Optimal maintenance policies for systems subject to a Markovian operating environment Yisha Xiang a,⇑ , C. Richard Cassady b,1 , Edward A. Pohl b,2 a Sun Yat-sen Business School, Sun Yat-sen University, 135 W. Xingang Rd., Guangzhou 510275, China b Department of Industrial Engineering, University of Arkansas, Fayetteville, AR 72701, USA article info Article history: Received 15 March 2011 Received in revised form 7 September 2011 Accepted 9 September 2011 Available online 17 September 2011 Keywords: Stochastic degradation Dynamic environment Condition-based maintenance abstract Many stochastic models of repairable equipment deterioration have been proposed based on the physics of failure and the characteristics of the operating environment, but they often lead to time to failure and residual life distributions that are quite complex mathematically. The first objective of our study is to investigate the potential for approximating these distributions with traditional time to failure distribu- tion. We consider a single-component system subject to a Markovian operating environment such that the system’s instantaneous deterioration rate depends on the state of the environment. The system fails when its cumulative degradation crosses some random threshold. Using a simulation-based approach, we approximate the time to first failure distribution for this system with a Weibull distribution and assess the quality of this approximation. The second objective of our study is to investigate the cost benefit of applying a condition-based maintenance paradigm (as opposite to a scheduled maintenance paradigm) to the repairable system of interest. Using our simulation model, we assess the cost benefits resulting from condition-based maintenance policy, and also the impact of the random prognostic error in estimat- ing system condition (health) on the cost benefits of the condition-based maintenance policy. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction A repairable system is a device or unit of equipment which after failure can be restored to an operating condition by maintenance actions including but not limited to replacing the entire system. The maintenance of a repairable system may include not only re- sponses to failures, but also actions intended to delay failures and improve the day-to-day performance of the system. Most industrial and military organizations depend upon the effective operation of individual repairable systems or fleets of repairable systems (e.g. vehicles, machines, etc.) to successfully complete their mission. In order to keep the system operating at a desirable condition, scheduled maintenance actions have traditionally been used to delay or prevent system failure. Scheduled maintenance is initiated based on some measure of elapsed time, and maintenance sched- ules are determined typically using a probabilistic model of repairable system operation, failure, and maintenance. The litera- ture on the use of mathematical modeling for analyzing and optimizing scheduled maintenance plans is extensive. Early re- views on scheduled maintenance include Pierskalla and Voelker (1976), Sherif and Smith (1981), Valdez-Flores and Feldman (1989), Cho and Parlar (1991) and Wang (2002). More recent work of scheduled maintenance in industrial applications can be found in Das and Acharya (2004), Budai, Huisman, and Dekker (2006), Kenné, Gharbi, and Beit (2007), Panagiotidou and Tagaras (2007), Alardhi and Labib (2008), Canto (2008), Samrout, Châtelet, Kouta, and Chebbo (2009) and Moghaddam and Usher (2011). Because scheduled maintenance policies are based on probabi- listic time to failure models, implementing scheduled maintenance policies does not eliminate the risk of system failure and implies that systems in an operating condition will be shut down for maintenance. Recently, condition-based maintenance policies have received more and more attentions. This type of policies takes into account updated risks of failure, and suggests system inspection and maintenance action based on the currently observed system state (Liao, Elsayed, & Chan, 2006). The ultimate aim of condi- tion-based maintenance is to eliminate the wasted operating time and risk of failure associated with using a scheduled maintenance policy. The available accurate sensor technologies that can continuously provide performance indicators at low cost make condition-based maintenance more appealing. Sensor data on system condition (health), especially if it is collected in real time, can be analyzed so that maintenance technicians can intervene 0360-8352/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2011.09.006 ⇑ Corresponding author. Tel.: +86 20 84112601; fax: +86 20 84036588. E-mail addresses: xiangysh@mail.sysu.edu.cn (Y. Xiang), cassady@uark.edu (C.R. Cassady), epohl@uark.edu (E.A. Pohl). 1 Tel.: +1 479 5756735. 2 Tel.: +1 479 5756042. Computers & Industrial Engineering 62 (2012) 190–197 Contents lists available at SciVerse ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie