{"id":"https://openalex.org/W2064812502","doi":"https://doi.org/10.1109/tim.2015.2393396","title":"Uncertainty Evaluation for a System of Weighing Equations for the Determination of Microgram Weights","display_name":"Uncertainty Evaluation for a System of Weighing Equations for the Determination of Microgram Weights","publication_year":2015,"publication_date":"2015-02-02","ids":{"openalex":"https://openalex.org/W2064812502","doi":"https://doi.org/10.1109/tim.2015.2393396","mag":"2064812502"},"language":"en","primary_location":{"id":"doi:10.1109/tim.2015.2393396","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2015.2393396","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Instrumentation and Measurement","raw_type":"journal-article"},"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/A5100370370","display_name":"Jian Wang","orcid":"https://orcid.org/0000-0001-8812-4398"},"institutions":[{"id":"https://openalex.org/I4210162136","display_name":"National Institute of Metrology","ror":"https://ror.org/05dw0p167","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210162136"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jian Wang","raw_affiliation_strings":["National Institute of Metrology, Beijing, China",", National Institute of Metrology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"National Institute of Metrology, Beijing, China","institution_ids":["https://openalex.org/I4210162136"]},{"raw_affiliation_string":", National Institute of Metrology, Beijing, China","institution_ids":["https://openalex.org/I4210162136"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032012682","display_name":"Peter Fuchs","orcid":"https://orcid.org/0000-0001-5308-9529"},"institutions":[{"id":"https://openalex.org/I4210103407","display_name":"Swiss Federal Institute of Metrology","ror":"https://ror.org/0115xv923","country_code":"CH","type":"government","lineage":["https://openalex.org/I4210103407"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Peter Fuchs","raw_affiliation_strings":["Federal Institute of Metrology, Bern, Switzerland",", Federal Institute of Metrology, Bern, Switzerland"],"affiliations":[{"raw_affiliation_string":"Federal Institute of Metrology, Bern, Switzerland","institution_ids":["https://openalex.org/I4210103407"]},{"raw_affiliation_string":", Federal Institute of Metrology, Bern, Switzerland","institution_ids":["https://openalex.org/I4210103407"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088983957","display_name":"S Russi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210103407","display_name":"Swiss Federal Institute of Metrology","ror":"https://ror.org/0115xv923","country_code":"CH","type":"government","lineage":["https://openalex.org/I4210103407"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Stefan Russi","raw_affiliation_strings":["Federal Institute of Metrology, Bern, Switzerland",", Federal Institute of Metrology, Bern, Switzerland"],"affiliations":[{"raw_affiliation_string":"Federal Institute of Metrology, Bern, Switzerland","institution_ids":["https://openalex.org/I4210103407"]},{"raw_affiliation_string":", Federal Institute of Metrology, Bern, Switzerland","institution_ids":["https://openalex.org/I4210103407"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056182966","display_name":"Xiaoping Ren","orcid":"https://orcid.org/0000-0003-0602-7055"},"institutions":[{"id":"https://openalex.org/I4210162136","display_name":"National Institute of Metrology","ror":"https://ror.org/05dw0p167","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210162136"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoping Ren","raw_affiliation_strings":["National Institute of Metrology, Beijing, China",", National Institute of Metrology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"National Institute of Metrology, Beijing, China","institution_ids":["https://openalex.org/I4210162136"]},{"raw_affiliation_string":", National Institute of Metrology, Beijing, China","institution_ids":["https://openalex.org/I4210162136"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101146797","display_name":"Changqing Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I4210162136","display_name":"National Institute of Metrology","ror":"https://ror.org/05dw0p167","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210162136"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changqing Cai","raw_affiliation_strings":["National Institute of Metrology, Beijing, China",", National Institute of Metrology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"National Institute of Metrology, Beijing, China","institution_ids":["https://openalex.org/I4210162136"]},{"raw_affiliation_string":", National Institute of Metrology, Beijing, China","institution_ids":["https://openalex.org/I4210162136"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071319432","display_name":"Nan Yang","orcid":"https://orcid.org/0000-0002-1610-5240"},"institutions":[{"id":"https://openalex.org/I4210162136","display_name":"National Institute of Metrology","ror":"https://ror.org/05dw0p167","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210162136"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nan Yang","raw_affiliation_strings":["National Institute of Metrology, Beijing, China",", National Institute of Metrology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"National Institute of Metrology, Beijing, China","institution_ids":["https://openalex.org/I4210162136"]},{"raw_affiliation_string":", National Institute of Metrology, Beijing, China","institution_ids":["https://openalex.org/I4210162136"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5100370370"],"corresponding_institution_ids":["https://openalex.org/I4210162136"],"apc_list":null,"apc_paid":null,"fwci":1.1866,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84861623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"64","issue":"8","first_page":"2272","last_page":"2279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9991000294685364,"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":0.9991000294685364,"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/T12564","display_name":"Sensor