Classical and Bayesian Estimation of Nadarajah–haghighi Reliability Measures Under Adaptive Progressive First-Failure Censoring With Applications

This paper investigates statistical inference for the Nadarajah–Haghighi distribution under the adaptive progressive first-failure censoring scheme, a flexible life-testing design that integrates adaptive time control with guaranteed failure termination. The censoring mechanism generalizes several classical structures and provides enhanced flexibility in managing experimental duration and resource allocation. Maximum likelihood estimation procedures are developed for the unknown model parameters and the associated reliability measures. Two types of approximate confidence intervals are constructed using the observed Fisher information matrix together with the delta method for reliability characteristics. From a Bayesian perspective, independent gamma prior distributions are assumed for the positive model parameters. Bayes estimators are obtained under the squared error loss function using the Markov chain Monte Carlo simulation implemented through the Metropolis–Hastings algorithm. The simulation-based approach also enables the construction of two types of credible intervals for the parameters and reliability measures. An extensive Monte Carlo study is conducted to assess the finite-sample performance of the proposed classical and Bayesian estimators under various censoring configurations. The proposed methods are further illustrated through the analysis of two real-data applications arising from distinct engineering and biomedical domains. These case studies are deliberately chosen to highlight the flexibility and robustness of the proposed methodology in capturing diverse data characteristics, including skewness, heterogeneity, and complex lifetime behavior. The findings demonstrate that the developed inferential framework provides reliable and efficient estimation for the Nadarajah–Haghighi model under complex adaptive censoring schemes.