A Study on Reliability Estimation with Progressively First Failure Censored Data Using xgamma Distribution

Progressively first failure censored (PFFC) data plays a pivotal role in reliability theory and life-testing experiments due to its ability to provide comprehensive insights into the reliability of systems and components. This approach facilitates more accurate estimation of reliability metrics and provides valuable insights into the performance and longevity of systems in life-testing experiments. In this article, we explore both classical and Bayesian approaches to estimate the model parameter and reliability characteristics of the xgamma distribution utilizing data from the PFFC dataset. In classical estimation, we analyze maximum likelihood estimators (MLEs) and derive asymptotic confidence intervals (ACIs). Within the Bayesian framework, we evaluate Bayes estimators using both non-informative and gamma informative priors, employing the squared error loss function (SELF) and utilizing Lindley approximation alongside the Metropolis-Hasting (M-H) algorithm. Furthermore, we construct highest probability density (HPD) intervals using the M-H algorithm. To assess the effectiveness of each estimation method, we conduct numerical computations through a simulation study. Lastly, we analyze a real dataset to demonstrate the practical utility of the xgamma distribution within a censoring framework.