Publicação
Total time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life models
| Resumo: | We propose a new goodness-of-fit procedure designed to verify the reciprocal property that characterizes the fatigue-life or Birnbaum-Saunders (BS) distribution. Under this property, scaling a random variable that takes positive values by its median results in the same distribution as its reciprocal, a feature frequently encountered in reliability and survival studies. Our procedure employs total time on test (TTT) curves to compare the behavior of the observed data and its reciprocal counterpart, capturing both local and global discrepancies through supremum- and area-based statistics. We establish the theoretical validity of these statistics under mild assumptions, showing that they deliver accurate inference for moderate to large samples. Simulation evidence indicates that our TTT-based procedures are sensitive to subtle departures from log-symmetry, particularly when the distribution underlying the data has heavier or lighter tails than the assumed one. Illustrative real data examples further reveal how overlooking deviations from the reciprocal property can distort reliability estimates and predictions of failure times, showing the practical importance of the new goodness-of-fit procedure. Overall, our findings strengthen the BS framework and provide robust tools for model validation and selection when log-symmetric modeling assumptions are in place. |
|---|---|
| Autores principais: | Castro, Cecilia |
| Outros Autores: | Azevedo, Marta Vasconcelos Castro; Leiva, Víctor; Machado, Luís Meira |
| Assunto: | Area-based statistic · Birnbaum–Saunders distributions Goodness-of fit · Maximum-based statistic Reciprocal property TTT plot Log-symmetry Model-calibrated diagnostic Paired empirical process Reciprocal symmetry Total time on test Ciências Naturais::Matemáticas Educação de qualidade |
| Ano: | 2025 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| _version_ | 1877774583726080000 |
|---|---|
| author | Castro, Cecilia |
| author2 | Azevedo, Marta Vasconcelos Castro Leiva, Víctor Machado, Luís Meira |
| author2_role | author author author |
| author_facet | Castro, Cecilia Azevedo, Marta Vasconcelos Castro Leiva, Víctor Machado, Luís Meira |
| author_role | author |
| contributor_name_str_mv | Universidade do Minho |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Castro, Cecilia\"},{\"Person.name\":\"Azevedo, Marta Vasconcelos Castro\"},{\"Person.name\":\"Leiva, Víctor\"},{\"Person.name\":\"Machado, Luís Meira\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Universidade do Minho |
| datacite.creators.creator.creatorName.fl_str_mv | Castro, Cecilia Azevedo, Marta Vasconcelos Castro Leiva, Víctor Machado, Luís Meira |
| datacite.date.Accepted.fl_str_mv | 2025-04-26T00:00:00Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Area-based statistic · Birnbaum–Saunders distributions Goodness-of fit · Maximum-based statistic Reciprocal property TTT plot Log-symmetry Model-calibrated diagnostic Paired empirical process Reciprocal symmetry Total time on test Ciências Naturais::Matemáticas Educação de qualidade |
| datacite.titles.title.fl_str_mv | Total time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life models |
| dc.contributor.none.fl_str_mv | Universidade do Minho |
| dc.creator.none.fl_str_mv | Castro, Cecilia Azevedo, Marta Vasconcelos Castro Leiva, Víctor Machado, Luís Meira |
| dc.date.Accepted.fl_str_mv | 2025-04-26T00:00:00Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/1822/102673 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Springer Nature |
| dc.rights.cclincense.fl_str_mv | http://creativecommons.org/licenses/by/4.0/ |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.rights.rights.copyright.fl_str_mv | openAccess |
| dc.subject.none.fl_str_mv | Area-based statistic · Birnbaum–Saunders distributions Goodness-of fit · Maximum-based statistic Reciprocal property TTT plot Log-symmetry Model-calibrated diagnostic Paired empirical process Reciprocal symmetry Total time on test Ciências Naturais::Matemáticas Educação de qualidade |
