Degradation Modeling under Dual Time Scales Based on an Autoregressive Model

For products suffering degradation, it is of vital importance to model the degradation trend and accordingly schedule maintenance actions. Most of the existing studies consider the degradation under a single time scale. However, the degradation of products in reality often occurs in multiple scales. In particular, most products can degrade along the calendar time as well as the usage. Therefore, this paper proposes a degradation model based on an autoregressive model to capture the degradation indexed by two time scales. The proposed model accounts for the degradation process along the calendar and the usage. The maximum likelihood estimation is used to estimate the model parameters, and the effectiveness of the method is verified by Monte Carlo simulations. A battery degradation dataset is analyzed to compare the proposed model and the existing ones, which demonstrates the superiority of the model.