Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair

This paper develops simultaneous confidence bands using computer intensive methods based on resampling, for the expected discounted warranty costs in coherent systems under physical minimal repair, that is, when the system is observed at its components level and only the component that causes the fa...

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Autores:
Lopera Gómez, Carlos Mario
Gónzalez Álvarez, Nelfi Gertrudis
Tipo de recurso:
Article of journal
Fecha de publicación:
2018
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66490
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66490
http://bdigital.unal.edu.co/67518/
Palabra clave:
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Central Limit Theorem
Coverage Probability
Point Process
Resampling
Semimartingales
Weak Convergence
convergencia débil
probabilidad de cobertura
proceso puntual
remuestreo
semimartingalas
teorema de límite central
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_6b867c144687f7a4833e3cda260ecf17
oai_identifier_str oai:repositorio.unal.edu.co:unal/66490
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair
title Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair
spellingShingle Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Central Limit Theorem
Coverage Probability
Point Process
Resampling
Semimartingales
Weak Convergence
convergencia débil
probabilidad de cobertura
proceso puntual
remuestreo
semimartingalas
teorema de límite central
title_short Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair
title_full Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair
title_fullStr Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair
title_full_unstemmed Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair
title_sort Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair
dc.creator.fl_str_mv Lopera Gómez, Carlos Mario
Gónzalez Álvarez, Nelfi Gertrudis
dc.contributor.author.spa.fl_str_mv Lopera Gómez, Carlos Mario
Gónzalez Álvarez, Nelfi Gertrudis
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
Central Limit Theorem
Coverage Probability
Point Process
Resampling
Semimartingales
Weak Convergence
convergencia débil
probabilidad de cobertura
proceso puntual
remuestreo
semimartingalas
teorema de límite central
dc.subject.proposal.spa.fl_str_mv Central Limit Theorem
Coverage Probability
Point Process
Resampling
Semimartingales
Weak Convergence
convergencia débil
probabilidad de cobertura
proceso puntual
remuestreo
semimartingalas
teorema de límite central
description This paper develops simultaneous confidence bands using computer intensive methods based on resampling, for the expected discounted warranty costs in coherent systems under physical minimal repair, that is, when the system is observed at its components level and only the component that causes the fault is minimally repaired. For this purpose, it is shown that, under the framework of the Martingale processes and the central limit resampling theorem (CLRT) over stochastic processes, the discounted warranty cost processes satisfy the conditions set by the central limit resampling theorem (CLRT). Additionally, a simulation study is performed on the most relevant variables, such that the finite sample features of the proposed bands may be assessed, based on their actual coverage probabilities. The results in the considered scenarios show that resampling-based simultaneous confidence bands have coverage probabilities that are close to the nominal coverage. In particular, the agreement is good when there are 100 systems or more where a large number of resamples are used for the approximation.
publishDate 2018
dc.date.issued.spa.fl_str_mv 2018-01-01
dc.date.accessioned.spa.fl_str_mv 2019-07-03T02:13:47Z
dc.date.available.spa.fl_str_mv 2019-07-03T02:13:47Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.issn.spa.fl_str_mv ISSN: 2389-8976
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/66490
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/67518/
identifier_str_mv ISSN: 2389-8976
url https://repositorio.unal.edu.co/handle/unal/66490
http://bdigital.unal.edu.co/67518/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/estad/article/view/59929
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Estadística
Revista Colombiana de Estadística
dc.relation.references.spa.fl_str_mv Lopera Gómez, Carlos Mario and Gónzalez Álvarez, Nelfi Gertrudis (2018) Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair. Revista Colombiana de Estadística, 41 (1). pp. 1-30. ISSN 2389-8976
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv 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
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadística
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/66490/1/59929-373847-1-PB.pdf
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
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spelling 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_abf2Lopera Gómez, Carlos Mario2a1416a6-a4d0-447e-9965-d7e3740713a0300Gónzalez Álvarez, Nelfi Gertrudis8f083ac9-5047-44a7-ae58-27a557f619983002019-07-03T02:13:47Z2019-07-03T02:13:47Z2018-01-01ISSN: 2389-8976https://repositorio.unal.edu.co/handle/unal/66490http://bdigital.unal.edu.co/67518/This paper develops simultaneous confidence bands using computer intensive methods based on resampling, for the expected discounted warranty costs in coherent systems under physical minimal repair, that is, when the system is observed at its components level and only the component that causes the fault is minimally repaired. For this purpose, it is shown that, under the framework of the Martingale processes and the central limit resampling theorem (CLRT) over stochastic processes, the discounted warranty cost processes satisfy the conditions set by the central limit resampling theorem (CLRT). Additionally, a simulation study is performed on the most relevant variables, such that the finite sample features of the proposed bands may be assessed, based on their actual coverage probabilities. The results in the considered scenarios show that resampling-based simultaneous confidence bands have coverage probabilities that are close to the nominal coverage. In particular, the agreement is good when there are 100 systems or more where a large number of resamples are used for the approximation.Este trabajo desarrolla bandas de confianza simultáneas usando métodos computacionales intensivos basados en remuestreo, para el costo medio de garantía descontado en sistemas coherentes bajo reparo mínimo físico, esto es, cuando el sistema es observado al nivel de sus componentes y sólo la componente que causa la falla es reparada mínimamente. Para ello se prueba que, bajo el marco teórico de los procesos martingala, los procesos de costos de garantía descontados cumplen las condiciones del teorema de límite central de remuestreo (CLRT). Un estudio de simulación Monte Carlo se realiza para evaluar, a través de las probabilidades de cobertura alcanzadas, el desempeño de las bandas propuestas en muestras finitas. Los resultados en los escenarios considerados muestran que las bandas de confianza basadas en remuestreo tienen probabilidades de cobertura con valores cercanos a los esperados, en particular para aquellas basadas en muestras con más de 100 sistemas donde el número de remuestras usado para la aproximación es grande.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadísticahttps://revistas.unal.edu.co/index.php/estad/article/view/59929Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de EstadísticaRevista Colombiana de EstadísticaLopera Gómez, Carlos Mario and Gónzalez Álvarez, Nelfi Gertrudis (2018) Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair. Revista Colombiana de Estadística, 41 (1). pp. 1-30. ISSN 2389-897651 Matemáticas / Mathematics31 Colecciones de estadística general / StatisticsCentral Limit TheoremCoverage ProbabilityPoint ProcessResamplingSemimartingalesWeak Convergenceconvergencia débilprobabilidad de coberturaproceso puntualremuestreosemimartingalasteorema de límite centralSimultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal RepairArtículo 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/ARTORIGINAL59929-373847-1-PB.pdfapplication/pdf914402https://repositorio.unal.edu.co/bitstream/unal/66490/1/59929-373847-1-PB.pdfeec63b5b448866fb5f68be5e3067ec27MD51THUMBNAIL59929-373847-1-PB.pdf.jpg59929-373847-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg6233https://repositorio.unal.edu.co/bitstream/unal/66490/2/59929-373847-1-PB.pdf.jpg34e9e5048c0b4a5598236fbe2d09cd8bMD52unal/66490oai:repositorio.unal.edu.co:unal/664902023-05-25 23:02:56.998Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co