APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY Appl. Stochastic Models Bus. Ind. 2009; 25:612–631 Published online 2 June 2009 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/asmb.790 Optimal corrective maintenance contract planning for aging multi-state system Yi Ding 1,3, ∗, † , Anatoly Lisnianski 2 , Ilia Frenkel 3 and Lev Khvatskin 3 1 Mechanical Engineering Department, University of Alberta Edmonton, AB, Canada T6G 2G8 2 The Israel Electric Corporation Ltd., P.O. Box 10, Bait Amir, Haifa 3100, Israel 3 Center for Reliability and Risk Management, Sami Shamoon College of Engineering, Beer Sheva, 84100, Israel SUMMARY This paper considers an aging multi-state system, where the system failure rate varies with time. After any failure, maintenance is performed by an external repair team. Repair rate and cost of each repair are determined by a corresponding corrective maintenance contract with a repair team. The service market can provide different kinds of maintenance contracts to the system owner, which also can be changed after each specified time period. The owner of the system would like to determine a series of repair contracts during the system life cycle in order to minimize the total expected cost while satisfying the system availability. Operating cost, repair cost and penalty cost for system failures should be taken into account. The paper proposes a method for determining such optimal series of maintenance contracts. The method is based on the piecewise constant approximation for an increasing failure rate function in order to assess lower and upper bounds of the total expected cost and system availability by using Markov models. The genetic algorithm is used as the optimization technique. Numerical example is presented to illustrate the approach. Copyright 2009 John Wiley & Sons, Ltd. Received 18 June 2008; Revised 1 April 2009; Accepted 2 April 2009 KEY WORDS: maintenance; contract planning; multi-state system; Markov reward model; total expected cost; reliability 1. INTRODUCTION Many technical systems are subjected to aging and degradation during their lifetime. Most of these systems are repairable. Maintenance and repair problems have been widely investigated in the literature. Barlow and Proshan [1], Gertsbakh [2], Valdez-Flores and Feldman [3], Pham and Wang [4], Wang [5] survey and summarize theoretical developments and practical applications of maintenance models. ∗ Correspondence to: Yi Ding, Mechanical Engineering Department, University of Alberta Edmonton, AB, Canada T6G 2G8. † E-mail: dingyi@ntu.edu.sg, yiding@pmail.ntu.edu.sg Copyright 2009 John Wiley & Sons, Ltd.