ABSTRACT
Maintenance planning and optimizations are very important issues in both theory and practice. In this paper, Hawkes processes, a tool for description of self-excited failure effects, are used to model the failure processes of single-unit systems under the assumption of neglected repair times. For such degraded single-unit systems, some maintenance planning estimations such as the distribution, mean and variance of failures or repairs by time , reliability, mean cost of maintenance, mean and variance of system lifetime are presented under the maximal entropy assumption on repair effects. Meanwhile, two optimization problems are developed by considering the lifetime mean of the single-unit system and total maintenance cost as objective functions and constraints alternatively. We have proved that both optimization problems can reduce to two simplified optimal cases, respectively, and their optimal policies are increasing stepwise sequences of increasing rates of failure rates, which greatly reduce the scope of optimal solutions. The relationships between the estimations and the optimizations are discussed. Furthermore, the detailed optimal maintenance policies for a special case are given as well including an algorithm.
Acknowledgments
This work is supported by NSFC under grant 71871021. We thank the AE and two referees for their suggestions on improving the paper.
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No potential conflict of interest was reported by the author(s).
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Notes on contributors
Lirong Cui
Mr. Kang is now my PhD student, and Dr. Shen was my former PhD student, Dr. Shen is an associate professor in School of Economics & Management, Nanjing University of Science & Technology, Nanjing, China. Cui is me, the author of this paper.