Two-phase degradation data analysis with change-point detection based on Gaussian process degradation model

Degradation paths of the products exhibiting two-phase patterns are commonly seen in practice due to the changeable internal mechanisms and external environments. In this paper, we propose a two-phase Gaussian process (TPGP) degradation model with a change-point, which comprises the Wiener process-based change-point models as special cases, to describe the degradation paths with two-phase patterns. The change-point is used to represent the transition of degradation characteristics. The degradation rates and variations in the two phases are assumed to be different. Therefore, both monotonically increasing and decreasing or nonmonotonic dispersion trends and complicated auto-correlations in the degradation measurements can be captured by TPGP. Joint methods of the parameter estimation and change-point detection is developed for two different engineering scenarios. The distributions of the first passage time and the remaining useful life are derived in closed-form to promote the mathematical trackability and the applicability of the TPGP model. A comprehensive simulation study shows the effectiveness and validity of the proposed model and method. Finally, we use two real applications to demonstrate the proposed models and methods.