Fuzzy Bayesian, E-Bayesian, and Hierarchical Bayesian Estimations of R = P(X>Y ) in Weibull Distribution under Type II censored Data

This study examines Bayesian, E-Bayesian (E-B), and hierarchical Bayesian (H-B) estimation methods for the stress-strength reliability parameter (SSRP) R = P(X>Y ), within the Weibull distribution framework under Type II censoring and fuzzy data conditions. Stress and strength random variables are modeled as Weibull distributions with distinct scale parameters but a common shape parameter. Estimations are conducted using the squared error (SE) loss function and Lindleys approximation. Furthermore, a comprehensive simulation study, complemented by real-world data analysis, has been carried out to assess and compare the performance of the proposed estimators. The results from both simulation and empirical analyses demonstrate that the H-B estimator consistently outperforms both the Bayesian and E-B estimators under the squared error (SE) loss function.