Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance

Abstract

This paper proposes the generalised random and age replacement policies for a multi-state system composed of multi-state elements. The degradation of the multi-state element is assumed to follow the non-homogeneous continuous time Markov process which is a continuous time and discrete state process. A recursive approach is presented to efficiently compute the time-dependent state probability distribution of the multi-state element. The state and performance distribution of the entire multi-state system is evaluated via the combination of the stochastic process and the Lz-transform method. The concept of customer-centred reliability measure is developed based on the system performance and the customer demand. We develop the random and age replacement policies for an aging multi-state system subject to imperfect maintenance in a failure (or unacceptable) state. For each policy, the optimum replacement schedule which minimises the mean cost rate is derived analytically and discussed numerically.

Keywords:

• maintenance
• optimisation
• reliability
• multi-state system
• non-homogeneous continuous time Markov process

Acknowledgements

The authors would like to thank the referees for their insightful comments and suggestions, which greatly enhanced the clarity of the article. All of the suggestions were incorporated directly in the text.

Additional information

Funding

This research was supported by the Ministry of Science and Technology, Taiwan, ROC [grant number NSC 102-2410-H-147-008], [grant number NSC102-2410-H-147-001].

Notes on contributors

Yen-Luan Chen

Yen-Luan Chen is an associate professor of the Department of Marketing Management at Takming University of Science and Technology. She received her MSc degree (1988) in statistics from National Chengchi University, and her PhD degree (2009) in business administration from the National Taiwan University of Science and Technology. Her recent research interests include reliability engineering, strategic management and statistics. Her publications have appeared in journals such as IEEE Transactions on Reliability, Emerging Markets Finance and Trade, Computers & Industrial Engineering, Applied Mathematical Modelling, and Communications in Statistics – Theory and Methods and several other international journals.

Chin-Chih Chang

Chin-Chih Chang is an assistant professor of the Department of Chains and Franchising Management at Takming University of Science and Technology. He received his M.Sc. degree (1988) in statistics from the National Chengchi University, and his PhD degree (2009) in industrial management from the National Taiwan University of Science and Technology. His current research interests include reliability engineering, maintenance policy and statistics. His publications have appeared in journals such as European Journal of Operational Research, IEEE Transactions on Reliability, International Journal of Systems Science, Computers & Industrial Engineering, Applied Mathematical Modelling and several other international journals.

Dwan-Fang Sheu

Dwan-Fang Sheu is an associate professor of the Department of Logistics Management at Takming University of Science and Technology. She received her MBA degree (1989) from Temple University in USA, and her PhD degree (2002) in management from the National Chiao Tung University in Taiwan. Her recent research focuses on management include inventory management and financial management. Her publications have appeared or accepted in journals such as Management Decision.