Journal of Advanced Statistics

Download PDF (523.7 KB) PP. 156 - 170 Pub. Date: September 1, 2016

DOI: 10.22606/jas.2016.13005

• Bander Al-Zahrani^*
  Department of Statistics, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia
• Samerah Basloom
  Department of Statistics, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia

The paper deals with the problem of estimating the reliability of a single and multicomponent stress-strength based on a three-parameter Dagum distribution. The maximum likelihood estimators and the Bayes estimators of R = P(Y < X) when X and Y are two independent random variables follow Dagum distribution and their asymptotic distributions are obtained. Also, the reliability of a multicomponent stress-strength model is estimated using the maximum likelihood. Consequently, the asymptotic confidence intervals of the reliability of a single and multicomponent stress-strength model are constructed. Gibbs and Metropolis sampling were used to provide sample-based estimates of the reliability and its associated credible intervals. Finally, Monte Carlo simulations are carried out for illustrative purposes.

Dagum distribution, maximum likelihood estimator, Bayes estimator, stress-strength models.

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