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...
- 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
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|
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 |
dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
dc.type.coarversion.spa.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
dc.type.content.spa.fl_str_mv |
Text |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/ART |
format |
http://purl.org/coar/resource_type/c_6501 |
status_str |
publishedVersion |
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 https://repositorio.unal.edu.co/bitstream/unal/66490/2/59929-373847-1-PB.pdf.jpg |
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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 |