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OPTIMALLY REPLACING MULTIPLE SYSTEMS IN A SHARED ENVIRONMENT

Published online by Cambridge University Press:  10 May 2017

David T. Abdul-Malak  and
Jeffrey P. Kharoufeh
David T. Abdul-Malak
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, 1025 Benedum Hall, 3700 O'Hara Street, Pittsburgh, PA 15261, USA E-mail: dta10@pitt.edu; jkharouf@pitt.edu
Jeffrey P. Kharoufeh
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, 1025 Benedum Hall, 3700 O'Hara Street, Pittsburgh, PA 15261, USA E-mail: dta10@pitt.edu; jkharouf@pitt.edu
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Abstract

We consider the problem of optimally replacing multiple stochastically degrading systems using condition-based maintenance. Each system degrades continuously at a rate that is governed by the current state of the environment, and each fails once its own cumulative degradation threshold is reached. The objective is to minimize the sum of the expected total discounted setup, preventive replacement, reactive replacement, and downtime costs over an infinite horizon. For each environment state, we prove that the cost function is monotone nondecreasing in the cumulative degradation level. Additionally, under mild conditions, these monotonicity results are extended to the entire state space. In the case of a single system, we establish that monotone policies are optimal. The monotonicity results help facilitate a tractable, approximate model with state- and action-space transformations and a basis-function approximation of the action-value function. Our computational study demonstrates that high-quality, near-optimal policies are attainable and significantly outperform heuristic policies.

Keywords

Maintenance optimizationapproximate dynamic programming
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 2 , April 2018 , pp. 179 - 206
Copyright
Copyright © Cambridge University Press 2017 

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