Designing optimal proactive replacement strategies for degraded systems subject to two types of external shocks

Abstract

This article mainly investigates a proactive replacement policy for a stochastically deteriorating system concurrently subject to two types of shocks. First, the closed-form representation of system reliability function suffering from both a degradation process and environmental shocks is derived based on the degradation-threshold-failure (DTS) modeling framework. An age- and state-dependent competing risks model with mutual dependence between the two failure processes is embedded into system reliability modeling, where two types of shocks are taken into consideration upon arrival of an external shock including a minor one and a major one. Based on which, a bivariate maintenance policy is put forward for the deteriorating system, where the system is proactively replaced before failure at a planned time, or at an appropriate number of minimal repairs, whichever takes place first. The expected long-run cost rate (ELRCR) is formulated, and optimal solutions are evaluated analytically for two special cases. Finally, an illustrative example is redesigned to validate the theoretical results, exploring the significance of two types of shocks and mutual dependence in system reliability modeling, and illustrating the potential applications in maintenance decisions in various manufacturing systems.

Keywords:

• Degradation modeling
• two types of shocks
• mutual dependence
• proactive replacement
• optimization

Disclosure statement

The authors report there are no competing interests to declare.

Acknowledgments

The authors appreciate the valuable suggestions from the Associate Editor and anonymous reviewers in improving the original manuscript. In addition, the first author would like to specially thank Prof. Shey-Huei Sheu and Prof. Xufeng Zhao for their supportive suggestions in exchanging opinions.

Additional information

Funding

This work was partly supported by the National Natural Science Foundation of China under grant numbers 72271124 and 72071111, the Talent Research Start-up Fund in NUAA under grant number 1009-YAH21001, a Project funded by China Postdoctoral Science Fundation under grant number 2022M721596, Jiangsu Funding Program for Excellent Postdoctoral Talent under grant number 2022ZB222, and an Open Fund of Jiangsu Province Key Laboratory of Aerospace Power System under grant number CEPE2022002.