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Inspection and maintenance policies of devices subject to deterioration

Published online by Cambridge University Press:  01 July 2016

Mohamed Abdel-Hameed
Mohamed Abdel-Hameed*
Affiliation:
Kuwait University
*
∗Postal address: Department of Mathematics, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait.
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Abstract

We determine the optimal inspection policy of a system subject to deterioration. The deterioration is assumed to be an increasing pure jump Markov process. The criteria used for optimality is the long-run average cost per unit of time.

Keywords

REPLACEMENT POLICIESPURE JUMP PROCESSESCONTROL-LIMIT POLICYCOMPOUND POISSON PROCESSESGAMMA PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 4 , December 1987 , pp. 917 - 931
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research supported by Kuwait University Grant SM 047.

References

[1] Abdel-Hameed, M. S. (1984) Life distribution properties of devices subject to a pure jump damage process. J. Appl. Prob. 21, 816–825.CrossRefGoogle Scholar
[2] Abdel-Hameed, M. S. and Shimi, I. N. (1978) Optimal replacement of damaged devices. J. Appl. Prob. 15, 153–161.CrossRefGoogle Scholar
[3] Blumentual, R. M. and Getoor, R. K. (1969) Markov Processes and Potential Theory. Academic Press, New York.Google Scholar
[4] Çinlar, E. and Jacod, J. (1981) Representation of semimartingale Markov processes in terms of Wiener and Poisson random measures. Seminar on Stochastic Processes, ed. Çinlar, E., Chung, K. L. and Getoor, R. K.. Birkhauser, Boston, 159–242.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 system 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] Lamperti, J. (1977) Stochastic Processes: A Survey of the Mathematical Theory. Springer-Verlag, New York.CrossRefGoogle Scholar
[10] Luss, H. (1976) Maintenance policies when deterioration can be observed by inspections. Operat. Res. 24, 359–366.CrossRefGoogle 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. (1978) Optimal replacement policy for the case where the damage process is a one-sided Lévy process. Stoch. Proc. Appl. 7, 141–151.CrossRefGoogle Scholar
[14] Zuckerman, D. (1980) Inspection and replacement policies. J. Appl. Prob. 17, 168–177.CrossRefGoogle Scholar