In this paper, a novel life test plan termed adaptive progressive first-failure censoring scheme is introduced. Under this scheme, statistical inference for the Weibull distribution is discussed utilizing both classical and Bayesian approaches. In classical inference, maximum likelihood estimates (MLEs) are derived, and asymptotic confidence intervals (ACIs) are constructed through the Fisher information matrix (FIM), allowing for reliable interval estimation. For Bayesian inference, the Markov chain Monte Carlo (MCMC) technique is provided to acquire Bayesian estimates based on a proposed method for eliciting the hyperparameters. In this context, the Bayesian estimates are obtained under both symmetric and asymmetric loss functions, and the corresponding credible intervals (CRIs) are also constructed. Besides, the Gelman-Rubin convergence statistic is utilized to assess the convergence of the MCMC simulations. Real-life data is provided for methodology elucidation purposes. Finally, computational results derived from Monte Carlo simulations are presented to assess the performance of the proposed methods and to examine the effect of time T on estimation efficiency.
Abdullah Fathi (Sat,) studied this question.