Analysis of Adaptive Progressively First-Failure Censored Burr Type-XII Data With Applications

Adaptive censoring schemes have attracted increasing attention in reliability and life-testing studies because they reduce experimental costs while maintaining statistical efficiency. The adaptive progressive first-failure censoring design provides a flexible testing framework that guarantees a predetermined number of failures while controlling the total test duration through adaptive group removals. However, statistical inference for flexible lifetime models under this scheme remains limited. This paper develops classical and Bayesian reliability estimation for the Burr type-XII distribution based on data generated under this censoring mechanism. Maximum likelihood estimation is employed, and approximate confidence intervals for model parameters and reliability measures are constructed using asymptotic theory and the delta method. A Bayesian framework is also established through suitable prior specifications, with estimation carried out under squared error and linear exponential loss functions. Since closed-form Bayesian estimators are unavailable, simulation-based sampling methods are implemented to obtain posterior summaries and credible intervals. The performance of the proposed procedures is examined through extensive simulation studies. Their practical usefulness is illustrated using two real datasets: a repairable mechanical equipment system from engineering and a bladder cancer dataset from clinical research.