Degradation data contain rich reliability information, providing a novel way to evaluate product reliability, especially for highly reliable products whose lifetime data are scarce. In engineering practice, due to certain unexpected conditions, extreme observations may arise, resulting in heavy-tailed degradation data. However, as a widely used degradation model in the literature, the Wiener process cannot capture the heavy tails, which may cause seriously biased reliability. To this end, we propose a family of heavy-tailed degradation models in this paper, which includes the existing Student-t process model as a member and also produces several new stochastic models. Our models consider the unit-to-unit heterogeneity simultaneously and have nice hierarchical structures that facilitate subsequent inference procedures. Additionally, we develop a simulation-based reliability assessment approach that is applicable to all proposed degradation models. Afterward, we propose an expectation-maximization algorithm to estimate the model parameters. Meanwhile, we conduct a simulation study to verify the proposed estimation method. Finally, our heavy-tailed degradation models are applied to the train wheel data and the infrared light-emitting diode data, and their utility and superiority are clearly demonstrated.
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.
