Censored Samples Bayesian Reliability Analysis And Applications

In this paper, The Burr Ⅻ distribution is discussed based on progressively type-Ⅱ censored samples and random censored samples. We firstly give Bayes estimators of the parameter and reliability performances;secondly, two-sample prediction intervals for future observation are obtained using Bayesian method;in the end, we research on the cold standby series system and derive the approximate confidence limits of the reliability performances.1. Based on progressively type-Ⅱ censored samples, the empirical estimators of reliability performances are researched under LINEX error loss. At the same time, in order to investigate the accuracy of estimations, an example is examined numerically by means of Monte-Carlo simulation.2. Approximate Bayes estimators of the two parameters, reliability, and failure rate functions for the Burr Ⅻ model are given by using the methods of Lindley based on progressively type-II censored samples. The bivariate prior density for the parameters and LINEX loss function are used;a numerical example is presented in the end.3. The Burr Ⅻ distribution is proposed to be the underlying model from which observables are to be predicted by using Bayesian approach. Prediction intervals are derived under progressively censored data in two-sample prediction. A numerical example is given to illustrate the performance of the procedures.4. Based on random censored data, Bayes estimators of the two parameters c, k, reliability, and failure rate are given under LINEX loss function;and Prediction intervals are derived under the same data in two-sample prediction. In order to show efficiency of the method, Monte-Carlo simulation is given at last.5. Based on fixed time censored sample, the approximate confidence limits of the reliability performances for cold standby series system are studied by using EB and MLE approaches. The formulae to calculate EB approximate confidence limits of the failure rate, the reliability function and average life are given. In the end, an illustrative example is examined numerically by means of the Monte-Carlo simulation and the accuracy of confidence limits is discussed.