Estimation of failure probability and its applications in lifetime data analysis (Q764466)

Summary: Since \textit{D.V. Lindley} and \textit{A.F.M. Smith} [J. R. Stat. Soc., Ser. B 34, 1--41 (1972; Zbl 0246.62050)] introduced the idea of hierarchical prior distributions, some results have been obtained on hierarchical Bayesian methods to deal with life time data. But all those results obtained by means of hierarchical Bayesian methods involve computing complicated integrations. Though some computing methods such as Markov chain Monte Carlo (MCMC) are available, doing integration is still very inconvenient for practical problems. This paper introduces a new method, named E-Bayesian estimation method, to estimate failure probabilities. 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 the properties of E-Bayesian estimation of the failure probabilities are also provided. Finally, calculations on practical problems show that the provided method is feasible and easy to perform.