Estimation for the exponentiated Weibull model with adaptive Type-Ⅱ progressive censored schemes

摘要

In reliability and life testing experiments, the censoring scheme which can balance between the total time spent for the experiment, the number of units used and the efficiency of statistical inference based on the results of the experiment is desirable. An adaptive Type-Ⅱ progressive censoring schemes have been shown to be useful in this case. This article deals with the problem of estimating parameters, reliability and hazard functions of the two-parameter exponentiated Weibull distribution, under adaptive progressive Type Ⅱ censoring samples using Bayesian and non-Bayesian approaches. Maximum likelihood estimates (M LEs) are proposed for unknown quantities. The asymptotic normality of the MLEs are used to compute the approximate confidence intervals for these quantities, parametric bootstrap confidence intervals are also constructed. Markov Chain Monte Carlo (MCMC) samples using importance sampling scheme are used to produce the Bayes estimates and the credible intervals for the unknown quantities. A real-life data-set is analyzed to illustrate the proposed methods of estimation. Finally, results from simulation studies assessing the performance of the maximum likelihood and Bayes estimators are discussed.