Hjorth Reliability Analysis and Its Applications Under Newly Adaptive Progressively First-Failure Censoring Plan

This paper investigates classical and Bayesian inferences for the parameters and reliability metrics of the Hjorth distribution using a new censoring mechanism called the adaptive progressive first-failure censoring scheme. This new strategy combines guaranteed observation of a fixed number of failures with adaptive control of test duration, providing a flexible and practically efficient framework for modern reliability experiments. The Hjorth distribution is considered due to its capability to model various hazard-rate shapes within a simple two-parameter structure. Maximum likelihood estimation is developed, and approximate confidence intervals are constructed using normal approximation and logarithmic transformation methods based on the observed Fisher information matrix and the delta method. A Bayesian framework is also established using independent gamma prior distributions, with posterior inference carried out through maximum a posteriori estimation and Markov chain Monte Carlo simulation. Bayes estimates and both equal-tail and highest-posterior-density credible intervals are obtained. The performance of the proposed methods is evaluated through simulation studies and illustrated using real lifetime data from an engineering domain consisting of the tensile strength of polyester fibers, demonstrating their effectiveness under adaptive censoring settings.