Reliability and maintenance of systems subject to Gamma degradation and shocks in dynamic environments

• Published in: Applied Mathematical Modelling 2021-08, Vol.96, p.367-381
• Main Authors: Wu, Bei, Cui, Lirong, Yin, Juan
• Format: Article
• Language: English
• Subjects: Algorithms; Computer simulation; Cumulative damage; Degradation; Distribution functions; Dynamic environment; First passage time; Gamma process; Lithium-ion batteries; Monte Carlo simulation; Random shock; Rechargeable batteries; Reliability analysis; System availability; Wear
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2021.03.009

•A system subject to both shocks and environment-affected degradation is investigated.•Maintenance actions related to randomly evolving environments are considered.•Explicit formulas for the cumulative distribution function of first passage time and system availability are derived.•A Monte Carlo simulation algorithm for computing the system first passage time is provided.•A detailed case study is conducted to demonstrate derived formulas. Many systems or devices may experience degradation and shocks simultaneously whose behaviors may have discrepancies in different system operating environments. In this paper, a reliability model is developed for systems subject to both sudden shocks and natural wear processes in randomly evolving environments. The natural wear behavior of the system under different environment is governed by a distinct Gamma process. The system fails when the overall degradation which contains the natural wear and the cumulative damage caused by previous arrival shocks hits a preset threshold. To calculate the cumulative distribution function of the first passage time, the explicit computation formula based on analytical methods and the simulation algorithm based on Monte Carlo simulation methods are provided, which could verify each other. Further, a corrective replacement policy is considered in the case where the environment switching process takes place only when the system is functioning, and then the formula for the system availability is analytically derived. Finally, a study case of the lithium-ion battery is given to illustrate the proposed model and obtained results.