Reliability Assessment of Harmonic Reducers Based on the Two-Phase Hybrid Stochastic Degradation Process

Harmonic reducers exhibit non-stationary and phase-dependent degradation behavior during long-term service, challenging the ability of classical stochastic degradation models to accurately assess reliability. To address phase-dependent differences in degradation behavior, this paper proposes a reliability assessment model based on a two-phase hybrid stochastic degradation process. In the proposed framework, the Wiener process is employed to characterize early-phase gradual degradation dominated by stochastic fluctuations, while the Inverse Gaussian process is used to describe later-phase monotonically accelerated degradation driven by cumulative damage. The framework allows for sample-level variability in transition times to more realistically capture individual degradation behavior. The Schwarz Information Criterion is also adopted to detect change points. Maximum likelihood estimation is performed for model parameter inference, and analytical expressions for the reliability function, cumulative distribution function, and probability density function are derived. Numerical results indicate that a change point exists for each tested product and that the proposed model achieves the best goodness of fit among the considered candidates, demonstrating its superiority in capturing phase-dependent characteristics of harmonic reducer degradation. In terms of reliability assessment bias, the proposed model (0.06%) significantly outperforms the Wiener degradation model (32%) and the IG degradation model (9.9%). These results further confirm that, under an identical failure threshold, the proposed approach yields more accurate and realistic reliability assessment outcomes.