Published

2017-01-16

Estimation a Stress-Strength Model for P (Yr:n1 < Xk:n2 ) Using the Lindley Distribution

En estimación del estrés fuerza modelo en la caja P(Yr:n1 < Xk:n2 ) de distribución Lindley

Keywords:

Bayes Estimator, Lindley Distribution, Maximum Likelihood Estimator, Order Statistics, Stress-Strength Model, Uniformly Minimum Variance Unbiased Estimator (en)
Distribución de Lindley, estadísticas de orden, estimador de Bayes, estimador insesgado de varianza uniformemente mínima, estimador insesgado de varianza mínima, modelo de estrés-fuerza (es)

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Authors

  • Marwa Khalil Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt

The problem of estimation reliability in a multicomponent stress-strength model, when the system consists of k components have strength each compo- nent 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 (M LE), uniformly minimum variance unbiased estimator (UMVUE) and Bayes esti- mator 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.

El problema de la fiabilidad de estimación en el modelo de estrés-fuerza multicomponente, cuando el sistema consta de componentes k tiene fuerza, cada componente experimentando un estrés al azar se considera en este documento. Se obtiene la fiabilidad de estos sistemas cuando las variables de fuerza y tensión están dadas por la distribución Lindley. El sistema es considerado como vivo solo si al menos r de k(r < k) fuerzas superan el estrés. La fiabilidad de varios componentes del sistema viene dado por Rr;k. El estimador de máxima verosimilitud (MLE), se obtienen estimadores insesgados de varianza uniformemente mínima (UMVUE) y el estimador de Bayes Rr;k. Se realizó un estudio de simulación para comparar los diferentes estimadores de Rr;k. Se utilizaron datos reales como aplicación práctica para el modelo propuesto.

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