Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution
In this study, we consider a multicomponent system which has k independent and identical strength components X1,...,Xk 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)...
- Autores:
-
Kizilaslan, Fatih
Nadar, Mustafa
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2015
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66537
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66537
http://bdigital.unal.edu.co/67565/
- Palabra clave:
- 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Stress-Strength Model
System Reliability
Weibull Distribution
DistribuciónWeibull
Modelo estrés-fuerza
Sistema de confiabilidad.
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Kizilaslan, Fatihf2143882-ceac-477a-b0fd-1c50749e5e30300Nadar, Mustafaf027230b-ef5b-4ab0-8488-130f81701df53002019-07-03T02:19:38Z2019-07-03T02:19:38Z2015-07-01ISSN: 2389-8976https://repositorio.unal.edu.co/handle/unal/66537http://bdigital.unal.edu.co/67565/In this study, we consider a multicomponent system which has k independent and identical strength components X1,...,Xk 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 Lindley's 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.En este estudio, consideramos un sistema multicomponente con k componentes de fuerza independientes 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.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadísticahttps://revistas.unal.edu.co/index.php/estad/article/view/51674Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de EstadísticaRevista Colombiana de EstadísticaKizilaslan, Fatih and Nadar, Mustafa (2015) Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution. Revista Colombiana de Estadística, 38 (2). pp. 467-484. ISSN 2389-897651 Matemáticas / Mathematics31 Colecciones de estadística general / StatisticsStress-Strength ModelSystem ReliabilityWeibull DistributionDistribuciónWeibullModelo estrés-fuerzaSistema de confiabilidad.Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull DistributionArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL51674-253070-1-PB.pdfapplication/pdf909528https://repositorio.unal.edu.co/bitstream/unal/66537/1/51674-253070-1-PB.pdf39f13e0225c84a1b4a23c5bd6fce9c2eMD51THUMBNAIL51674-253070-1-PB.pdf.jpg51674-253070-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg5581https://repositorio.unal.edu.co/bitstream/unal/66537/2/51674-253070-1-PB.pdf.jpga2743d67e0a4207752f4162227f0bd37MD52unal/66537oai:repositorio.unal.edu.co:unal/665372023-05-25 23:03:08.695Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution |
| title |
Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution |
| spellingShingle |
Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution 51 Matemáticas / Mathematics 31 Colecciones de estadística general / Statistics Stress-Strength Model System Reliability Weibull Distribution DistribuciónWeibull Modelo estrés-fuerza Sistema de confiabilidad. |
| title_short |
Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution |
| title_full |
Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution |
| title_fullStr |
Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution |
| title_full_unstemmed |
Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution |
| title_sort |
Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution |
| dc.creator.fl_str_mv |
Kizilaslan, Fatih Nadar, Mustafa |
| dc.contributor.author.spa.fl_str_mv |
Kizilaslan, Fatih Nadar, Mustafa |
| dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics 31 Colecciones de estadística general / Statistics |
| topic |
51 Matemáticas / Mathematics 31 Colecciones de estadística general / Statistics Stress-Strength Model System Reliability Weibull Distribution DistribuciónWeibull Modelo estrés-fuerza Sistema de confiabilidad. |
| dc.subject.proposal.spa.fl_str_mv |
Stress-Strength Model System Reliability Weibull Distribution DistribuciónWeibull Modelo estrés-fuerza Sistema de confiabilidad. |
| description |
In this study, we consider a multicomponent system which has k independent and identical strength components X1,...,Xk 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 Lindley's 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. |
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2015 |
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2015-07-01 |
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2019-07-03T02:19:38Z |
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2019-07-03T02:19:38Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/resource_type/c_6501 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Text |
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http://purl.org/redcol/resource_type/ART |
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publishedVersion |
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ISSN: 2389-8976 |
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https://repositorio.unal.edu.co/handle/unal/66537 |
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http://bdigital.unal.edu.co/67565/ |
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ISSN: 2389-8976 |
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https://repositorio.unal.edu.co/handle/unal/66537 http://bdigital.unal.edu.co/67565/ |
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spa |
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spa |
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https://revistas.unal.edu.co/index.php/estad/article/view/51674 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Estadística Revista Colombiana de Estadística |
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Kizilaslan, Fatih and Nadar, Mustafa (2015) Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution. Revista Colombiana de Estadística, 38 (2). pp. 467-484. ISSN 2389-8976 |
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Derechos reservados - Universidad Nacional de Colombia |
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http://purl.org/coar/access_right/c_abf2 |
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Atribución-NoComercial 4.0 Internacional |
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info:eu-repo/semantics/openAccess |
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Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2 |
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