{"id":"https://openalex.org/W4226013350","doi":"https://doi.org/10.1109/tr.2022.3154770","title":"Software Belief Reliability Growth Model Based on Uncertain Differential Equation","display_name":"Software Belief Reliability Growth Model Based on Uncertain Differential Equation","publication_year":2022,"publication_date":"2022-03-15","ids":{"openalex":"https://openalex.org/W4226013350","doi":"https://doi.org/10.1109/tr.2022.3154770"},"language":"en","primary_location":{"id":"doi:10.1109/tr.2022.3154770","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2022.3154770","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/A5100462372","display_name":"Zhe Liu","orcid":"https://orcid.org/0000-0002-6013-1745"},"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":"Zhe Liu","raw_affiliation_strings":["School of Reliability and Systems Engineering, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-6013-1745","affiliations":[{"raw_affiliation_string":"School of Reliability and Systems Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037089910","display_name":"Shunkun Yang","orcid":"https://orcid.org/0000-0002-8226-4477"},"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":false,"raw_author_name":"Shunkun Yang","raw_affiliation_strings":["School of Reliability and Systems Engineering, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-8226-4477","affiliations":[{"raw_affiliation_string":"School of Reliability and Systems Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027059634","display_name":"Minghao Yang","orcid":"https://orcid.org/0000-0003-3243-0569"},"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":false,"raw_author_name":"Minghao Yang","raw_affiliation_strings":["School of Reliability and Systems Engineering, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-3243-0569","affiliations":[{"raw_affiliation_string":"School of Reliability and Systems Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102026831","display_name":"Rui Kang","orcid":"https://orcid.org/0000-0002-4488-6574"},"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":false,"raw_author_name":"Rui Kang","raw_affiliation_strings":["School of Reliability and Systems Engineering, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-4488-6574","affiliations":[{"raw_affiliation_string":"School of Reliability and Systems Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100462372"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":9.6862,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.98366718,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"71","issue":"2","first_page":"775","last_page":"787"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12423","display_name":"Software Reliability and Analysis Research","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12423","display_name":"Software Reliability and Analysis Research","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/uncertainty-theory","display_name":"Uncertainty theory","score":0.7116311192512512},{"id":"https://openalex.org/keywords/software-quality","display_name":"Software quality","score":0.6897976398468018},{"id":"https://openalex.org/keywords/reliability-theory","display_name":"Reliability theory","score":0.6742595434188843},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.6533975601196289},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6235432028770447},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.6078386902809143},{"id":"https://openalex.org/keywords/reliability-engineering","display_name":"Reliability engineering","score":0.5853425860404968},{"id":"https://openalex.org/keywords/software-reliability-testing","display_name":"Software reliability testing","score":0.5573500990867615},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4140642583370209},{"id":"https://openalex.org/keywords/software-development","display_name":"Software development","score":0.36329275369644165},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23732122778892517},{"id":"https://openalex.org/keywords/failure-rate","display_name":"Failure rate","score":0.1994490921497345},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1464974284172058}],"concepts":[{"id":"https://openalex.org/C51152595","wikidata":"https://www.wikidata.org/wiki/Q7882501","display_name":"Uncertainty theory","level":2,"score":0.7116311192512512},{"id":"https://openalex.org/C117447612","wikidata":"https://www.wikidata.org/wiki/Q1412670","display_name":"Software quality","level":4,"score":0.6897976398468018},{"id":"https://openalex.org/C201729545","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability theory","level":3,"score":0.6742595434188843},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.6533975601196289},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6235432028770447},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.6078386902809143},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.5853425860404968},{"id":"https://openalex.org/C52928878","wikidata":"https://www.wikidata.org/wiki/Q7554226","display_name":"Software reliability testing","level":5,"score":0.5573500990867615},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4140642583370209},{"id":"https://openalex.org/C529173508","wikidata":"https://www.wikidata.org/wiki/Q638608","display_name":"Software development","level":3,"score":0.36329275369644165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23732122778892517},{"id":"https://openalex.org/C163164238","wikidata":"https://www.wikidata.org/wiki/Q2737027","display_name":"Failure