HIERARCHICAL BAYES ESTIMATION FOR THE EXPONENTIAL-MULTINOMIAL MODEL IN RELIABILITY AND COMPETING RISKS

Summ. & Conclusions - The exponential-multinomial distribution arises from: 1) observing the system failure of a series system with p compon ents having independent exponential lifetimes, or 2) a competing-risks model with p sources of failure, as well as 3) the Marshall-Olkin mul tivariate exponential distribution under a series sampling scheme, Hie rarchical Bayes (HB) estimators of the component sub-survival function and the system reliability are obtained using the Gibbs sampler, A la rge-sample approximation of the posterior pdf is used to derive the HB estimators of the parameters of the model with respect to the quadrat ic loss function, The exact risk of the HE estimator is obtained and i s compared with those corresponding to some other estimators such as B ayes, maximum likelihood, and minimum variance unbiased estimators.