A Two-phase General Path Model with Random Initiation Time

Lots of products exhibit a two-phase degradation pattern. Although plenty of models have been developed to describe the two-phase degradation phenomenon, seldom of them consider the random initial degradation problem. In this paper, we assume that the initial degradation is induced by an early degradation before the start of degradation test. Based on this assumption, a two-phase general path model is proposed with consideration of random initiation time. Unit-to-unit variability of degradation rates and changing time is also considered in the proposed model. A three-step procedure combines least square method and maximum likelihood method is developed for model parameter estimation. Monte Carlo simulation is employed for reliability assessment. In the simulation study, the parameter estimation procedure performs a satisfactory result in a group of simulated data. Finally, the proposed model is applied to a dataset of lithium-ion battery degradation, and reliability of the battery is assessed based on a 20% capacity degradation rate.