Reliability analysis for a system experiencing dependent degradation processes and random shocks based on a nonlinear Wiener process model

Complex systems usually fail due to competing failure modes caused by multiple degradation processes (i.e., soft failures) and random shocks (i.e., hard failures). The dependence of these competing failure modes, including the one among the degradation processes and the one between degradation and random shocks, must be considered in reliability analysis. In this paper, a more general reliability model that takes into account such complex dependence is developed based on a nonlinear Wiener process model and time-varying copula method. First, the nonlinear Wiener process model is used to characterize the degradation behavior of the system. Then, the impact of random shocks on the increments and rate of a degradation process along with the impact of the degradation process on random shocks are investigated. The role of the time-varying copula method is to characterize the dependence among multiple failure processes. A numerical example and a real application on a type of MEMS oscillator are provided to illustrate the use of the proposed mathematical model in practice, and a sensitivity analysis is conducted to gain insights into the impact of key parameters of random shocks on system reliability.