Bayesian Reliability Inference for the Truncated Cauchy-Power Burr XII Distribution with Progressive Type-II Censoring als

Abstract

This paper presents a reliability analysis for the Truncated Cauchy-Power Burr XII (TCPBXII) distribution under progressive Type-II censoring with binomial removals. The proposed model provides a flexible framework for analyzing lifetime data characterized by skewness and complex tail behavior, which commonly arise in reliability and survival studies. The main statistical properties of the TCPBXII distribution are derived, including the probability density function, cumulative distribution function, survival function, and hazard rate function. Bayesian estimation of the unknown parameters is developed using the non-informative Jeffreys prior under the squared error loss function (SELF) {and LINEX loss function}. Since the posterior distributions do not admit closed-form expressions, the Metropolis–Hastings algorithm is implemented to obtain the Bayes estimates. A comprehensive Monte Carlo simulation study is conducted to assess the performance of the proposed estimation method under different sample sizes and censoring levels. The estimation accuracy is evaluated in terms of the {bias and} mean squared error (MSE). Finally, the applicability of the proposed model is demonstrated using a real hydrological dataset of annual river flow measurements. The results indicate that the TCPBXII distribution provides a competitive and flexible model for analyzing lifetime data under progressive censoring schemes with random removals.