Bayesian Reliability Assessment of Birnbaum–Saunders Model With Partial Prior Information Using Improved Adaptive Progressively Censored Samples

This paper investigates inference for the Birnbaum–Saunders lifetime model under an improved adaptive Type-II progressive censoring scheme. We develop both classical and Bayesian methodologies to estimate model parameters, the reliability function, and the hazard rate. In the classical approach, maximum likelihood estimators are derived by numerically solving the score equations, and approximate confidence intervals are constructed using normal approximations on both the original and log-transformed scales to adhere to parameter bounds. In the Bayesian approach, we consider Jeffreys’ prior as well as a prior that incorporates partial prior information. Posterior computations are conducted using Markov chain Monte Carlo methods, specifically employing a Metropolis–Hastings algorithm calibrated from the observed information. This yields posterior means, equal-tailed Bayesian credible intervals, and highest posterior density intervals for the parameters and reliability measures. A simulation study assesses the root-mean-square error, empirical coverage probability, and average interval length across various censoring levels and test-plan settings. Two real-data examples are presented to illustrate the implementation and interpretation of the proposed methodologies. The results underscore the advantages of the improved censoring scheme in obtaining informative samples within predetermined timeframes.