Optimally maintaining a Markovian deteriorating system with limited imperfect repairs

• Published in: European journal of operational research Vol. 205; no. 2; pp. 368 - 380
• Main Authors: Kurt, Murat, Kharoufeh, Jeffrey P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2010; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Cost reduction; Decision making models; Decision theory. Utility theory; Exact sciences and technology; Limited repairs; Markov analysis; Markov decision processes; Operational research and scientific management; Operational research. Management science; Reliability; Reliability Limited repairs Threshold-type policy Markov decision processes; Reliability theory. Replacement problems; Repair & maintenance; Studies; Threshold-type policy; Threshold-type policy; Markov decision processes; Reliability; Limited repairs; Markov process; Costs; Markov decision; Inspection policy; Discount; Markovian system; Decision making; Replacement problem; Optimal policy; Rupture; Replacement; Maintenance; Markov model; Discrete time processes; Failures; Defect; Cost function; Infinite horizon; Repair; Monitoring
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2010.01.009

We consider the problem of optimally maintaining a periodically inspected system that deteriorates according to a discrete-time Markov process and has a limit on the number of repairs that can be performed before it must be replaced. After each inspection, a decision maker must decide whether to repair the system, replace it with a new one, or leave it operating until the next inspection, where each repair makes the system more susceptible to future deterioration. If the system is found to be failed at an inspection, then it must be either repaired or replaced with a new one at an additional penalty cost. The objective is to minimize the total expected discounted cost due to operation, inspection, maintenance, replacement and failure. We formulate an infinite-horizon Markov decision process model and derive key structural properties of the resulting optimal cost function that are sufficient to establish the existence of an optimal threshold-type policy with respect to the system’s deterioration level and cumulative number of repairs. We also explore the sensitivity of the optimal policy to inspection, repair and replacement costs. Numerical examples are presented to illustrate the structure and the sensitivity of the optimal policy.