Algorithms and approximations for the modified Weibull model under censoring with application to the lifetimes of electrical appliances

The modified Weibull model (MWM) is one of the type-2 Weibull distributions that can be used for modeling lifetime data. It is important due to its simplicity and flexibility of the failure rate, and ease of parameter estimation using the least squares method. In this study, we introduce novel methods for estimating the parameters in step-stress partially accelerated life testing (SSPALT) in the context of progressive Type-II censoring (PT-II) under Constant-Barrier Removals (CBRs) for the MWM. We conduct a comparative analysis between Expectation Maximization (EM) and Stochastic Expectation Maximization (SEM) techniques with Bayes estimators under Markov Chain Monte Carlo (MCMC) methods. Specifically, we focus on Replica Exchange MCMC, the Hamiltonian Monte Carlo (HMC) algorithm, and the Riemann Manifold Hamiltonian Monte Carlo (RMHMC), emphasizing the use of the Linear Exponential (LINEX) loss function. Additionally, highest posterior density (HPD) intervals derived from the RMHMC sampler consistently outperform asymptotic and bootstrap confidence intervals, providing the shortest credible regions while maintaining nominal coverage across all censoring levels and stress conditions. A comprehensive Monte Carlo simulation study is conducted to assess the performance of these methods. Furthermore, the proposed methodology is applied to a real dataset comprising lifetimes of electrical appliances, demonstrating the practical effectiveness of the MWM in modeling real-world reliability data. Results show that the Bayesian RMHMC approach offers superior accuracy and convergence properties.