Robust Bayesian estimation of the Weibull reliability function under prior contamination: a comparative Monte Carlo study

This study examines classical, Bayesian, and robust Bayesian estimators for the Weibull reliability function under prior contamination. The Bayesian framework uses independent normal and log-normal priors, while robustness is achieved via ϵ-contaminated prior models to address possible prior misspecification. Estimation procedures compared include Maximum Likelihood Estimation, Method of Moments, White's regression method, standard Bayesian estimators, and three proposed robust Bayesian estimators. An extensive Monte Carlo simulation evaluates performance across sample sizes, contamination levels, and Weibull parameter configurations, using Integrated Mean Squared Error, Integrated Mean Absolute Relative Error, Mean Absolute Percentage Error, and pointwise Mean Squared Error. Results show that contamination adversely affects all methods, particularly for small samples, whereas the proposed robust Bayesian estimators consistently achieve greater stability and lower error, with reduced sensitivity to prior misspecification, especially in the tail region. These findings demonstrate the effectiveness of robust Bayesian estimation for Weibull reliability analysis under uncertainty and contamination.