Optimisation of preventive maintenance policies with replacement first and last for systems subject to shocks

Abstract

This paper addresses preventive replacement policies for operating systems subject to non-homogeneous Poisson process shocks. A shock causes two types of system failures with number-dependent probability: type-I (repairable or minor) failures can be rectified by minimal repair; type-II (non-repairable or catastrophic) failures must be removed by corrective replacement. A preventive replacement model is designed to replace the system before a type-II failure occurs. Similar to conventional replacement models, our model bases replacement on type-II failures at age T or number of working times N; however, contrary to conventional models, our model replaces the system at the last occurring age or working time. Thus, we refer to our model as a preventive replacement last model and existing methods as conventional replacement first models. Comparisons between these models are discussed in detail. The optimal schedule that minimises the mean cost rate of each preventive replacement model is derived analytically and computed numerically. The proposed model provides a general framework for analysing policies and other special cases of previous models.

Keywords:

• optimisation
• preventive maintenance
• random working time
• replacement
• minimal repair
• reliability

Acknowledgements

The author 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 of Taiwan, ROC [grant number MOST103-2410-H-147-004].

Notes on contributors

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. (1988) in Statistics from the National Chengchi University, and his Ph.D. (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.

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 M.Sc. (1988) in Statistics from National Chengchi University, and her Ph.D. (2009) in Business Administration from the National Taiwan University of Science and Technology. Her recent research interests include strategic management, reliability engineering, 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, International Journal of Systems Science, and Communications in Statistics–Theory and Methods, and several other international journals.