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An optimal inspection and replacement policy for a deteriorating system

Published online by Cambridge University Press:  24 August 2016

Masamitsu Ohnishi ,
Hajime Kawai  and
Hisashi Mine
Masamitsu Ohnishi*
Affiliation:
Kyoto University
Hajime Kawai*
Affiliation:
University of Osaka Prefecture
Hisashi Mine*
Affiliation:
Kansai University
*
∗Postal address: Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan.
∗∗Postal address: Department of Business Administration, School of Economics, University of Osaka Prefecture, Osaka 591, Japan.
∗∗∗Postal address: Department of Management Engineering, Faculty of Engineering, Kansai University, Osaka 564, Japan.
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Abstract

This paper investigates a system whose deterioration is expressed as a continuous-time Markov process. It is assumed that the state of the system cannot be identified without inspection. This paper derives an optimal policy minimizing the expected total long-run average cost per unit time. It gives the optimal time interval between successive inspections and determines the states at which the system is to be replaced. Furthermore, under some reasonable assumptions reflecting the practical meaning of the deterioration, it is shown that the optimal policy has monotonic properties. A control limit rule holds for replacement, and the time interval between successive inspections decreases as the degree of deterioration increases.

Keywords

CONTINUOUS-TIME MARKOVIAN DETERIORATIONEXPECTED TOTAL LONG-RUN AVERAGE COST
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 973 - 988
Copyright
Copyright © Applied Probability Trust 1986 

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