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Reliability modeling and optimal maintenance strategies for stochastically deteriorating systems with random degradation latency

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Abstract

This paper mainly deals with the reliability modeling and optimal preventive replacement policies for a stochastically deteriorating system with random shocks. Specifically, the system is subject to stochastic performance deterioration, in which it is described with a Gamma process and degrades after a random degradation latency period. At the same time, a random shock process with a non-homogenous Poisson process is incorporated into system degradation modeling, where two kinds of shock effectiveness are formed upon arrival. The dependence between the degradation-induced failure and the shock-induced failure is bidirectional in this research. Based on system survival function, a periodic replacement policy and an inspection replacement policy are respectively investigated. The optimal solutions to the two preventive replacement policies are sought analytically and their resulting long-run average cost rates are compared to decide which one is more profitable. Finally, an illustrative example of the gas insulated transmission line is surveyed to validate the theoretical results, demonstrating that the random degradation onset time and two kinds of shocks are significant factors to system reliability evaluation and maintenance decisions.

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Acknowledgements

The manuscript is an extension of the oral report presented on the 27th International Conference on Industrial Engineering and Engineering Management (IE&EM 2023). The authors would like to thank Prof. Xufeng Zhao from Nanjing University of Aeronautics and Astronautics for his kind help. All constructive comments from the professional reviewers are taken into account. In addition, this work was partly supported by the National Natural Science grant number of National Natural Science Foundation of China: 72401132, 72371128, 72271124, 72271120 and 72071111, the Fundamental Research Funds for the Central Universities under grant number NS2023043, a project funded by China Postdoctoral Science Fundation under grant number 2022M721596, Jiangsu Funding Program for Excellent Postdoctoral Talent under grant number 2022ZB222, and the Natural Science Foundation of Jiangsu Province under grant number BK20230870.

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Authors and Affiliations

  1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, People’s Republic of China

    Wenjie Dong & Jingru Zhang

  2. College of Management, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    Yingsai Cao

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  1. Wenjie Dong
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Correspondence to Wenjie Dong.

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Dong, W., Cao, Y. & Zhang, J. Reliability modeling and optimal maintenance strategies for stochastically deteriorating systems with random degradation latency. Ann Oper Res 345, 105–124 (2025). https://doi.org/10.1007/s10479-024-06334-5

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  • DOI: https://doi.org/10.1007/s10479-024-06334-5

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