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

Abstract

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.