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ESTIMACIÓN DE CONFIABILIDAD EN LA RESISTENCIA AL ESTRÉS DE MULTICOMPONENTES BASADO EN LA DISTRIBUCIÓN EXPONENCIAL GENERALIZADA
ESTIMATION OF RELIABILITY IN MULTICOMPONENT STRESS-STRENGTH BASED ON GENERALIZED EXPONENTIAL DISTRIBUTION
Keywords:
confiabilidad, estimación máximo verosímil, intervalos de confianza asintóticos, modelo de resistencia-estrés (es)Asymptotic confidence interval, Maximum likelihood estimation, Reliability, Stress-strength model (en)
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1Dilla University, School of Mathematical and Computer Sciences, Department of Statistics, Dilla, Ethiopia. Professor. Email:gaddesrao@yahoo.com
A multicomponent system of k components having strengths following k- independently and identically distributed random variables X1, X2,\ldots,Xk and each component experiencing a random stress Y is considered. The system is regarded as alive only if at least s out of k (s < k) strengths exceed the stress. The reliability of such a system is obtained when strength and stress variates are given by generalized exponential distribution with different shape parameters. The reliability is estimated using ML method of estimation in samples drawn from strength and stress distributions. The reliability estimators are compared asymptotically. The small sample comparison of the reliability estimates is made through Monte Carlo simulation. Using real data sets we illustrate the procedure.
Key words: Asymptotic confidence interval, Maximum likelihood estimation, Reliability, Stress-strength model.
Se considera un sistema de k multicomponentes que tiene resistencias que se distribuyen como k variables aleatorias independientes e idénticamente distribuidas X1, X2,\ldots, Xk y cada componente experimenta un estrés aleatorio Y. El sistema se considera como vivo si y solo si por lo menos s de k (s < k) resistencias exceden el estrés. La confiabilidad de este sistema se obtiene cuando las resistencias y el estrés se distribuyen como una distribución exponencial generalizada con diferentes parámetros de forma. La confiabilidad es estimada usando el método ML de estimación en muestras extraídas tanto para distribuciones de resistencia como de estrés. Los estimadores de confiabilidad son comparados asintóticamente. La comparación para muestras pequeñas de los estimadores de confiabilidad se hace a través de simulaciones Monte Carlo. El procedimiento también se ilustra mediante una aplicación con datos reales.
Palabras clave: confiabilidad, estimación máximo verosímil, intervalos de confianza asintóticos, modelo de resistencia-estrés.
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References
1. Gupta, R. D. & Kundu, D. (2002), 'Generalized exponential distributions; statistical inferences', Journal of Statistical Theory and Applications 1, 101-118.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv35n1a05,AUTHOR = {Rao, Gadde Srinivasa},
TITLE = {{Estimation of Reliability in Multicomponent Stress-strength Based on Generalized Exponential Distribution}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2012},
volume = {35},
number = {1},
pages = {67-76}
}
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