Bayesian Approach for Stress-Strength Reliability Under Bivariate Exponential Model
by
Navin Chandra
Department of Zoology, Banaras Hindu University, Varanasi-221 005, INDIA
Coauthors: Manju Pandey, Department of Zoology, Banaras Hindu University, Varanasi-221 005, INDIA

Bayesian Approach For Stress-Strength Reliability Under Bivariate Exponential Model

In this paper we focus on the estimation of reliability of a component for the stress-strength set-up. Several well known researchers like Bhattacharya and Johnson(1974,1975,1977), Draper and Guttman (1978), Ebrahimi(1982), Pandey and Upadhyay(1986), and Johnson(1986), Pandey and Uddin(1991) , Pandey, Uddin and Ferdous(1992) , Uddin, Pandey,Ferdous and Bhuiyan(1993) , Pandey and Chandra(2002) have considered the problem concered with the Stress-Strength Reliability for various non-bivariate life testing models.

Chandra and Owen(1975), Hanagal(1996,1999) have attempted estimation of reliability of a component under bivariate exponential stress-strength setup proposed by Freund(1961), Marshall-Olkin(1967), Block-Basu(1974), Proschan-Sullo(1974).

In this paper, we assume that the two stresses (i.e. X1 and X2 which are dependent) and the strength of the component (Y) is independent of the stresses, follow a Bivariate exponential distributions. Applicability of the Bayes estimators of reliability are studied to explore the bivariate exponential models of the stresses, proposed by the Marshall-Olkin and Proschan-Sullo. Numerical comparison of Bayes estimators of reliability are done on the basis of absolute bias and relative efficiency of the said estimators by using Monte-Carlo Integration and Gibbs Sampling Technique.

Date received: October 19, 2004