%0 Journal Article
%T Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme
%A Sanjay Kumar Singh
%A Umesh Singh
%A Vikas Kumar Sharma
%J Journal of Probability and Statistics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/146140
%X We have developed the Bayesian estimation procedure for flexible Weibull distribution under Type-II censoring scheme assuming Jeffrey's scale invariant (noninformative) and Gamma (informative) priors for the model parameters. The interval estimation for the model parameters has been performed through normal approximation, bootstrap, and highest posterior density (HPD) procedures. Further, we have also derived the predictive posteriors and the corresponding predictive survival functions for the future observations based on Type-II censored data from the flexible Weibull distribution. Since the predictive posteriors are not in the closed form, we proposed to use the Monte Carlo Markov chain (MCMC) methods to approximate the posteriors of interest. The performance of the Bayes estimators has also been compared with the classical estimators of the model parameters through the Monte Carlo simulation study. A real data set representing the time between failures of secondary reactor pumps has been analysed for illustration purpose. 1. Introduction In reliability/survival analysis, generally, life test experiments are performed to check the life expectancy of the manufactured product or items/units before products produced in the market. But in practice, the experimenters are not able to observe the failure times of all the units placed on a life test due to time and cost constraints or due to some other uncertain reasons. Data obtained from such experiments are called censored sample. Keeping time and cost constraints in mind, many types of censoring schemes have been discussed in the statistical literature named as Type-I censoring, Type-II censoring and progressive censoring schemes, and so forth. In this paper, Type-II censoring scheme is considered. In Type-II censoring scheme, the life test is terminated as soon as a prespecified number (say, ) of units have failed. Therefore, out of units put on test, only first failures will be observed. The data obtained from such a restrained life test will be referred to as a Type-II censored sample. Prediction of the lifetimes of future items based on censored data is very interesting and valuable topic for researchers, engineers and reliability practitioners. In predictive inference, In predictive Inference, we can infer about the lifetimes of the future items using observed data. The future prediction problem can be classified into two types: (1) one-sample prediction problem. (2) two-sample prediction problem. In one-sample prediction problem, the variable to be predicted comes from the same sequence of variables
%U http://www.hindawi.com/journals/jps/2013/146140/