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An inspection–repair–replacement model for a deteriorating system with unobservable state

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Lam Yeh
Lam Yeh*
Affiliation:
Northeastern University at Qinhuangdao and University of Hong Kong
*
∗Postal address: Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong. Email address: ylam@hkustasc.hku.hk
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Abstract

In this paper, an inspection–repair–replacement (IRR) model for a deteriorating system with unobservable state is studied. Assume that the system state can only be diagnosed by inspection and an inspection is imperfect. After inspection, if the system is diagnosed as being in a down state, a minimal repair will be undertaken, otherwise we do nothing. Assume further that the system lifetime is a random variable having increasing failure rate. A feasible IRR policy is studied. An algorithm is then suggested for determining an optimal feasible IRR policy for minimizing the long-run average cost per unit time after a finite-step search.

Keywords

Minimal repairincreasing failure raterenewal reward processfeasible IRR policy

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1031 - 1042
Copyright
Copyright © Applied Probability Trust 2003 

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