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Since Lindley and Smith introduced the idea of hierarchical prior distribution, someresults have been obtained on hierarchical Bayesian method to deal with lifetime data.But all those results obtained by means of hierarchical Bayesian methods involvecomplicated integration compute. Though some computing methods such as MarkovChain Monte Carlo (MCMC) are available, doing integration is still very inconvenientfor practical problems. This paper introduces a new method, named E-Bayesianestimation method, to estimate failure probability. In the case of one hyperparameter,the definition of E-Bayesian estimation of the failure probability is provided; moreover,the formulas of E-Bayesian estimation and hierarchical Bayesian estimation and theproperty of E-Bayesian estimation of the failure probability are also provided. Finally,calculation on practical problems shows that the provided method is feasible and easyto perform

Estimation of Failure Probability and Its Applications in Lifetime Data Analysis