Abstract: This paper develops a new method of parameter estimation, which is named as E-Bayesian estimation method. In the case of zero-failure data, the defined of E-Bayesian estimation of the failure probability is provided, and more the formulas of E-Bayesian estimation of the failure probability is provided also on the base. Then discusses the character of E-Bayesian estimation-----the relations between E-Bayesian estimation and hierarchical
Bayesian estimation. Finally, calculations are performed according to simulation example, which show that the method provided in the paper is practicable and easy to operate.

Key words: Reliability, Zero-failure data, Failure probability, E-Bayesian estimation, Hierarchical Bayesian estimation