Reliability Prediction Using Physics–Statistics-Based Degradation Model

The reliability and life predictions of products using small samples represent a major challenge to reliability engineers. In this paper, we develop a physics-statistics (P-S)-based model and an adaptive Kalman filter approach for reliability and life predictions. The P-S-based model combines the physics-of-failure models with the statistics models to consider the randomness among identical products. The degradation path is modeled with a time-scale transformation Brownian motion with drift, which is updated by the Kalman filter. Time-scale transformation is used to adapt the linearly increasing drift for modeling a nonlinear degradation process. The degradation of units over time is used to obtain the parameters of the proposed model. The parameters in the model are estimated using the maximum-likelihood estimation and particle swarm optimization methods with the accelerated degradation data, so that it provides more prior information and the empirical model for reliability prediction. The validity of the proposed approach is demonstrated with an illustrative example using the data collected from an accelerated degradation test of accelerometers. The proposed method is compared with the basic one in terms of their accuracy of reliability and life predictions.