rate","level":2,"score":0.1994490921497345},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1464974284172058},{"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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"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/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.2022.3154770","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2022.3154770","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":[],"awards":[{"id":"https://openalex.org/G7090823840","display_name":null,"funder_award_id":"62073009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W22166167","https://openalex.org/W124052719","https://openalex.org/W130666128","https://openalex.org/W819619936","https://openalex.org/W1544461401","https://openalex.org/W1972467266","https://openalex.org/W1980595883","https://openalex.org/W2001604487","https://openalex.org/W2002420562","https://openalex.org/W2022026029","https://openalex.org/W2043667559","https://openalex.org/W2045891420","https://openalex.org/W2047164750","https://openalex.org/W2067402508","https://openalex.org/W2072359179","https://openalex.org/W2106079023","https://openalex.org/W2109621739","https://openalex.org/W2111959010","https://openalex.org/W2117039703","https://openalex.org/W2120876822","https://openalex.org/W2126041859","https://openalex.org/W2126151844","https://openalex.org/W2127366088","https://openalex.org/W2127740852","https://openalex.org/W2128376191","https://openalex.org/W2132842594","https://openalex.org/W2136646228","https://openalex.org/W2139905755","https://openalex.org/W2143091165","https://openalex.org/W2144683585","https://openalex.org/W2151376743","https://openalex.org/W2152380123","https://openalex.org/W2153242493","https://openalex.org/W2157904088","https://openalex.org/W2164919501","https://openalex.org/W2170105447","https://openalex.org/W2198656879","https://openalex.org/W2346233588","https://openalex.org/W2766491475","https://openalex.org/W2773235479","https://openalex.org/W2803460043","https://openalex.org/W2900597024","https://openalex.org/W2903838979","https://openalex.org/W2909518840","https://openalex.org/W2972346427","https://openalex.org/W3037727996","https://openalex.org/W3083797856","https://openalex.org/W3086511271","https://openalex.org/W3093697920","https://openalex.org/W3094344238","https://openalex.org/W3164683041","https://openalex.org/W3181864547","https://openalex.org/W3186096993","https://openalex.org/W4234521054","https://openalex.org/W4236577982","https://openalex.org/W4281775731","https://openalex.org/W6678868654","https://openalex.org/W6682597882","https://openalex.org/W6687332652"],"related_works":["https://openalex.org/W1521772560","https://openalex.org/W4226182203","https://openalex.org/W4238386252","https://openalex.org/W234065253","https://openalex.org/W3185885951","https://openalex.org/W111546663","https://openalex.org/W2047750899","https://openalex.org/W1966392103","https://openalex.org/W3088925126","https://openalex.org/W4226060998"],"abstract_inverted_index":{"Software":[0],"reliability":[1,14,90,116,137,143,149],"plays":[2],"an":[3,193],"important":[4],"role":[5],"in":[6,24,82,156,171,184],"modern":[7],"society.":[8],"To":[9,52],"evaluate":[10],"software":[11,13,22,83,89,114,136,195],"reliability,":[12],"growth":[15,117],"models":[16],"(SRGMs)":[17],"investigate":[18],"the":[19,25,40,96,126],"number":[20],"of":[21,98,134,186],"faults":[23],"testing":[26,29,41,44,48],"phase.":[27],"Obviously,":[28],"progresses":[30],"are":[31,61,139,158],"inevitably":[32],"influenced":[33],"by":[34],"dynamic":[35,55],"indeterministic":[36],"fluctuations":[37],"such":[38],"as":[39],"effort":[42],"expenditure,":[43],"efficiency":[45],"and":[46,50,111,164,173,189],"skill,":[47],"method,":[49],"strategy.":[51],"model":[53,118],"these":[54],"fluctuations,":[56],"several":[57,180],"probability":[58,64,109],"theory-based":[59],"SRGMs":[60,183],"proposed.":[62],"However,":[63],"theory":[65],"is":[66,102,146,198],"suitable":[67],"for":[68,125,153],"dealing":[69],"with":[70,77],"aleatory":[71],"uncertainty,":[72],"but":[73],"fails":[74],"to":[75],"deal":[76],"epistemic":[78],"uncertainty":[79,99],"widely":[80],"existing":[81],"faults.":[84],"Therefore,":[85],"this":[86,131],"article":[87],"considers":[88],"from":[91,108],"a":[92,103,113,147],"new":[93,104],"perspective":[94],"under":[95,141],"framework":[97],"theory,":[100,110,144],"which":[101,145],"mathematical":[105],"system":[106],"different":[107],"proposes":[112],"belief":[115,142],"(SBRGM)":[119],"based":[120],"on":[121,130],"uncertain":[122],"differential":[123],"equations":[124],"first":[127],"time.":[128],"Based":[129],"SBRGM,":[132],"properties":[133],"essential":[135],"metrics":[138],"investigated":[140],"brand-new":[148],"theory.":[150],"Parameter":[151],"estimations":[152],"unknown":[154],"parameters":[155],"SBRGM":[157],"presented.":[159],"Furthermore,":[160],"some":[161],"numerical":[162],"examples":[163],"real":[165],"data":[166],"analyses":[167],"illustrate":[168],"our":[169],"methodology":[170],"detail,":[172],"show":[174],"that":[175],"it":[176],"performs":[177],"better":[178],"than":[179],"famous":[181],"probability-based":[182],"terms":[185],"fitting":[187],"ability":[188],"prediction":[190],"ability.":[191],"Finally,":[192],"optimal":[194],"release":[196],"policy":[197],"discussed.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-20T08:49:12.498775","created_date":"2025-10-10T00:00:00"}
