Reliability modeling of systems considering the mutual dependence between degradation and shock processes with threshold effects

This paper develops a reliability model for systems subject to coupled degradation and shock processes with mutual dependence. Unlike existing models that typically assume a single failure threshold and a homogeneous degradation process, the proposed model introduces a three-stage threshold mechanism to capture multi-phase degradation behavior. In the proposed model, degradation levels determine the impact of shock damage, while the degradation rate and volatility are dynamically modified by the cumulative effects of shocks. This state-dependent interaction enables the model to describe nonlinear degradation trajectories with distinct transition stages. Two modeling approaches are considered, including a general path model and a Wiener process-based model. An analytical reliability expression is derived for the general path model, while a numerical solution is developed for the Wiener process model. Monte Carlo simulations are conducted to demonstrate the effectiveness of the proposed method. The results show that the proposed model provides a more flexible and realistic framework for reliability analysis of systems with staged deterioration processes.