Variance analyzed under E-Bayesian Estimation and Hierarchical Bayesian Estimation for diagnosing failure rates

In the timed censored tests under zero-failure data diagnosis, when prior distribution of failure rates is in the form of Gamma distribution, the paper discusses the variance of failure rates under E-Bayesian Estimation and the variance of failure rates under Hierarchical Bayesian Estimation, finds the hyper parameter relational expression by which the minimum variance is obtained, and proves the variance under E-Bayesian Estimation and the variance under Hierarchical Bayesian Estimation have a gradual equal relationship. Finally, through the calculation result acquired by an application instance, the paper verifies that the gradual equal relationship between E-Bayesian Estimation and Hierarchical Bayesian Estimation, and that the former is more advantageous to the latter.