Optimally maintaining a multi-state system with limited imperfect preventive repairs

Abstract

In this paper, the optimal maintenance policy for a multi-state system with no observation is considered. Different from most existing works, only a limited number of imperfect preventive maintenance actions can be performed between two successive replacements. Assume that the system's deterioration state cannot be observed during its operation expected after each replacement, and it evolves as a discrete-time Markov chain with a finite state space. After choosing the information state as state variable, the problem is then formulated as a Markov decision process over the infinite time horizon. In order to increase the computational efficiency, several key structural properties are developed by minimising the total expected cost per unit time. The existence of the optimal threshold-type maintenance policy is proved and the monotonicity of the threshold is obtained. Finally, a numerical example is given to illustrate the optimal policy.

Keywords:

• maintenance
• replacement
• imperfect maintenance
• Markov decision process
• repair restriction

Acknowledgements

The authors would like to thank the journal editors and the anonymous referees for their helpful comments and suggestions that greatly improve this paper. In addition, this work was supported by the NSFC under grants 61174030 and 61104223.

Additional information

Notes on contributors

Hongdong Fan

Hongdong Fan received his BEng degree in mechanical and electrical engineering, MSc., and PhD degrees in control engineering all from Xi'an Institute of Hi-Tech, Xi'an, China, in 2003, 2006 and 2012, respectively. He is currently a lecturer of Xi'an Institute of Hi-Tech. His current research interest is in the area of reliability analysis, fault prognosis and predictive maintenance.

Zhe Xu

Zhe Xu received his BEng, MSc and PhD degrees in control engineering all from Xi'an Institute of Hi-Tech, Xi'an, China, in 2002, 2005 and 2009, respectively. He is currently a lecturer of Xi'an Institute of Hi-Tech. His current research interest is in the area of reliability analysis, fault prognosis and predictive maintenance.

Shiwei Chen

Shiwei Chen received his BEng, and MSc degrees in control engineering both from Xi'an Institute of Hi-Tech, Xi'an, China, in 2003 and 2006, respectively. He is currently a lecturer of Xi'an Institute of Hi-Tech. His current research interest is in the area of reliability analysis, predictive maintenance and image processing.