Reliability modeling of two-phase nonlinear exponential diffusion processes with random effects

This research introduces a novel two-phase Tweedie Exponential Dispersion (TED) process model incorporating random effects to address the critical challenge of modeling multi-phase degradation processes with unit-to-unit variability for Remaining Useful Life (RUL) prediction. Conventional stochastic processes, including Wiener and Inverse Gaussian (IG) processes, demonstrate limited capability in universally characterizing heterogeneous degradation paths and inherent phase transitions. The proposed TED process framework effectively subsumes these classical models, offering superior flexibility through its exponential dispersion structure. The methodology derives RUL distributions based on First Passage Time (FPT) theory, employing saddle point approximation to resolve analytical intractability. Furthermore, a Bayesian hierarchical framework is implemented, utilizing Gibbs sampling for robust parameter estimation in high-dimensional spaces. Comprehensive simulation studies and an empirical case analysis confirm the model’s enhanced performance in identifying phase-change points and generating accurate RUL predictions compared to conventional phase-type stochastic processes. This investigation establishes a theoretically grounded and statistically rigorous approach for prognostic and health management of complex engineering systems.