A family of heavy-tailed stochastic degradation models

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.