Random Removals in Generalized Progressive Type‐II Hybrid Censoring: Inference for Weibull Distribution With Applications

This study introduces an enhanced generalized progressive Type‐II hybrid censoring scheme incorporating binomial random removals, which provides a more realistic alternative to fixed removal patterns commonly assumed in practice. The proposed framework is employed to investigate the estimation of Weibull model parameters and associated survival measures, along with the binomial removal parameter. Both classical and Bayesian approaches are considered for point and interval estimation. Classical inference is developed using maximum likelihood estimation and asymptotic confidence intervals, while Bayesian inference is carried out under squared error loss with corresponding credible intervals. A comprehensive simulation study is conducted to assess the performance of the proposed estimators under various experimental designs. Two cancer datasets are analyzed to illustrate the practical applicability of the proposed methods, and the results demonstrate improved inferential performance and support the adequacy of the Weibull model.