Introduction The two-parameter Burr type XII (Burr(, ,, )) distribution has been proposed as a lifetime model and a model in accelerated life test data representing times to breakdown of an insulating fluid. A classical method for estimating the parameter of interest is based on sample information, for example, calculating the maximum likelihood estimator (MLE). A Bayesian approach to a statistical problem requires defining a prior distribution over the parameter space and loss function. Many Bayesians believe that just one prior can be elicited. In practice, the prior knowledge is vague, and any produced prior distribution is only an approximation to the true one. Various solutions to this problem, such as robust Bayesian Estimation, have been proposed. Another method is E-Bayesian Estimation, introduced by Han (١, ٩, ٩, ٧, ), obtained by the expectation of a Bayes estimate of the unknown parameter over the hyperparameters. Material and Methods Suppose that n devices are placed on test simultaneously, and the test will finish immediately after r components have failed. r is fixed, and the length of the experiment is a random variable. This is a type-II censoring type, and data consisting of the r smallest lifetimes are x = (x1, : : :, xr). In some Estimation problems, using an unbounded loss function may be inappropriate. For example, in estimating the mean life of the components of an aircraft, the amount of loss for estimating the parameter by an estimator is essentially bounded. We consider the Burr type XII model and obtain the Bayesian and E-Bayesian Estimation of ,using censored data under a reflected gamma loss function. The uniqueness of this study comes from the fact that, thus far, no attempt has been made to use the E-Bayesian method for Estimation in the Burr type XII model under the reflected gamma loss function. The method of E-Bayesian Estimation is based on the expectation of Bayesian Estimation over the hyperparameters of the prior distribution. The properties of EBayesian Estimations and asymptotic relations are computed. A simulation study is conducted for comparison of the performances of proposed estimators. Results and Discussion A simulation study is performed to compare the proposed estimators. The samples are generated from the Burr(1,0: 1) distribution for selected values of n, and censored samples are obtained using some selected values of r. The Bayesian and E-Bayesian Estimations are computed for selected values of c,u and v. The estimated bias and risks are calculated for repeated 10000 times. It is observed from the simulation study that the performances of E-Bayesian estimates improve by increasing n (and r). Moreover, the estimator ^ , EB3 has the most minor estimated bias and risk and therefore, it is proposed for Estimation of , .