Bayesian Analysis Of Failure Data Reliability And Ge Distribution Scale Parameter Empirical Bayes Estimation

With the development of science and technology, the quality of the product is better and better. Consequently, in type-I life testing, zero-failure data is of frequent occurrence, especially in high reliability and small sampling tests. Therefore the problem of zero-failure data has become a hot research focus in reliability engineering.This paper is composed of three parts:Part 1: When zero-failure data has the exponential distribution, the Bayes estimation and hierarchical Bayesian estimation of failure-rate are given in this paper which are based on the decreasing function method given by Han Ming in 1997. The synthetic estimation of failure-rate is also discussed with many examples when the first prior distribution is beta-exponential distrbution , incomplete beta-exponential distribution ,and second prior distribution is uniform distribution. Part 2: For the negative binomial distribution ,the Bayes estimation and hierarchical Bayes estimation of the realiability are given on the basis of the increasing function method which Han Ming gave in 1997. Part 3; Recently the bi-parameter generalized exponential (GE) distribution proposed by Gupta and Kundu (1999), has been extensively studied by many scholors .This paper gives the empirical Bayes estimation of the shape parameter,realiability function and failure function. The Bayes estimators of loss function and risk function of unknown shape parameter to G E distribution are investigated. Finally the property and rationality of the Bayes estimators are discussed.