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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.41 no.2 Bogotá July/Dec. 2018

http://dx.doi.org/10.15446/rce.v41n2.69621 

Artículos originales de investigación

On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution

Sobre la fiabilidad en un modelo multicomponente de resistencia al

Abbas Pak1  a  , Arjun Kumar Gupta2  b  , Nayereh Bagheri Khoolenjani3  c 

1 Department of Computer Sciences, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran

2 Department of Mathematics and Statistics, Bowling Green State University, New York, United States

3 Department of Statistics, Isfahan University, Isfahan, Iran

Abstract

In this paper we study the reliability of a multicomponent stress-strength model assuming that the components follow power Lindley model. The maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval are obtained. Applying the parametric Bootstrap technique, interval estimation of the reliability is presented. Also, the Bayes estimate and highest posterior density credible interval of the reliability parameter are derived using suitable priors on the parameters. Because there is no closed form for the Bayes estimate, we use the Markov Chain Monte Carlo method to obtain approximate Bayes estimate of the reliability. To evaluate the performances of different procedures, simulation studies are conducted and an example of real data sets is provided.

Key words: Bayesian inference; Bootstrap confidence interval; Maximum likelihood estimation; Stress-strength model

Resumen

En este trabajo, estudiamos la fiabilidad de un modelo multicomponente de resistencia al estrés suponiendo que los componentes siguen el modelo Lindley de potencia. Se obtiene la estimación de máxima verosimilitud del parámetro de confiabilidad y su intervalo de confianza asintótico. Aplicando la técnica Bootstrap paramétrica, se presenta la estimación de intervalo de la confiabilidad. Además, la estimación de Bayes y el intervalo creíble de la densidad posterior más alta del parámetro de confiabilidad se obtienen utilizando los antecedentes adecuados sobre los parámetros. Debido a que no existe una forma cerrada para la estimación de Bayes, utilizamos el método de Markov Chain Monte Carlo para obtener una estimación aproximada de Bayes de la confiabilidad. Para evaluar el rendimiento de diferentes procedimientos, se realizan estudios de simulación y se proporciona un ejemplo de conjuntos de datos reales.

Palabras-clave: Inferencia bayesiana; intervalo de confianza Bootstrap; estimación de máxima verosimilitud; modelo de resistencia al estrés

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Received: March 2017; Accepted: May 2018

a E-mail: Abbas.pak1982@gmail.com

b E-mail: gupta@bgsu.edu

c E-mail: n.b.khoolenjani@gmail.com

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