Parameter estimation and reliability analysis of Burr XII distribution under generalized type-II censoring

A generalized type-II censoring scheme is proposed based on the traditional type-II censoring scheme. Maximum likelihood estimators of the parameters are developed and approximate confidence intervals are constructed for generalized type-II censored sample and Burr XII distribution. The bootstrap method is used to derive two types of confidence intervals for the parameters. Under the squared error loss function, Bayesian estimates of the parameters are obtained using Lindley's approximation and Markov chain Monte Carlo (MCMC) methods. In addition, the estimation of reliability for series and parallel systems is also discussed. Comparison through Monte Carlo simulation reveals that Bayesian estimation significantly outperforms maximum likelihood estimation under the mean square error criterion. Finally, the validity and practicability of the proposed methods is verified through actual data analysis.