Xinyu Wu

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.

This paper investigates statistical inference for the Shannon entropy of the Transmuted Weibull Distribution under progressively Type-II censored samples. The Transmuted Weibull Distribution is obtained by applying the quadratic rank transmutation map to the cumulative distribution function of the two-parameter Weibull distribution, thereby substantially enhancing its modeling flexibility while preserving the analytical tractability of the baseline distribution. Consequently, it provides greater flexibility for modeling lifetime data exhibiting pronounced skewness and complex hazard rate behaviors. First, a closed-form expression for the Shannon entropy of the Transmuted Weibull Distribution is derived. From a frequentist perspective, the maximum likelihood estimators of the model parameters are obtained numerically using the Newton–Raphson algorithm, and the corresponding maximum likelihood estimator of Shannon entropy is derived through the invariance property of maximum likelihood estimation. To quantify estimation uncertainty, asymptotic confidence intervals are constructed using the Delta method together with the observed Fisher information matrix, while Bootstrap confidence intervals are also developed to improve finite-sample inference. From a Bayesian perspective, posterior inference is conducted using a hybrid Gibbs sampling algorithm within the Markov chain Monte Carlo framework. Bayesian point estimators of Shannon entropy are obtained under the squared error loss function, the absolute error loss function, and the 0–1 loss function, corresponding to the posterior mean, posterior median, and posterior mode, respectively. In addition, highest posterior density credible intervals are constructed for the Shannon entropy. The proposed methods are evaluated through an extensive Monte Carlo simulation study under three representative progressively Type-II censoring schemes. Estimation performance is assessed in terms of bias, mean squared error, interval coverage probability, and average interval length. The simulation results demonstrate that the Bayesian estimators consistently outperform the maximum likelihood estimator, particularly for small sample sizes and heavy censoring, while the highest posterior density credible intervals achieve more accurate coverage probabilities and shorter interval lengths. Finally, the proposed inferential procedures are illustrated using a real dataset consisting of remission times from 128 bladder cancer patients, demonstrating their practical applicability and robustness.