Table of Contents
International Journal of Quality, Statistics, and Reliability
Volume 2011, Article ID 719534, 6 pages
http://dx.doi.org/10.1155/2011/719534
Research Article

Estimation of Failure Probability and Its Applications in Lifetime Data Analysis

Department of Mathematics and Physics, Fujian University of Technology, Fuzhou Fujian, 350108, China

Received 28 June 2010; Accepted 13 January 2011

Academic Editor: Mohammad Modarres

Copyright © 2011 Ming Han. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Since Lindley and Smith introduced the idea of hierarchical prior distribution, some results have been obtained on hierarchical Bayesian method to deal with lifetime data. But all those results obtained by means of hierarchical Bayesian methods involve complicated integration compute. 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 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 the property of E-Bayesian estimation of the failure probability are also provided. Finally, calculation on practical problems shows that the provided method is feasible and easy to perform.