Technology and Measurement Systems","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13928","display_name":"Advanced Sensor Technologies Research","score":0.9031000137329102,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.7750427722930908},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6908286213874817},{"id":"https://openalex.org/keywords/mass-matrix","display_name":"Mass matrix","score":0.6546123027801514},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5621058344841003},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5517987608909607},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5325257778167725},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5152166485786438},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5044995546340942},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.4829792082309723},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42913752794265747},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38879072666168213},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34110134840011597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32469257712364197},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17334187030792236},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.16900822520256042},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.07964000105857849}],"concepts":[{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.7750427722930908},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6908286213874817},{"id":"https://openalex.org/C135585149","wikidata":"https://www.wikidata.org/wiki/Q339704","display_name":"Mass matrix","level":3,"score":0.6546123027801514},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5621058344841003},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5517987608909607},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5325257778167725},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5152166485786438},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5044995546340942},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.4829792082309723},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42913752794265747},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38879072666168213},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34110134840011597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32469257712364197},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17334187030792236},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.16900822520256042},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07964000105857849},{"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/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C185544564","wikidata":"https://www.wikidata.org/wiki/Q81197","display_name":"Nuclear physics","level":1,"score":0.0},{"id":"https://openalex.org/C147176958","wikidata":"https://www.wikidata.org/wiki/Q77590","display_name":"Civil engineering","level":1,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tim.2015.2393396","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2015.2393396","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Instrumentation and Measurement","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1985956577","https://openalex.org/W2021404852","https://openalex.org/W2029724728","https://openalex.org/W2153231645","https://openalex.org/W2162274254","https://openalex.org/W4239332446"],"related_works":["https://openalex.org/W2384806462","https://openalex.org/W4389950792","https://openalex.org/W2375549870","https://openalex.org/W4376632515","https://openalex.org/W2163269603","https://openalex.org/W2180954594","https://openalex.org/W4205312897","https://openalex.org/W2795347481","https://openalex.org/W2750153370","https://openalex.org/W1106115901"],"abstract_inverted_index":{"Subdivision":[0],"comparisons":[1],"of":[2,34,60,98,112,123,136,152,157],"mass":[3,10,18,35,47,58],"measurement":[4,36,48],"are":[5,37,49,73,78,166],"usually":[6],"used":[7],"in":[8,39,145,163,167,170],"the":[9,40,54,68,82,96,104,113,150,158,171],"dissemination":[11],"for":[12,46,94,133],"class":[13],"E":[14],"<sub":[15],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[16],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[17],"standards":[19],"from":[20,27,125],"1":[21,24,28],"kg":[22],"to":[23,29,52,120,127,148],"mg":[25],"or":[26,56],"50":[30,128],"kg.":[31],"Many":[32],"equations":[33,100,138],"included":[38],"subdivision":[41],"comparisons.":[42],"Therefore,":[43],"matrix":[44,66,92,137,159],"calculations":[45],"very":[50],"convenient":[51],"get":[53],"true":[55],"conventional":[57,65],"value":[59],"every":[61],"weight":[62],"compared.":[63],"In":[64,85],"equations,":[67],"important":[69],"air":[70],"buoyancy":[71],"corrections":[72],"completely":[74],"neglected,":[75],"and":[76],"uncertainties":[77,135],"normally":[79],"calculated":[80],"using":[81,108],"variance-covariance":[83],"matrix.":[84],"this":[86,146,164],"paper,":[87,147],"we":[88],"propose":[89],"a":[90,121],"new":[91],"calculation":[93,151],"both":[95],"system":[97],"weighing":[99],"as":[101,103],"well":[102],"corresponding":[105],"uncertainty":[106,153],"budget":[107,154],"directly":[109],"partial":[110],"derivations":[111],"weighting":[114],"equations.":[115],"The":[116],"method":[117,132],"is":[118,139],"applied":[119],"set":[122],"weights":[124],"500":[126],"\u03bcg.":[129],"An":[130],"alternative":[131],"evaluating":[134],"by":[140,155],"Monte":[141],"Carlo":[142],"simulation,":[143],"introduced":[144],"validate":[149],"means":[156],"method.":[160],"(Some":[161],"figures":[162],"paper":[165],"color":[168],"only":[169],"electronic":[172],"version.)":[173]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}