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Bayes and ML estimations for the exponentiated Weibull distribution based an adaptive progressive censoring have been obtained.• The MLEs, the bootstrap confidence intervals and the asymptotic confidence intervals have been obtained and discussed.• The Bayes estimates cannot be obtained in explicit form.• We used MCMC samples to compute the approximate Bayes estimates and constructed the credible intervals.• The performance of different methods was compared via a Monte Carlo simulation.Abstract: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 adaptiveType-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 analysed to illustrate the proposed methods of estimation. Finally, results from simulation studies assessing the performance of the maximum likelihood and Bayes estimators are discussed.