Reliability Evaluation of Two Complementary Unit Weibull Populations Using Joint Progressively Type-II Censored Samples With Three Engineering Applications

This work looks into the difficulties connected with estimating the parameters and reliability function of the complementary unit Weibull distribution using joint progressive Type-II censored samples. We suggest using maximum likelihood and Bayesian estimations to get point and interval estimates for the distribution’s unknown parameters alongside the reliability function. In Bayesian inference, we use the squared error loss function and the Markov Chain Monte Carlo technique to generate Bayes point estimates and the highest posterior credible intervals. Prior distributions are selected according to the unknown parameter theoretical support, using gamma distributions for shape parameters and beta distributions for median parameters. A simulation analysis is carried out to assess the performance of the suggested approaches under various censorship scenarios to confirm their accuracy. The real-world use of the suggested methodologies is illustrated through the examination of three real-world engineering data sets that represent the time to failure of unit capacity aspects, repairable mechanical equipment, and insulating liquid breakdown. The results highlight the efficiency of the approaches in reliability evaluation, verifying them as useful tools for applications in reality.