Abstract
This article introduces a new parameter estimation method, named E-Bayesian estimation method, to estimate failure rate derived from exponential distribution, in the case of data with only one failure. Firstly, the definition of E-Bayesian estimation is provided. Moreover, formulas of E-Bayesian estimation and hierarchical Bayesian estimation are provided. Secondly, properties of E-Bayesian estimation are discussed. Finally, the calculated results of a practical problem show that the proposed method is feasible and convenient in engineering application.
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