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On the optimality of repair-cost-limit policies

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

Published online by Cambridge University Press:  14 July 2016

Xiaoyue Jiang ,
Kan Cheng  and
Viliam Makis
Xiaoyue Jiang*
Affiliation:
University of Toronto
Kan Cheng*
Affiliation:
Academia Sinica
Viliam Makis*
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: Institute of Applied Mathematics, Academia Sinica, Beijing, 100080, P.R. China.
∗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

An optimal repair/replacement problem for a single-unit repairable system with minimal repair and random repair cost is considered. The existence of the optimal policy is established using results of the optimal stopping theory, and it is shown that the optimal policy is a ‘repair-cost-limit’ policy, that is, there is a series of repair-cost-limit functions gn(t), n = 1, 2,…, such that a unit of age t is replaced at the nth failure if and only if the repair cost C(n, t) ≥ gn(t); otherwise it is minimally repaired. If the repair cost does not depend on n, then there is a single repair cost limit function g(t), which is uniquely determined by a first-order differential equation with a boundary condition.

Keywords

Minimal 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
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 4 , December 1998 , pp. 936 - 949
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

Research supported by the Natural Science Foundation of China and by the Natural Sciences and Engineering Research Council of Canada.

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