Hierarchical Bayes estimation for the exponential-multinomial model in reliability and competing risks

Author

Papadopoulos, Alex S. ; Tiwari, Ram C. ; Zalkikar, Jyoti N.

Author_Institution

North Carolina Univ., Charlotte, NC, USA

Volume

45

Issue

3

fYear

1996

fDate

9/1/1996 12:00:00 AM

Firstpage

477

Lastpage

484

Abstract

The exponential-multinomial distribution arises from: (1) observing the system failure of a series system with p components having independent exponential lifetimes, or (2) a competing-risks model with p sources of failure, as well as (3) the Marshall-Olkin multivariate exponential distribution under a series sampling scheme. Hierarchical Bayes (HB) estimators of the component sub-survival function and the system reliability are obtained using the Gibbs sampler. A large-sample approximation of the posterior pdf is used to derive the HB estimators of the parameters of the model with respect to the quadratic loss function. The exact risk of the HE estimator is obtained and is compared with those corresponding to some other estimators such as Bayes, maximum likelihood, and minimum variance unbiased estimators

Keywords

Bayes methods; exponential distribution; gamma distribution; maximum likelihood estimation; normal distribution; reliability theory; Gibbs sampler; Marshall-Olkin multivariate exponential distribution; competing risks; component sub-survival function; exponential lifetimes; exponential-multinomial model; gamma distribution; hierarchical Bayes estimation; maximum likelihood estimator; minimum variance unbiased estimator; posterior pdf; quadratic loss function; reliability; series sampling scheme; series system failure; Exponential distribution; Gaussian distribution; Maximum likelihood estimation; Parameter estimation; Petroleum; Reliability; Sampling methods;

fLanguage

English

Journal_Title

Reliability, IEEE Transactions on

Publisher

ieee

ISSN

0018-9529

Type

jour

DOI

10.1109/24.537019

Filename

537019