Estimation a Stress-Strength Model for P(Yr:n_1< Xk:n_2) Using the Lindley Distribution

• Main Author: MARWA KH HASSAN
• Format: Article
• Language: English
• Published: Universidad Nacional de Colombia 2017-01-01
• Series: Revista Colombiana de Estadística
• Subjects: distribución de Lindley; estadísticas de orden; estimador de Bayes; estimador insesgado de varianza uniformemente mínima; estimador insesgado de varianza mínima; modelo de estrés-fuerza
• Online Access: http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512017000100005&lng=en&tlng=en
• ISSN: 0120-1751

The problem of estimation reliability in a multicomponent stress-strength model, when the system consists of k components have strength each component experiencing a random stress, is considered in this paper. The reliability of such a system is obtained when strength and stress variables are given by Lindley distribution. The system is regarded as alive only if at least r out of k (r< k) strength exceeds the stress. The multicomponent reliability of the system is given by Rr,k. The maximum likelihood estimator (MLE), uniformly minimum variance unbiased estimator (UMVUE) and Bayes estimator of Rr,k are obtained. A simulation study is performed to compare the different estimators of Rr,k. Real data is used as a practical application of the proposed model.