Bayesian Inference with binomial removal for type II heavy-tailed Weibull distribution under unified progressive-hybrid censoring: simulation and application

Abstract

In this manuscript, both classical and Bayesian methods were used to estimate the parameters of the type II Heavy-Tailed Weibull (TII-HTW) distribution under a unified progressive-hybrid censoring scheme (UPHCS) that allows testing to be stopped at a fixed time or after a predefined number of failures, and under random binomial removal (BR) for items. Heavy-tailed distributions are very flexible models, they offer many advantages for reliability analysis, whether with complete or censored data. A simulation experiment was done to determine the efficiency of the methods used to estimate the parameters under BR. The confidence intervals were estimated using several methods for both classical and Bayesian estimators. Simulation studies using maximum product of spacings (MPS) and Bayesian MCMC inference were used to demonstrate significant improvements in estimation for heavy-tailed Weibull reliability data under unified progressive-hybrid censoring with binomial removal. The reliability measures were estimated. Concluding results were deduced from the simulation tables. Data analysis was conducted to assess the distribution's performance relative to its rivals. We compared our model using four data sets from engineering, business, and medical sources. Important results were recorded from the real data analysis. Finally, future works and directions were proposed at the end of the paper.