Reliability Analysis of Lithium-Ion Battery Aging Lifetime Based on Adaptive Progressive Type-II Censored Data

Lithium-ion battery accelerated aging tests are costly and use small samples, while conventional censoring ignores electrochemical degradation dynamics and biases lifetime estimates. The power Rayleigh distribution has a monotonically increasing hazard rate consistent with aging from solid electrolyte interphase thickening and lithium plating. We combine it with adaptive progressive Type-II censoring that stops early sample withdrawals once failure capacity crosses the end-of-life threshold, preserving right tail degradation information. Parameters are estimated by maximum likelihood with multiple starts and limited memory BFGS, and by hybrid Metropolis–Hastings Markov chain Monte Carlo Bayesian inference, validated by Monte Carlo simulation and NASA 4 °C cycling data. Mild censoring retains roughly 10% more right tail information than heavy censoring. For point estimation, maximum likelihood has slightly lower bias for the moderate sample (n = 66), whereas Bayesian estimation is more robust under small sample censoring (n = 40); the highest posterior density credible interval is on average 12% narrower than the asymptotic interval while keeping nominal coverage. Although this distribution reparametrizes the two-parameter Weibull family with identical fit indices, its Shannon entropy and quantile functions have elementary closed forms, avoiding nested numerical integration and delivering about 740 times faster Bayesian sampling per chain with better numerical stability for onboard computation. Sensitivity analysis shows removing one extreme cell weakens the fit, so the framework suits homogeneous cell subpopulations under uniform conditions. Validation remains limited to low-temperature cycling; extending it to combined temperature and charge rate stresses is our immediate priority.