{"id":"https://openalex.org/W2212424223","doi":"https://doi.org/10.1186/s40467-015-0041-9","title":"An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method","display_name":"An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2212424223","doi":"https://doi.org/10.1186/s40467-015-0041-9","mag":"2212424223"},"language":"en","primary_location":{"id":"doi:10.1186/s40467-015-0041-9","doi":"https://doi.org/10.1186/s40467-015-0041-9","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40467-015-0041-9","pdf_url":"https://juaa-journal.springeropen.com/counter/pdf/10.1186/s40467-015-0041-9","source":{"id":"https://openalex.org/S4210219051","display_name":"Journal of Uncertainty Analysis and Applications","issn_l":"2195-5468","issn":["2195-5468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Uncertainty Analysis and Applications","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://juaa-journal.springeropen.com/counter/pdf/10.1186/s40467-015-0041-9","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079442967","display_name":"Heejin Cho","orcid":"https://orcid.org/0000-0003-2789-510X","observed_orcids":["https://orcid.org/0000-0003-2789-510X"]},"institutions":[{"id":"https://openalex.org/I99041443","display_name":"Mississippi State University","ror":"https://ror.org/0432jq872","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I99041443"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Heejin Cho","raw_affiliation_strings":["Department of Mechanical Engineering, Mississippi State University, PO Box 9552, Mississippi State, MS, 39762, USA"],"raw_orcid":"https://orcid.org/0000-0003-2789-510X","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Mississippi State University, PO Box 9552, Mississippi State, MS, 39762, USA","institution_ids":["https://openalex.org/I99041443"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111726520","display_name":"Rogelio Luck","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99041443","display_name":"Mississippi State University","ror":"https://ror.org/0432jq872","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I99041443"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rogelio Luck","raw_affiliation_strings":["Department of Mechanical Engineering, Mississippi State University, PO Box 9552, Mississippi State, MS, 39762, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Mississippi State University, PO Box 9552, Mississippi State, MS, 39762, USA","institution_ids":["https://openalex.org/I99041443"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010726008","display_name":"James W. Stevens","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I888729015","display_name":"University of Colorado Colorado Springs","ror":"https://ror.org/054spjc55","country_code":"US","type":"education","lineage":["https://openalex.org/I888729015"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James W. Stevens","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Colorado at Colorado Springs, Colorado Springs, CO, 80918, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Colorado at Colorado Springs, Colorado Springs, CO, 80918, USA","institution_ids":["https://openalex.org/I888729015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079442967"],"corresponding_institution_ids":["https://openalex.org/I99041443"],"apc_list":null,"apc_paid":null,"fwci":1.5181,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.86580771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"3","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9779999852180481,"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":0.9779999852180481,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.015300000086426735,"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":0.00279999990016222,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/measurement-uncertainty","display_name":"measurement uncertainty","score":0.7099999785423279},{"id":"https://openalex.org/keywords/least-squares-regression","display_name":"least squares regression","score":0.7110000252723694},{"id":"https://openalex.org/keywords/sensitivity-coefficients","display_name":"sensitivity coefficients","score":0.9629999995231628},{"id":"https://openalex.org/keywords/taylor-expansion","display_name":"Taylor series expansion","score":0.6970000267028809},{"id":"https://openalex.org/keywords/numerical-differentiation","display_name":"numerical differentiation","score":0.48500001430511475},{"id":"https://openalex.org/keywords/central-differences","display_name":"central differences","score":0.4180000126361847}],"concepts":[{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.5902743935585022},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5651058554649353},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.5379866361618042},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5076843500137329},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5003230571746826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4946694076061249},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.4896290898323059},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.4849555492401123},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.44549819827079773},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4397755563259125},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.436400830745697},{"id":"https://openalex.org/C137209882","wikidata":"https://www.wikidata.org/wiki/Q1403517","display_name":"Measurement