Bayesian Analysis of Accelerated Trend Renewal Processes With Application to Lithium-Ion Battery Data

During battery reliability tests, quality characteristic (QC) values like capacitance, voltage, or current are repeatedly observed during the cyclic charge-discharge processes. The battery's lifetime is determined by the first cycle where QC values drop below a specific threshold. Despite the recurrent nature of this cyclic data, performance declines with each charge-discharge cycle. The trend renewal process (TRP) transforms this periodic data through a trend function to ensure independent and stationary increments in the transformed data. However, combining the trend function with the renewal distribution complicates the resulting likelihood function. In typical battery reliability tests, sample sizes are small, and batteries exhibit heterogeneous differences. This article examines the inverse Gaussian accelerated trend-renewal process (ATRP) model for analyzing discharge-capacity battery data under various discharge currents, with model parameters being log-linear in discharge current. A hierarchical Bayesian approach is employed for three ATRP random-effects models, introducing latent variables to capture unit-to-unit variation among batteries. By selecting the most appropriate model based on the largest log marginal likelihood, predictive lifetime inference under normal discharging current is derived using the Markov chain Monte Carlo procedure. Monte-Carlo simulations validate the numerical calculations, and the proposed method is successfully applied to lithium-ion battery accelerated degradation test data.