{"id":"https://openalex.org/W2525082097","doi":"https://doi.org/10.1109/tr.2016.2604121","title":"Improve the Accuracy of Asymptotic Approximation in Reliability Problems Involving Multimodal Distributions","display_name":"Improve the Accuracy of Asymptotic Approximation in Reliability Problems Involving Multimodal Distributions","publication_year":2016,"publication_date":"2016-09-26","ids":{"openalex":"https://openalex.org/W2525082097","doi":"https://doi.org/10.1109/tr.2016.2604121","mag":"2525082097"},"language":"en","primary_location":{"id":"doi:10.1109/tr.2016.2604121","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2016.2604121","pdf_url":null,"source":{"id":"https://openalex.org/S87725633","display_name":"IEEE Transactions on Reliability","issn_l":"0018-9529","issn":["0018-9529","1558-1721"],"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 Reliability","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/A5047693161","display_name":"Jingjing He","orcid":"https://orcid.org/0000-0003-2236-254X"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jingjing He","raw_affiliation_strings":["School of Reliability and System Engineering, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Reliability and System Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007911718","display_name":"Xuefei Guan","orcid":"https://orcid.org/0000-0002-5928-3039"},"institutions":[{"id":"https://openalex.org/I4210137693","display_name":"Siemens (United States)","ror":"https://ror.org/04axb7e79","country_code":"US","type":"company","lineage":["https://openalex.org/I1325886976","https://openalex.org/I4210137693"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xuefei Guan","raw_affiliation_strings":["Siemens Corporation, Corporate Technology, Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Siemens Corporation, Corporate Technology, Princeton, NJ, USA","institution_ids":["https://openalex.org/I4210137693"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064117164","display_name":"R. Jha","orcid":"https://orcid.org/0000-0001-5025-0129"},"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":"Ratneshwar Jha","raw_affiliation_strings":["Department of Aerospace Engineering, Raspet Flight Research Laboratory, Mississippi State University, Starkville, MS, USA"],"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, Raspet Flight Research Laboratory, Mississippi State University, Starkville, MS, USA","institution_ids":["https://openalex.org/I99041443"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047693161"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":2.4488,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.91092469,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"65","issue":"4","first_page":"1724","last_page":"1736"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10396","display_name":"Fatigue and fracture mechanics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.8269655704498291},{"id":"https://openalex.org/keywords/laplaces-method","display_name":"Laplace's method","score":0.5779944062232971},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.5663883686065674},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.5648794174194336},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5457439422607422},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49093034863471985},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4513026475906372},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42526930570602417},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4094352424144745},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36204269528388977},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14036238193511963}],"concepts":[{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.8269655704498291},{"id":"https://openalex.org/C22243797","wikidata":"https://www.wikidata.org/wiki/Q2058297","display_name":"Laplace's method","level":3,"score":0.5779944062232971},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.5663883686065674},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.5648794174194336},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5457439422607422},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49093034863471985},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4513026475906372},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42526930570602417},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4094352424144745},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36204269528388977},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14036238193511963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tr.2016.2604121","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2016.2604121","pdf_url":null,"source":{"id":"https://openalex.org/S87725633","display_name":"IEEE