¹Gebze Technical University, Faculty of Science, Department of Mathematics, Kocaeli, Turkey. Ph.D. Student. Email: kizilaslan@gtu.edu.tr
²Istanbul Technical University, Faculty of Arts and Sciences, Department of Mathematical Engineering, Istanbul, Turkey. Associate Professor. Email: nadar@itu.edu.tr

In this study, we consider a multicomponent system which has k independent and identical strength components X₁...,X_k and each component is exposed to a common random stress Y when the underlying distributions are Weibull. The system is regarded as operating only if at least s out of k (1≤ s≤ k) strength variables exceeds the random stress. We estimate the reliability of the system by using frequentist and Bayesian approaches. The Bayes estimate of the reliability has been developed by using Lindleys approximation and the Markov Chain Monte Carlo methods due to the lack of explicit forms. The asymptotic confidence interval and the highest probability density credible interval are constructed for the reliability. The comparison of the reliability estimators is made in terms of the estimated risks by the Monte Carlo simulations.

Key words: Stress-Strength Model, System Reliability, Weibull\linebreak Distribution.

En este estudio, consideramos un sistema multicomponente con k componentes de fuerzaindependientes y cada componente expuesto a un estrés común aleatorio Y cuando seconsidera una distribución Bernoulli. El sistema se considera operativo si por lo menos s de los k (1≤ s≤ k) exceden el estrés aleatorio. Se estima la confiabilidad del sistema usando métodos bayesianos y frecuentistas. La estimación de Bayes de la confiabilidad ha sido desarrollada usando una aproximación de Lindley y métodos MCMC debido a la falta de formas explícitas. El intervalo de confianza asintótico y el intervalo de la densidad deprobabilidad más alta se construyen para la confiabilidad. La comparación de los estimadores de confiabilidad se hace en término de los riesgos estimados por medio de simulaciones Monte Carlo.

Palabras clave: distribución Weibull, modelo estrés-fuerza, sistema de confiabilidad.

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