E-Bayesian Estimation of Failure Probability under Zero-failure Data with Double Hyper Parameters

摘要

This paper presents the Bayesian analysis of the zero-failure data with double hyper parameters a, b. We take prior distribution of failure probability pi be its conjugated distribution-Beta (pi-1, 1, 1, b) and hyper parameter b as the uniform distribution in (1, c). With quadratic loss function, If{formula}, the E-Bayesian estimation of p_t is {formula} When 0 < c < S_i, {formual} and satisfy (I) {formual} > {formual} ;(Ⅱ) {formual} = {formual}. The results satisfy{formual}. The properties of E-Bayesian estimation are given. A Simulation example is discussed, which shows that the method is both efficiency and easy to operate.