Accelerated Degradation Process Analysis Based on the Generalized Wiener Process with Mixed Random Effects

This paper investigates degradation modeling and failure time prediction for constant-stress accelerated degradation tests (CSADT) using a generalized Wiener process. Owing to differences in manufacturing processes and operating environments, the degradation trajectories may vary across individual units of the same product. To more accurately characterize such complex degradation behavior, this paper proposes a generalized Wiener process model with mixed random effects that account for heterogeneity in both the drift coefficient and the diffusion coefficient, and develops corresponding parameter estimation methods. Using the total probability formula, we derive an approximate expression for the probability density function (PDF) of the failure time distribution, thereby providing a theoretical basis for product reliability assessment. The necessity of the proposed model is verified through simulation examples, and a case study on circuit voltage performance degradation demonstrates the effectiveness and practicality of the proposed model. The results show that the proposed model can improve the accuracy of product failure time and reliability predictions, demonstrating its practical value in engineering applications.