Reliability Inference for Time Parameters of the Newly Weibull Extended Model With Biomedical and Industrial Applications

ABSTRACT A new 3‐parameter extended Weibull distribution, called Y‐Weibull, is adopted as a more flexible alternative capable of capturing a wide range of hazard‐rate patterns encountered in practical applications. This study develops Bayesian and non‐Bayesian inferential frameworks for the Y‐Weibull distribution under the unified progressive Type‐II hybrid censoring scheme. Maximum likelihood estimation is employed to obtain estimators of the model parameters as well as the associated reliability and hazard rate functions. The corresponding interval estimates are constructed using both normal and log‐normal approximation techniques. From the Bayesian standpoint, independent gamma priors are assumed for the unknown parameters, and posterior inference is carried out through a Metropolis‐Hastings Markov chain Monte Carlo algorithm. Bayesian point estimates, credible intervals, and highest posterior density intervals are subsequently derived. The practical performance of the proposed inferential procedures is investigated through an extensive Monte Carlo simulation study encompassing various sample sizes, censoring scenarios, and progressive removal patterns. The simulation findings indicate that estimation accuracy improves as the amount of available information increases. Moreover, Bayesian procedures, particularly those HPD‐based intervals, generally exhibit superior performance relative to frequentist methods. The study also highlights the impact of censoring designs on statistical efficiency and provides practical guidance for planning reliability experiments. Two real datasets arising from biomedical and engineering applications are analyzed to demonstrate the practical usefulness of the proposed methodology. The empirical results confirm the remarkable flexibility of the Y‐Weibull model in describing complex lifetime behaviors and suggest that it constitutes a competitive and effective alternative to several Weibull‐type distributions, including Weibull, Exponentiated‐Weibull, Alpha Power Weibull, and Power Generalized Weibull, among others, for the analysis of censored reliability data.