Transactions on Reliability","issn_l":"0018-9529","issn":["0018-9529","1558-1721"],"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 Reliability","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8100000023841858,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320307782","display_name":"Siemens USA","ror":"https://ror.org/04axb7e79"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W232805744","https://openalex.org/W1556911442","https://openalex.org/W1965777485","https://openalex.org/W1965920338","https://openalex.org/W1966667501","https://openalex.org/W1968543489","https://openalex.org/W1970360305","https://openalex.org/W1971722701","https://openalex.org/W1972955129","https://openalex.org/W1978625350","https://openalex.org/W1992086890","https://openalex.org/W1999091229","https://openalex.org/W2003094496","https://openalex.org/W2004885162","https://openalex.org/W2005142092","https://openalex.org/W2008034786","https://openalex.org/W2013065734","https://openalex.org/W2013164703","https://openalex.org/W2013196923","https://openalex.org/W2024826731","https://openalex.org/W2029538494","https://openalex.org/W2032751439","https://openalex.org/W2033057584","https://openalex.org/W2033320212","https://openalex.org/W2034795216","https://openalex.org/W2038603943","https://openalex.org/W2040390190","https://openalex.org/W2040932457","https://openalex.org/W2045973738","https://openalex.org/W2047735376","https://openalex.org/W2053656087","https://openalex.org/W2053786598","https://openalex.org/W2057533129","https://openalex.org/W2059003472","https://openalex.org/W2071517573","https://openalex.org/W2079781067","https://openalex.org/W2080735494","https://openalex.org/W2123838014","https://openalex.org/W2124514594","https://openalex.org/W2124800952","https://openalex.org/W2138309709","https://openalex.org/W2139580271","https://openalex.org/W2140223291","https://openalex.org/W2162733643","https://openalex.org/W2166670624","https://openalex.org/W2178829616","https://openalex.org/W2314675611","https://openalex.org/W3020882730","https://openalex.org/W4232000820","https://openalex.org/W4248373945","https://openalex.org/W4255299209","https://openalex.org/W4300906944"],"related_works":["https://openalex.org/W2180954594","https://openalex.org/W2052835778","https://openalex.org/W2049003611","https://openalex.org/W2887005408","https://openalex.org/W4289676468","https://openalex.org/W4310826001","https://openalex.org/W2041486430","https://openalex.org/W2086883878","https://openalex.org/W3114582462","https://openalex.org/W4386236780"],"abstract_inverted_index":{"Asymptotic":[0],"approximations":[1],"such":[2,46],"as":[3],"the":[4,86,111,146,194,199],"first-":[5],"and":[6,31,77,106,133,150,173,196],"second-order":[7],"reliability":[8,16,131],"method":[9,43,129,144,162],"(FORM,":[10],"SORM)":[11],"are":[12,82,98,186],"sometimes":[13],"preferred":[14],"in":[15,39,64,104,120],"analysis":[17,158,179],"due":[18],"to":[19,66,84,153,165,192],"their":[20],"efficiency.":[21],"Bayesian":[22,178],"updating":[23],"for":[24,57,91,130],"practical":[25],"engineering":[26,167],"problems":[27],"can":[28,44,115],"produce":[29,116],"unnormalized":[30,138],"multimodal":[32,92,139],"distributions,":[33],"which":[34],"cannot":[35],"be":[36,61],"directly":[37],"used":[38],"FORM.":[40],"The":[41,54,94,143,160],"Laplace":[42,89,147],"approximate":[45],"distributions":[47,140],"using":[48],"a":[49,73,155,174],"weighted":[50],"multivariate":[51],"normal":[52],"distribution.":[53],"weighting":[55,75,80,96,102,113],"scheme":[56,76,81],"different":[58],"modes":[59],"must":[60],"carefully":[62],"made":[63],"order":[65],"achieve":[67],"accurate":[68,118],"results.":[69],"In":[70],"this":[71],"paper,":[72],"new":[74],"an":[78,126],"optimal":[79],"proposed":[83,95,112],"improve":[85],"accuracy":[87,197],"of":[88,198],"approximation":[90,128],"distributions.":[93],"schemes":[97,103,114],"compared":[99,187],"with":[100,180,188],"existing":[101,189],"detail,":[105],"it":[107],"is":[108,141,163],"shown":[109],"that":[110],"more":[117],"results":[119],"some":[121],"cases.":[122],"Based":[123],"on":[124],"that,":[125],"asymptotic":[127,157],"estimation":[132],"system":[134],"response":[135],"predictions":[136],"involving":[137],"proposed.":[142],"integrates":[145],"method,":[148],"FORM,":[149],"inverse":[151],"FORM":[152],"formulate":[154],"completely":[156],"cycle.":[159],"overall":[161],"applied":[164],"two":[166],"cases:":[168],"A":[169],"simplified":[170],"bridge":[171],"model":[172],"steam":[175],"turbine":[176],"rotor":[177],"real":[181],"ultrasonic":[182],"inspection":[183],"data.":[184],"Results":[185],"simulation-based":[190],"methods":[191],"investigate":[193],"efficiency":[195],"method.":[200]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}