case where the damage process is a one-sided Lévy process. Stoch. Proc. Appl. 7, 141–151.Google Scholar