The lifetimes of random variables are assumed to be independent identically distributed and have a one-parameter exponential distribution. The survivor function can be estimated by the maximum likelihood estimator (MLE) and the Bayes estimator under the conjugate prior distribution when the experiment is in the Type II censoring with finite replacement and Type III censoring. In this study, we derive the MLE and the Bayes estimator when the survivor function extend to the progressive Type II and Type III censoring in k-stage for non-changing failure rate. Then we calculate the approximate formula of the bias, varivance and mean square error(MSE) for the MLE and the Bayes estimator. The comparison of the MLE and the Bayes estimator are investigated based on the MSE criterion. Finally, we discuss the efficiency of the progressive Type II censoring.

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