Bayesian Estimation of the Reliability Function of the Exponentiated Weibull Distribution from Progressive Type II Censored Data

The Exponentiated Weibull distribution as extension of the well-known Weibull distribution has been applied in areas of reliability, quality control, duration and failure time modeling. We have concerns that Maximum Likelihood Estimation(MLE) and Bayes estimates for the parameter and the reliability function of this distribution are obtained based on progressive Type II censored samples. In order to Bayes estimates, we consider the two loss functions such as Squared Error Loss(SEL) and LINEX loss function. An approximation is based on the Laplace approximation method developed by Tierney and Kadane(1986). These estimates are compared via Monte Carlo simulation study. In the sense of comparing the Root Mean-Square Error(RMSE) of the estimates. the Bayes estimates of the parameter θ and the reliability function r( t) are better than MLE.