| dc.title.fl_str_mv | Total time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life models |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | We propose a new goodness-of-fit procedure designed to verify the reciprocal property that characterizes the fatigue-life or Birnbaum-Saunders (BS) distribution. Under this property, scaling a random variable that takes positive values by its median results in the same distribution as its reciprocal, a feature frequently encountered in reliability and survival studies. Our procedure employs total time on test (TTT) curves to compare the behavior of the observed data and its reciprocal counterpart, capturing both local and global discrepancies through supremum- and area-based statistics. We establish the theoretical validity of these statistics under mild assumptions, showing that they deliver accurate inference for moderate to large samples. Simulation evidence indicates that our TTT-based procedures are sensitive to subtle departures from log-symmetry, particularly when the distribution underlying the data has heavier or lighter tails than the assumed one. Illustrative real data examples further reveal how overlooking deviations from the reciprocal property can distort reliability estimates and predictions of failure times, showing the practical importance of the new goodness-of-fit procedure. Overall, our findings strengthen the BS framework and provide robust tools for model validation and selection when log-symmetric modeling assumptions are in place. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| funder_facet_str_mv | FCT{{{_:::_}}}Fundação para a Ciência e a Tecnologia, I.P. FCT{{{_:::_}}}Fundação para a Ciência e a Tecnologia, I.P. |
| funding.funder.alternateName_str_mv | FCT FCT |
| funding.funder.identifier_str_mv | http://doi.org/10.13039/501100001871 http://doi.org/10.13039/501100001871 |
| funding.funder.name_str_mv | Fundação para a Ciência e a Tecnologia, I.P. Fundação para a Ciência e a Tecnologia, I.P. |
| funding.identifier_str_mv | 2023.14897.PEX UID/00013/2025 |
| funding.name_str_mv | Concurso de Projetos Exploratórios em Todos os Domínios Científicos 2023 Avaliação UID 2023/2024 |
| funding_str_mv | 2023.14897.PEX https://hdl.handle.net/1822/99238 UID/00013/2025 https://hdl.handle.net/1822/98696 |
| id | rum_0ab4d5230d4ec6c2db36a5afd093081f |
| identifier.url.fl_str_mv | https://hdl.handle.net/1822/102673 |
| inst_facet_str | urn:organizationAcronym:repositorium{{{_:::_}}}Universidade do Minho |
| instacron_str | repositorium |
| institution | Universidade do Minho |
| instname_str | Universidade do Minho |
| language | eng |
| network_acronym_str | rum |
| network_name_str | RepositóriUM - Universidade do Minho |
| oai_identifier_str | oai:repositorium.uminho.pt:1822/102673 |
| organization_str_mv | urn:organizationAcronym:repositorium |
| person_str_mv | Castro, Cecilia Azevedo, Marta Vasconcelos Castro Leiva, Víctor Machado, Luís Meira |
| publishDate | 2025 |
| publisher.none.fl_str_mv | Springer Nature |
| repo_facet_str | urn:repositoryAcronym:rum{{{_:::_}}}RepositóriUM - Universidade do Minho |
| reponame_str | RepositóriUM - Universidade do Minho |
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| service_str_mv | urn:repositoryAcronym:rum |
| spelling | engSpringer NatureengWe propose a new goodness-of-fit procedure designed to verify the reciprocal property that characterizes the fatigue-life or Birnbaum-Saunders (BS) distribution. Under this property, scaling a random variable that takes positive values by its median results in the same distribution as its reciprocal, a feature frequently encountered in reliability and survival studies. Our procedure employs total time on test (TTT) curves to compare the behavior of the observed data and its reciprocal counterpart, capturing both local and global discrepancies through supremum- and area-based statistics. We establish the theoretical validity of these statistics under mild assumptions, showing that they deliver accurate inference for moderate to large samples. Simulation evidence indicates that our TTT-based procedures are sensitive to subtle departures from log-symmetry, particularly when the distribution underlying the data has heavier or lighter tails than the assumed one. Illustrative