uncertainty","level":2,"score":0.4362880289554596},{"id":"https://openalex.org/C177803969","wikidata":"https://www.wikidata.org/wiki/Q29205","display_name":"Uncertainty analysis","level":2,"score":0.43084225058555603},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40861964225769043},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3698968291282654},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2977498173713684},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.1784418225288391},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11610198020935059},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10043108463287354},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1186/s40467-015-0041-9","doi":"https://doi.org/10.1186/s40467-015-0041-9","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40467-015-0041-9","pdf_url":"https://juaa-journal.springeropen.com/counter/pdf/10.1186/s40467-015-0041-9","source":{"id":"https://openalex.org/S4210219051","display_name":"Journal of Uncertainty Analysis and Applications","issn_l":"2195-5468","issn":["2195-5468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Uncertainty Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1186/s40467-015-0041-9","doi":"https://doi.org/10.1186/s40467-015-0041-9","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40467-015-0041-9","pdf_url":"https://juaa-journal.springeropen.com/counter/pdf/10.1186/s40467-015-0041-9","source":{"id":"https://openalex.org/S4210219051","display_name":"Journal of Uncertainty Analysis and Applications","issn_l":"2195-5468","issn":["2195-5468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Uncertainty Analysis and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2212424223.pdf","grobid_xml":"https://content.openalex.org/works/W2212424223.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W588710955","https://openalex.org/W1563612452","https://openalex.org/W1575805520","https://openalex.org/W1619787994","https://openalex.org/W1667165204","https://openalex.org/W1992801522","https://openalex.org/W2005684852","https://openalex.org/W2012572800","https://openalex.org/W2029063272","https://openalex.org/W2030082083","https://openalex.org/W2033999198","https://openalex.org/W2055445699","https://openalex.org/W2055747980","https://openalex.org/W2056663488","https://openalex.org/W2069143626","https://openalex.org/W2083506864","https://openalex.org/W2116278711","https://openalex.org/W2315214008","https://openalex.org/W2920875148","https://openalex.org/W2923994282","https://openalex.org/W3028291807","https://openalex.org/W3081274109","https://openalex.org/W3144258617","https://openalex.org/W4232398379","https://openalex.org/W4235876623"],"related_works":["https://openalex.org/W884615847","https://openalex.org/W2047686669","https://openalex.org/W2146910333","https://openalex.org/W149424466","https://openalex.org/W314811971","https://openalex.org/W2111151137","https://openalex.org/W4210691042","https://openalex.org/W1625066217","https://openalex.org/W255632510","https://openalex.org/W2086904869"],"abstract_inverted_index":{"Linear":[0],"uncertainty":[1,49,67,72],"analysis":[2,50],"based":[3,107],"on":[4,108],"a":[5,58,157],"first":[6],"order":[7],"Taylor":[8],"series":[9],"expansion,":[10],"described":[11],"in":[12,30,40,47,81,174],"ASME":[13],"PTC":[14],"(Performance":[15],"Test":[16],"Code)":[17],"19.1":[18],"\u201cTest":[19],"Uncertainty\u201d":[20],"and":[21,42,71],"the":[22,26,34,61,66,82,95,104,130,133,138,146,150,154,163,179,182],"ISO":[23],"Guide":[24],"for":[25,161],"\u201cExpression":[27],"of":[28,60,99,129,132,140,145,152,181],"Uncertainty":[29],"Measurement,\u201d":[31],"has":[32],"been":[33],"most":[35],"widely":[36],"technique":[37,166],"used":[38],"both":[39],"industry":[41],"academia.":[43],"A":[44,142],"common":[45],"approach":[46,148],"linear":[48,116,164],"is":[51,89,119,149,167],"to":[52,64,77,122,177],"use":[53],"local":[54],"derivative":[55,87,98,106],"information":[56,88],"as":[57],"measure":[59],"sensitivity":[62,124],"needed":[63],"calculate":[65],"percentage":[68],"contribution":[69],"(UPC)":[70],"magnification":[73],"factors":[74],"(UMF)":[75],"due":[76],"each":[78],"independent":[79],"variable":[80],"measurement/process":[83],"being":[84],"examined.":[85],"The":[86],"typically":[90],"obtained":[91],"by":[92],"either":[93],"taking":[94],"symbolic":[96],"partial":[97],"an":[100],"analytical":[101],"expression":[102],"or":[103],"numerical":[105],"central":[109],"difference":[110],"techniques.":[111],"This":[112],"paper":[113,176],"demonstrates":[114],"that":[115,126],"multivariable":[117],"regression":[118],"better":[120],"suited":[121],"obtain":[123],"coefficients":[125],"are":[127,172],"representative":[128],"behavior":[131],"data":[134],"reduction":[135],"equations":[136],"over":[137],"region":[139],"interest.":[141],"main":[143],"advantage":[144],"proposed":[147,183],"possibility":[151],"extending":[153],"range,":[155],"within":[156],"fixed":[158],"tolerance":[159],"level,":[160],"which":[162],"approximation":[165],"valid.":[168],"Three":[169],"practical":[170],"examples":[171],"presented":[173],"this":[175],"demonstrate":[178],"effectiveness":[180],"least-squares":[184],"method.":[185]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2016-06-24T00:00:00"}
