Change point testing for two phase Wiener process with nonlinear drift

With the advancement and development of science and technology, critical equipment in the aerospace and electronics fields has gradually evolved toward multifunctionality, long life, and high reliability. In practical applications, influenced by factors such as changes in their physical and chemical properties, structural modifications, or environmental stress, the degradation processes of equipment exhibit significant differences across various life stages, resulting in a multi-phase degradation pattern. Since degradation modelling serves as the foundation of performance degradation theory, the accuracy of the degradation model in describing performance degradation laws determines the precision of product life assessment and remaining useful life prediction. Therefore, it is important to detect change points in the degradation process and evaluate product reliability or predict remaining useful life based on degradation models incorporating change points. Targeting degradation processes with nonlinear drift terms and two-phase degradation patterns, this paper investigates the change point detection problem for Wiener processes based on the Wiener process. The nonlinear drift term of the Wiener process is approximated using B-spline functions, and a generalized gradient projection algorithm(GPA) is proposed to calculate the maximum likelihood estimates of related parameters. The convergence of the proposed GPA algorithm is rigorously established. For the change point detection problem in Wiener process parameters, a change point detection method based on the MIC criterion is proposed, and the asymptotic distribution of the corresponding statistic is derived. Following simulation studies, extensive sensitivity analysis is conducted to evaluate the robustness of the proposed method. The results demonstrate that the MIC-based change point detection method exhibits superior robustness across various parameter settings, maintaining stable and reliable testing power even under challenging conditions such as small sample sizes and change points located at the boundaries. The proposed method is then applied to the accelerated degradation test data analysis of MOS tubes in the Tiangong series spacecraft. The results indicate that the degradation pattern of the spacecraft MOS tubes changes after the application of stress, necessitating adjustments to the degradation model to accurately predict the remaining useful life of the MOS tubes.