{"id":"https://openalex.org/W2151000533","doi":"https://doi.org/10.1088/0026-1394/39/4/5","title":"A classical method for uncertainty analysis with multidimensional data","display_name":"A classical method for uncertainty analysis with multidimensional data","publication_year":2002,"publication_date":"2002-08-01","ids":{"openalex":"https://openalex.org/W2151000533","doi":"https://doi.org/10.1088/0026-1394/39/4/5","mag":"2151000533"},"language":"en","primary_location":{"id":"doi:10.1088/0026-1394/39/4/5","doi":"https://doi.org/10.1088/0026-1394/39/4/5","is_oa":false,"landing_page_url":"https://doi.org/10.1088/0026-1394/39/4/5","pdf_url":null,"source":{"id":"https://openalex.org/S7291761","display_name":"Metrologia","issn_l":"0026-1394","issn":["0026-1394","1681-7575"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Metrologia","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078594911","display_name":"Robin Willink","orcid":"https://orcid.org/0000-0002-5447-3626","observed_orcids":["https://orcid.org/0000-0002-5447-3626"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R Willink","raw_affiliation_strings":["Applied Mathematics, Industrial Research Ltd, PO Box 31-310, Lower Hutt, New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics, Industrial Research Ltd, PO Box 31-310, Lower Hutt, New Zealand","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079491459","display_name":"Blair D. Hall","orcid":"https://orcid.org/0000-0002-4249-6863","observed_orcids":["https://orcid.org/0000-0002-4249-6863"]},"institutions":[{"id":"https://openalex.org/I4387153315","display_name":"Measurement Standards Laboratory of New Zealand","ror":"https://ror.org/04022gq47","country_code":"NZ","type":"government","lineage":["https://openalex.org/I4387153315"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"B D Hall","raw_affiliation_strings":["Measurement Standards Laboratory of New Zealand, PO Box 31-310, Lower Hutt, New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Measurement Standards Laboratory of New Zealand, PO Box 31-310, Lower Hutt, New Zealand","institution_ids":["https://openalex.org/I4387153315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3325,"currency":"USD","value_usd":3325},"apc_paid":null,"fwci":3.1579,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.9265896,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"39","issue":"4","first_page":"361","last_page":"369"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uncertainty-analysis","display_name":"uncertainty analysis","score":0.9340000152587891},{"id":"https://openalex.org/keywords/multidimensional-data","display_name":"multidimensional data","score":0.7889999747276306},{"id":"https://openalex.org/keywords/effective-degrees-of-freedom","display_name":"effective degrees of freedom","score":0.9800000190734863},{"id":"https://openalex.org/keywords/type-a-evaluation","display_name":"Type A evaluation","score":0.8640000224113464},{"id":"https://openalex.org/keywords/measurement-uncertainty","display_name":"measurement uncertainty","score":0.656000018119812}],"concepts":[{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.6302331686019897},{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.5617293119430542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5297927260398865},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5178797245025635},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48805201053619385},{"id":"https://openalex.org/C2776292839","wikidata":"https://www.wikidata.org/wiki/Q5179217","display_name":"Coverage probability","level":3,"score":0.4670613706111908},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.4392920732498169},{"id":"https://openalex.org/C143380155","wikidata":"https://www.wikidata.org/wiki/Q5160088","display_name":"Confidence region","level":3,"score":0.43286460638046265},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.42769432067871094},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.41666707396507263},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39452236890792847},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3283578157424927},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1173962950706482},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1088/0026-1394/39/4/5","doi":"https://doi.org/10.1088/0026-1394/39/4/5","is_oa":false,"landing_page_url":"https://doi.org/10.1088/0026-1394/39/4/5","pdf_url":null,"source":{"id":"https://openalex.org/S7291761","display_name":"Metrologia","issn_l":"0026-1394","issn":["0026-1394","1681-7575"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Metrologia","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, justice, and strong institutions"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1973158119","https://openalex.org/W2062989416","https://openalex.org/W2112440119","https://openalex.org/W2113525985","https://openalex.org/W2413573154","https://openalex.org/W3148198191"],"related_works":["https://openalex.org/W2357266745","https://openalex.org/W2103836094","https://openalex.org/W2983662580","https://openalex.org/W1986065291","https://openalex.org/W4280620415","https://openalex.org/W1970749726","https://openalex.org/W7148562368","https://openalex.org/W3112081670","https://openalex.org/W2782778704","https://openalex.org/W2017582578"],"abstract_inverted_index":{"A":[0,92],"method":[1,25,81,96],"of":[2,20,38,79,108],"uncertainty":[3,32],"analysis":[4],"based":[5],"on":[6],"classical":[7],"statistical":[8],"principles":[9],"is":[10,16,97,110],"presented":[11],"for":[12,57,103],"a":[13,17,29,58,106],"measurand":[14,28,43,70],"that":[15],"linear":[18],"combination":[19],"multidimensional":[21,54],"input":[22,84],"quantities.":[23],"The":[24,77],"assigns":[26],"the":[27,42,53,65,69,80,90,95,100],"combined":[30],"standard":[31],"matrix":[33],"and":[34],"an":[35,48,113],"effective":[36],"degrees":[37],"freedom,":[39],"which":[40,109],"allows":[41],"to":[44,67,86,99],"be":[45,87],"estimated":[46],"by":[47,89],"ellipsoidal":[49],"confidence":[50,62],"region":[51],"in":[52,112],"space.":[55],"Simulations":[56],"95":[59],"%":[60],"nominal":[61],"level":[63],"show":[64],"ellipsoids":[66],"contain":[68],"with":[71],"probability":[72],"approximately":[73],"0.95,":[74],"as":[75],"required.":[76],"derivation":[78,107],"assumes":[82],"all":[83],"uncertainties":[85],"evaluated":[88],"Type":[91],"method.":[93],"So":[94],"analogous":[98],"Welch-Satterthwaite":[101],"formula":[102],"one-dimensional":[104],"data,":[105],"given":[111],"appendix.":[114]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2016-06-24T00:00:00"}
