Generalized degradation reliability model considering phase transition

Aiming to evaluate the reliability of phase-transition degrading systems, a generalized stochastic degradation model with phase transition is constructed, and the corresponding analytical reliability function is formulated under the concept of the first hitting time. The phase-varying stochastic property and the phase-varying nonlinearity are considered simultaneously in the proposed model. To capture the phase-varying stochastic property, a Wiener process is adopted to model the non -monotonous degradation phase, while a Gamma process is utilized to model the monotonous one. In addition, the phase-varying non linearity is captured by different transformed time scale functions. To facilitate the practical application of the proposed model, identification of phase model type and estimation of model parameters are discussed, and the initial guesses for parameters optimization are also given. Based on the constructed model, two simulation studies are carried out to verify the analytical reliability function and analyze the influence of model misspecification. Finally, a practical case study is conducted for illustration.