A generalized reliability analysis framework for dependent competing failure processes with dynamic-zoned shocks

The increasing integration of intelligent systems and harsh operational environments has led to complex interactions between random shocks and natural degradation, making it critical to capture the dynamic reliability behavior of such systems. Traditional reliability models typically focus on failure probabilities or failure rates, lacking the ability to describe the continuous evolution of system states. To address this limitation, this paper proposes a generalized reliability analysis framework for Dependent Competing Failure Processes with Dynamic-Zoned Shocks (DCFP-DS), with a particular focus on the evolution of probability density functions (PDFs). First, a novel modeling approach is introduced by defining dynamic-zoned shocks, which systematically characterize the bidirectional dependency between degradation and shocks. The reliability model is then formulated using Piecewise-Deterministic Markov Processes (PDMPs) to unify continuous degradation and discrete shock events. To analyze the probabilistic dynamics, stochastic semigroup theory is employed to derive the Probability Density Evolution Equation (PDEE), providing a rigorous operator-theoretic foundation for modeling state evolution. For solving the resulting PDEEs efficiently, the Physics-Informed Neural Network (PINN) method is incorporated as a mesh-free computational scheme. Finally, the proposed framework is applied to a micro-electro-mechanical system (MEMS) case study. The results demonstrate the framework’s capability in capturing the state evolution and improving the accuracy and interpretability of reliability analysis under complex failure mechanisms.