Abstract: Likelihood function of the samples is got by type-II censored life test data. Taking the prior distribution of the shape parameter as conjugate prior distribution and Jeffreys prior distribution respectively, posterior distribution of the shape parameter is obtained according to the Bayesian formula, and further the posterior distribution of the failure rate and reliability are obtained. When choosing square loss and entropy loss function, based on the principle of minimum posterior risk, Bayesian estimation of the failure rate and reliability are obtained through the Bayesian statistical method. Mean and mean square error of the failure rate and reliability are obtained through the computer's 1000 times stochastic simulation. Several estimates are compared from two aspects of mean and mean square error. Further if there is no sufficient prior information can be used, and more accurate estimation of super parameters a, b could not be obtained, it is recommended to use Jeffreys prior.