Optimal maintenance policies for multi-level preventive maintenance with complex effects

Abstract

We consider the problem of optimally maintaining a periodically inspected system with multi-level preventive maintenance whose effects are complex. At each inspection, the maintenance decision concerns whether a preventive maintenance action is needed and which level should be selected if preventive maintenance is desired. The objective is to minimize the total expected discounted cost including inspection and maintenance costs. We formulate an infinite-horizon Markov decision process model and establish sufficient conditions to ensure the existence of an optimal monotone control-limit type policy with respect to the system’s deterioration level and age. We also numerically explore the structure of the optimal policy with respect to two additional system states, the level of the last maintenance action and the time since the last maintenance action. Real-world pavement deterioration data is used in our computational experiments, and the results show that the optimal policy is typically of monotone control-limit type.

Keywords:

• Multi-level preventive maintenance
• complex effects
• Markov decision process
• monotone control-limit policy

Acknowledgements

The authors would like to thank Lisa M. Maillart and her insightful comments which helped us to improve the manuscript. The authors also appreciate constructive comments and suggestions from the Editor and the anonymous referees.

Additional information

Funding

This study is partially supported by the U.S. National Science Foundation through Award 1728257.

Notes on contributors

Yue Shi

Yue Shi is currently a Ph.D. student in the Department of Industrial, Manufacturing & Systems Engineering at Texas Tech University. She received a B.S. degree in E-commerce from Guangdong University of Foreign Studies, Guangzhou, P. R. China, in 2014 and an M.S. degree in management science and engineering from Sun Yat-sen University, Guangzhou, P. R. China, in 2016. Her research interests include maintenance optimization and Markov decision processes. She is a student member of IISE and INFORMS.

Yisha Xiang

Yisha Xiang is an assistant professor in the Department of Industrial, Manufacturing & Systems Engineering at Texas Tech University. She received a B.S. in industrial engineering from Nanjing University of Aeronautics and Astronautics, P.R. China and subsequently was awarded M.S and Ph.D. degrees in industrial engineering by the University of Arkansas. Her current research and teaching interests involve reliability analysis and maintenance optimization. She has published articles in refereed journals, such as IIE Transactions, European Journal of Operational Research, and IEEE Transactions on Reliability. She received the Oftshun Best Paper Award from the Society of Reliability Engineering, and R.A. Evans/P.K. McElroy RAMS Best Conference Paper Award in 2013. She is a member of SRE, IISE, and INFORMS.

Mingyang Li

Mingyang Li is an assistant professor in the Department of Industrial & Management Systems Engineering at the University of South Florida. He received his Ph.D. in systems & industrial engineering and his M.S. in statistics from the University of Arizona in 2015 and 2013, respectively. He also received an M.S. in mechanical & industrial engineering from the University of Iowa in 2010 and a B.S. in control science & engineering from Huazhong University of Science and Technology in 2008. His research interests focus on data analytics and system informatics with diverse applications in reliability & quality, healthcare, energy, homeland security, manufacturing, etc. He is a member of INFORMS, IISE and ASQ.