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Optimal repair/replacement policy for a general repair model

Part of: Special processes Stochastic processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Xiaoyue Jiang ,
Viliam Makis  and
Andrew K. S. Jardine
Xiaoyue Jiang*
Affiliation:
University of Toronto
Viliam Makis*
Affiliation:
University of Toronto
Andrew K. S. Jardine*
Affiliation:
University of Toronto
*
∗ Postal address: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8.
∗ Postal address: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8.
∗ Postal address: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8.
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Abstract

In this paper, we study a maintenance model with general repair and two types of replacement: failure and preventive replacement. When the system fails a decision is made whether to replace or repair it. The repair degree that affects the virtual age of the system is assumed to be a random function of the repair-cost and the virtual age at failure time. The system can be preventively replaced at any time before failure. The objective is to find the repair/replacement policy minimizing the long-run expected average cost per unit time. It is shown that a generalized repair-cost-limit policy is optimal and the preventive replacement time depends on the virtual age of the system and on the length of the operating time since the last repair. Computational procedures for finding the optimal repair-cost limit and the optimal average cost are developed. This model includes many well-known models as special cases and the approach provides a unified treatment of a wide class of maintenance models.

Keywords

general repairoptimal stoppingrepair-cost-limit policy

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 90B25: Reliability, availability, maintenance, inspection
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 1 , March 2001 , pp. 206 - 222
Copyright
Copyright © Applied Probability Trust 2001 

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References

[1] Aven, T. and Bergman, B. (1986). Optimal replacement times—a general set-up. J. Appl. Prob. 23, 432–442.Google Scholar
[2] Baxter, L.A., Kijima, M. and Tortorella, M. (1996). A point process model for reliability of maintained system subject to general repair. Stoch. Models 12, 37–65.Google Scholar
[3] Beichelt, F. (1993). A unified treatment of replacement policies with minimal repair. Naval Res. Logist. 40, 51–67.3.0.CO;2-V>CrossRefGoogle Scholar
[4] Dagpunar, J. S. (1998). Some properties and computational results for a general repair process. Naval Res. Logist. 45, 391–405.Google Scholar
[5] Jensen, U. (1989). Monotone stopping rules for stochastic processes in a semimartingale representation with applications. Optimization 20, 837–852.Google Scholar
[6] Jiang, X., Cheng, K. and Makis, V. (1998). On the optimality of repair-cost-limit policies. J. Appl. Prob. 35, 936–949.Google Scholar
[7] Kijima, M. (1989). Some results for repairable systems with general repair. J. Appl. Prob. 26, 89–102.Google Scholar
[8] Kijima, M., Morimura, H. and Suzuki, Y. (1988). Periodical replacement without assuming minimal repair. Eur. J. Operat. Res. 37, 194–203.Google Scholar
[9] L'Ecuyer, P. and Haurie, A. (1987). The repair vs. replacement problem: a stochastic control approach. Optimal Control Appl. Meth. 8, 219–230.Google Scholar
[10] Makis, V. and Jardine, A. K. S. (1993). A note on optimal replacement policy under general repair. Eur. J. Operat. Res. 69, 75–82.Google Scholar
[11] Makis, V., Jiang, X. and Cheng, K. (2000). Optimal preventive replacement under minimal repair and random repair cost. Math. Operat. Res. 25, 141–156.Google Scholar
[12] Scarsini, M. and Shaked, M. (2000). On the value of an item subject to general repair or maintenance. Eur. J. Operat. Res. 122, 625–637.Google Scholar
[13] Stadje, W. and Zuckerman, D. (1991). Optimal maintenance strategies for repairable systems with general degree of repair. J. Appl. Prob. 28, 384–396.Google Scholar
[14] Zhang, Z. G. and Love, C. E. (2000). A simple recursive Markov chain model to determine the optimal replacement policy under general repairs. Comput. Operat. Res. 27, 321–333.CrossRefGoogle Scholar