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OPTIMAL REPLACEMENT POLICIES UNDER ENVIRONMENT-DRIVEN DEGRADATION

Published online by Cambridge University Press:  08 June 2012

M. Yasin Ulukus ,
Jeffrey P. Kharoufeh  and
Lisa M. Maillart
M. Yasin Ulukus
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, 3700 O'Hara Street, Pittsburgh, PA 15261 E-mail: myu1@pitt.edu; jkharouf@pitt.edu; maillart@pitt.edu
Jeffrey P. Kharoufeh
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, 3700 O'Hara Street, Pittsburgh, PA 15261 E-mail: myu1@pitt.edu; jkharouf@pitt.edu; maillart@pitt.edu
Lisa M. Maillart
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, 3700 O'Hara Street, Pittsburgh, PA 15261 E-mail: myu1@pitt.edu; jkharouf@pitt.edu; maillart@pitt.edu
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Abstract

We examine the problem of optimally maintaining a stochastically degrading system using preventive and reactive replacements. The system's rate of degradation is modulated by an exogenous stochastic environment process, and the system fails when its cumulative degradation level first reaches a fixed deterministic threshold. The objective is to minimize the total expected discounted cost of preventively and reactively replacing such a system over an infinite planning horizon. To this end, we present and analyze a Markov decision process model. It is shown that, for each environment state, there exists an optimal threshold-type replacement policy. Additionally, empirical evidence suggests that, when the environment process is monotone, and the state-dependent degradation rates are totally ordered, the optimal threshold is monotone. Lastly, we derive closed-form bounds on the optimal thresholds.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 3 , July 2012 , pp. 405 - 424
Copyright
Copyright © Cambridge University Press 2012

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