Reliability Analysis for Systems Working in Dynamic Environment With Dependent Competing Failure Processes

ABSTRACT This paper aims to conduct the reliability analysis for systems working in random environments. The system's internal degradation follows a gamma process, whereas external environmental shocks follow a Poisson process. The environment varies over time, which is characterized by a continuous‐time Markov process. In different environments, both the system degradation evolution and shock occurrence process are different. A shock either fails the system immediately or increases its degradation amount, which depends on the shock load. The soft failure of the system takes place when the system's total degradation amount exceeds a given threshold. The system breaks down when a soft failure occurs or a hard failure occurs, whichever occurs first. Based on the technique of Laplace–Stieltjes (L‐S) transform and matrix operation, an analytical formula of the reliability function is obtained in the form of double L‐S transform. An approximate algorithm is developed to calculate the reliability of the system efficiently. Finally, examples are provided to show the effectiveness of the proposed method and the applicability of our model.