Reliability of Multicomponent Stress-Strength Model Based on Bivariate Generalized Exponential Distribution

Abstract

This paper deals with a system consisting of k identical strength components where each side of a given component is composed of a pair of dependent elements. These elements $(X_{11},X_{12});(Y_{11},Y_{12}),\dots ,(X_{k1},X_{k2});(Y_{k1},Y_{k2})$ have bivariate generalized exponential distribution and each element is put through a common random stress T which has generalized exponential distribution. The system is considered as working only if at least s out of $k(1\le s\le k)$ strength random variables overcome the random stress. The multicomponent reliability of the system is defined by $R_s{,}_k=P($ at least s of the $(U_1,\dots ,U_k)$ exceed $T)$ where $U_i=\min (Z_{i1},Z_{i2}),Z_{i1}=\max (X_{i1},X_{i2})$ and $Z_{i2}=\max (Y_{i1},Y_{i2}),$ for $i=1,\dots ,k.$ Estimation of the multicomponent reliability may help the safety management and prevent some catastrophic disaster. We estimate multicomponent reliability $R_s{,}_k$ by using classical and Bayesian approaches. Since the explicit form of stress-strength reliability estimate is not accessible, Lindley’s approximation and the Markov Chain Monte Carlo (MCMC) methods are used to develop Bayes estimate of $R_s{,}_k.$ Further, numerical studies are conducted and the reliability estimators are compared through the estimated risks (ER).

KEYWORDS AND PHRASES:

• Bivariate generalized exponential distribution
• stress-strength model
• system reliability

Mathematics Subject Classification (2010)::

• 62F10
• 62F15
• 62N05

Acknowledgements

The authors sincerely thank the editor and anonymous referees for their valuable comments that allowed us to improve this article.