Multicomponent stress-strength reliability analysis under upper records with applications to reservoir and forest cover data

Abstract

This article deals with the reliability estimation of the multicomponent stress--strength system. The system consists of $k$ strength components, of which at least $s$ components should exceed the common stress component. Reliability based on upper records is estimated under classical and Bayesian techniques when all strength and stress components follow the Lindley distribution. Under the classical scheme, the maximum likelihood estimation of the reliability is evaluated along with the asymptotic confidence interval and the bootstrap confidence intervals. Bayesian analysis of reliability is computed under the squared error loss function and the linear exponential loss function using the MCMC technique. In addition to this, the Bayesian credible interval and the highest posterior density credible interval are determined. The performance of the estimators is compared using various criteria. The proposed methodology is illustrated using water release data from the Bhakra reservoir and the forest cover area of India.

Keywords

• Bayesian credible interval
• bootstrap confidence intervals
• highest posterior density credible interval
• Lindley distribution
• LINEX loss function
• multicomponent reliability
• squared error loss function
• upper record values.

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