real data examples further reveal how overlooking deviations from the reciprocal property can distort reliability estimates and predictions of failure times, showing the practical importance of the new goodness-of-fit procedure. Overall, our findings strengthen the BS framework and provide robust tools for model validation and selection when log-symmetric modeling assumptions are in place.application/pdfengTotal time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life modelsCastro, CeciliaAzevedo, Marta Vasconcelos CastroLeiva, VíctorMachado, Luís MeiraHostingInstitutionOrganizationalUniversidade do Minhoe-mailmailto:repositorium@usdb.uminho.ptrepositorium@usdb.uminho.ptPMID40285949ISSNIsPartOf1380-7870EISSNIsPartOf1572-9249DOIIsPartOf10.1007/s10985-025-09653-2URLHasVersionhttps://link.springer.com/article/10.1007/s10985-025-09653-22025-04-262025-04-26T00:00:00ZHandlehttps://hdl.handle.net/1822/102673http://purl.org/coar/access_right/c_abf2open accessArea-based statistic· Birnbaum–Saunders distributionsGoodness-of fit· Maximum-based statisticReciprocal propertyTTT plotLog-symmetryModel-calibrated diagnosticPaired empirical processReciprocal symmetryTotal time on testhttp://www.oecd.org/science/inno/38235147.pdfFields of Science and Technology (FOS)Ciências Naturais::Matemáticashttps://sdgs.un.org/goalsSustainable Development Goals (SDG)Educação de qualidade414949 bytesFundação para a Ciência e a Tecnologia, I.P.Complex Time-to-Event Analysis: Multistate Models and Cohort-Based Studies [2023.14897.PEX]Concurso de Projetos Exploratórios em Todos os Domínios Científicos 2023https://hdl.handle.net/1822/992382023.14897.PEXCrossref Funder IDhttp://doi.org/10.13039/501100001871Fundação para a Ciência e a Tecnologia, I.P.Center of Mathematics of the University of Minho [UID/00013/2025]Avaliação UID 2023/2024https://hdl.handle.net/1822/98696UID/00013/2025Crossref Funder IDhttp://doi.org/10.13039/501100001871literaturehttp://purl.org/coar/resource_type/c_6501journal article2025-04-26http://creativecommons.org/licenses/by/4.0/openAccesshttp://purl.org/coar/access_right/c_abf2application/pdfhttps://repositorium.uminho.pt/bitstreams/cf697702-04a0-4934-813f-6602a68b034f/download26422441 |
| spellingShingle | Total time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life models Castro, Cecilia Area-based statistic · Birnbaum–Saunders distributions Goodness-of fit · Maximum-based statistic Reciprocal property TTT plot Log-symmetry Model-calibrated diagnostic Paired empirical process Reciprocal symmetry Total time on test Ciências Naturais::Matemáticas Educação de qualidade |
| status | SINGLETON |
| subject.fl_str_mv | Area-based statistic · Birnbaum–Saunders distributions Goodness-of fit · Maximum-based statistic Reciprocal property TTT plot Log-symmetry Model-calibrated diagnostic Paired empirical process Reciprocal symmetry Total time on test |
| subject.other.fl_str_mv | Ciências Naturais::Matemáticas Educação de qualidade |
| title | Total time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life models |
| title_full | Total time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life models |
| title_fullStr | Total time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life models |
| title_full_unstemmed | Total time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life models |
| title_short | Total time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life models |
| title_sort | Total time on test-based goodness-of-fit statistics for the reciprocal property in fatigue-life models |
| topic | Area-based statistic · Birnbaum–Saunders distributions Goodness-of fit · Maximum-based statistic Reciprocal property TTT plot Log-symmetry Model-calibrated diagnostic Paired empirical process Reciprocal symmetry Total time on test Ciências Naturais::Matemáticas Educação de qualidade |
| topic_facet | Area-based statistic · Birnbaum–Saunders distributions Goodness-of fit · Maximum-based statistic Reciprocal property TTT plot Log-symmetry Model-calibrated diagnostic Paired empirical process Reciprocal symmetry Total time on test Ciências Naturais::Matemáticas Educação de qualidade |
| url | https://hdl.handle.net/1822/102673 |
| visible | 1 |