Weibull accelerated life testing analysis with several variables using multiple linear regression

In Weibull accelerated life test analysis (ALT) with two or more variables (X2, X3, ... Xk), we estimated, in joint form, the parameters of the life stress model r{X(t)} and one shape parameter β. These were then used to extrapolate the conclusions to the operational level. However, these conclusion...

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Autores:
Piña-Monarrez, Manuel R.
Ávila-Chávez, Carlos A.
Márquez-Luévano, Carlos D.
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/60704
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/60704
http://bdigital.unal.edu.co/59036/
Palabra clave:
62 Ingeniería y operaciones afines / Engineering
ALT analysis
Weibull analysis
multiple linear regression
experiment design.
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openAccess
License
Atribución-NoComercial 4.0 Internacional
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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_abf2Piña-Monarrez, Manuel R.aa3acc89-846c-47ec-aeff-00f0cf9c0e94300Ávila-Chávez, Carlos A.d255040b-6429-4c8b-9a27-063b37318e7f300Márquez-Luévano, Carlos D.46e92c0b-ea8f-426f-acc8-ee3418613fc43002019-07-02T18:55:29Z2019-07-02T18:55:29Z2015-05-01ISSN: 2346-2183https://repositorio.unal.edu.co/handle/unal/60704http://bdigital.unal.edu.co/59036/In Weibull accelerated life test analysis (ALT) with two or more variables (X2, X3, ... Xk), we estimated, in joint form, the parameters of the life stress model r{X(t)} and one shape parameter β. These were then used to extrapolate the conclusions to the operational level. However, these conclusions are biased because in the experiment design (DOE) used, each combination of the variables presents its own Weibull family (βi, ηi). Thus the estimated β is not representative. On the other hand, since (βi, ηi) is determined by the variance of the logarithm of the lifetime data σt2 , the response variance σy2 and the correlation coefficient R2, which increases when variables are added to the analysis, β is always overestimated. In this paper, the problem is statistically addressed and based on the Weibull families (βi, ηi) a vector Yη is estimated and used to determine the parameters of r{X(t)}. Finally, based on the variance σy2 of each level, the variance of the operational level σop2 is estimated and used to determine the operational shape parameter βop. The efficiency of the proposed method is shown by numerical applications and by comparing its results with those of the maximum likelihood method (ML).application/pdfspaUniversidad Nacional de Colombia (Sede Medellín). Facultad de Minas.https://revistas.unal.edu.co/index.php/dyna/article/view/43533Universidad Nacional de Colombia Revistas electrónicas UN DynaDynaPiña-Monarrez, Manuel R. and Ávila-Chávez, Carlos A. and Márquez-Luévano, Carlos D. (2015) Weibull accelerated life testing analysis with several variables using multiple linear regression. DYNA, 82 (191). pp. 156-162. ISSN 2346-218362 Ingeniería y operaciones afines / EngineeringALT analysisWeibull analysismultiple linear regressionexperiment design.Weibull accelerated life testing analysis with several variables using multiple linear regressionArtículo 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/ARTORIGINAL43533-250857-1-PB.pdfapplication/pdf473289https://repositorio.unal.edu.co/bitstream/unal/60704/1/43533-250857-1-PB.pdff0f210f3e14853855d1b51a421aed266MD51THUMBNAIL43533-250857-1-PB.pdf.jpg43533-250857-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg9351https://repositorio.unal.edu.co/bitstream/unal/60704/2/43533-250857-1-PB.pdf.jpg91731975b973921a2b5bf817b34a1769MD52unal/60704oai:repositorio.unal.edu.co:unal/607042024-04-14 23:11:38.463Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Weibull accelerated life testing analysis with several variables using multiple linear regression
title Weibull accelerated life testing analysis with several variables using multiple linear regression
spellingShingle Weibull accelerated life testing analysis with several variables using multiple linear regression
62 Ingeniería y operaciones afines / Engineering
ALT analysis
Weibull analysis
multiple linear regression
experiment design.
title_short Weibull accelerated life testing analysis with several variables using multiple linear regression
title_full Weibull accelerated life testing analysis with several variables using multiple linear regression
title_fullStr Weibull accelerated life testing analysis with several variables using multiple linear regression
title_full_unstemmed Weibull accelerated life testing analysis with several variables using multiple linear regression
title_sort Weibull accelerated life testing analysis with several variables using multiple linear regression
dc.creator.fl_str_mv Piña-Monarrez, Manuel R.
Ávila-Chávez, Carlos A.
Márquez-Luévano, Carlos D.
dc.contributor.author.spa.fl_str_mv Piña-Monarrez, Manuel R.
Ávila-Chávez, Carlos A.
Márquez-Luévano, Carlos D.
dc.subject.ddc.spa.fl_str_mv 62 Ingeniería y operaciones afines / Engineering
topic 62 Ingeniería y operaciones afines / Engineering
ALT analysis
Weibull analysis
multiple linear regression
experiment design.
dc.subject.proposal.spa.fl_str_mv ALT analysis
Weibull analysis
multiple linear regression
experiment design.
description In Weibull accelerated life test analysis (ALT) with two or more variables (X2, X3, ... Xk), we estimated, in joint form, the parameters of the life stress model r{X(t)} and one shape parameter β. These were then used to extrapolate the conclusions to the operational level. However, these conclusions are biased because in the experiment design (DOE) used, each combination of the variables presents its own Weibull family (βi, ηi). Thus the estimated β is not representative. On the other hand, since (βi, ηi) is determined by the variance of the logarithm of the lifetime data σt2 , the response variance σy2 and the correlation coefficient R2, which increases when variables are added to the analysis, β is always overestimated. In this paper, the problem is statistically addressed and based on the Weibull families (βi, ηi) a vector Yη is estimated and used to determine the parameters of r{X(t)}. Finally, based on the variance σy2 of each level, the variance of the operational level σop2 is estimated and used to determine the operational shape parameter βop. The efficiency of the proposed method is shown by numerical applications and by comparing its results with those of the maximum likelihood method (ML).
publishDate 2015
dc.date.issued.spa.fl_str_mv 2015-05-01
dc.date.accessioned.spa.fl_str_mv 2019-07-02T18:55:29Z
dc.date.available.spa.fl_str_mv 2019-07-02T18:55:29Z
dc.type.spa.fl_str_mv Artículo de revista
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identifier_str_mv ISSN: 2346-2183
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http://bdigital.unal.edu.co/59036/
dc.language.iso.spa.fl_str_mv spa
language spa
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dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Dyna
Dyna
dc.relation.references.spa.fl_str_mv Piña-Monarrez, Manuel R. and Ávila-Chávez, Carlos A. and Márquez-Luévano, Carlos D. (2015) Weibull accelerated life testing analysis with several variables using multiple linear regression. DYNA, 82 (191). pp. 156-162. ISSN 2346-2183
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
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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 Medellín). Facultad de Minas.
institution Universidad Nacional de Colombia
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