Abstract
The semi-Markov decision model is a powerful tool in analyzing sequential decision processes with random decision epochs for a multi-state deteriorating system subject to aging and fatal shocks. In this paper, we propose a model for a two-unit standby system where a cold standby unit is attached to an operating (active) one. For this model, the active unit goes through a finite number of states of successive degradation preceding the failure, while the other one is in cold standby state. At each deterioration state of the active unit, two types of maintenance are considered, minimal and major, depending on the degrading level. The minimal maintenance aims to improve the degradation of the unit by recovering it to the previous degradation stage. The maximum allowable number of minimal maintenances for all states of the active unit must not exceed a certain limit. On the other hand, the major maintenance is necessary when the active unit fails. Once this maintenance is completed, the unit is restored to as good as new. To make the system operate more time without any interruption, the standby unit can be switched online until the active unit finishes its minimal or major maintenance. The switch between the two units is perfect and switchover is instantaneous. After using the standby unit, it is serviced or overhauled to maintain it in as good as new state. We use an iterative numerical approach, based on the policy iteration method, to drive the optimal state-dependent maintenance policy that minimizes the long-run expected cost rate of the system. Finally, numerical examples are given to illustrate and evaluate the performance of the proposed policy.
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References
Sim SH, Endrenyi J (1988) Optimal preventive maintenance with repair. IEEE Trans Reliab 37:92–96
Legat V, Zaludova AH, Cervenka V, Jurca V (1996) Contribution to optimization of preventive maintenance. Reliab Eng Syst Saf 51:259–266
Chen D, Trivedi KS (2005) Optimization for condition-based maintenance with semi-Markov decision process. Reliab Eng Syst Saf 90:25–29
Vaurio J (1997) On time-dependent availability and maintenance optimization of standby units under various maintenance policies. Reliab Eng Syst Saf 56:79–89
Moustafa MS, Abdel Maksoud EY, Sadek S (2004) Optimal major and minimal maintenance policies for deteriorating systems. Reliab Eng Syst Saf 83:363–368
Sherif YS, Smith ML (1981) Optimal maintenance models for systems subject to failure: a survey. Naval Res Logist Quart 28:47–74
Valdez-Flores C, Feldman RM (1989) A survey of preventive maintenance models for stochastically deteriorating single-unit systems. Naval Res Logist Quart 36:419–446
Lam CT, Yeh RH (1994) Optimal maintenance policies for deteriorating systems under various maintenance strategies. IEEE Trans Reliab 43:423–430
Dekker R (1996) Applications of maintenance optimization models: a review and analysis. Reliab Eng Syst Saf 51:229–240
Scarf PA (1997) On the application of mathematical models in maintenance. Eur J Oper Res 99:493–506
Wang H (2002) A survey of maintenance policies of deteriorating systems. Eur J Oper Res 139:469–489
Chiang JH, Yuan J (2001) Optimal maintenance policy for a Markovian system under periodic inspection. Reliab Eng Syst Saf 71:165–172
Yeh RH (1997) Optimal state-dependent replacement policy for deteriorating systems. Reliability. Qual Saf Eng 4:349–356
Chen M, Feldman RM (1997) Optimal replacement policies with minimal repair and age-dependent costs. Eur J Oper Res 98:75–84
Ross SM (1992) Applied probability models with optimization applications. Dover, New York
Ohnishi M, Kawai H, Mine H (1986) An optimal inspection and replacement policy for a deteriorating system. Appl Probab 23:973–988
Tijms HC (1994) Stochastic models: an algorithmic approach. Wiley, Chichester
Taha HA (2003) Operation research: an introduction. Prentice Hall, New Jersey
Van der Duyn Schouten FA, Wartenhorst P (1994) Transient analysis of a two-unit standby system. Manage Soc 40:418–428
Zhang YL (1999) An optimal geometric process model for a cold standby repairable system. Reliab Eng Syst Saf 63:107–110
Montoro-Cazorla D, Perez-Ocon R (2006) A deteriorating two-system with two repair modes and sojourn times phase-type distributed. Reliab Eng Syst Saf 91:1–9
So KC (1992) Optimality of control limits policies in replacement models. Naval Res Logist Quart 21:685–697
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The authors would like to thank the referees for their highly valuable comments and suggestions that greatly enhanced the contribution and the clarity of the paper. All of their suggestions were incorporated directly in the text.
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Abdel Maksoud, E.Y., Moustafa, M.S. A semi-Markov decision algorithm for the optimal maintenance of a multistage deteriorating two-unit standby system. Oper Res Int J 9, 167–182 (2009). https://doi.org/10.1007/s12351-008-0022-6
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DOI: https://doi.org/10.1007/s12351-008-0022-6