{"id":"https://openalex.org/W4390479422","doi":"https://doi.org/10.3390/sym16010057","title":"Multi-Performance Degradation System Reliability Analysis with Varying Failure Threshold Based on Copulas","display_name":"Multi-Performance Degradation System Reliability Analysis with Varying Failure Threshold Based on Copulas","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4390479422","doi":"https://doi.org/10.3390/sym16010057"},"language":"en","primary_location":{"id":"doi:10.3390/sym16010057","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym16010057","pdf_url":"https://www.mdpi.com/2073-8994/16/1/57/pdf?version=1704101080","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/1/57/pdf?version=1704101080","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034120382","display_name":"Weizheng Gan","orcid":"https://orcid.org/0009-0002-8125-9278"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weizheng Gan","raw_affiliation_strings":["Department of Mathematics, Southwest Jiaotong University, Chengdu 611756, China"],"raw_orcid":"https://orcid.org/0009-0002-8125-9278","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southwest Jiaotong University, Chengdu 611756, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065230448","display_name":"Jiayin Tang","orcid":"https://orcid.org/0000-0002-4516-6026"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiayin Tang","raw_affiliation_strings":["Department of Mathematics, Southwest Jiaotong University, Chengdu 611756, China"],"raw_orcid":"https://orcid.org/0000-0002-4516-6026","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southwest Jiaotong University, Chengdu 611756, China","institution_ids":["https://openalex.org/I4800084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065230448"],"corresponding_institution_ids":["https://openalex.org/I4800084"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.1719,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72973436,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"16","issue":"1","first_page":"57","last_page":"57"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9998999834060669,"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/T12423","display_name":"Software Reliability and Analysis Research","score":0.9954000115394592,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9951000213623047,"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/copula","display_name":"Copula (linguistics)","score":0.7875826358795166},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.6345906257629395},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.5199345946311951},{"id":"https://openalex.org/keywords/degradation","display_name":"Degradation (telecommunications)","score":0.511991560459137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5100467801094055},{"id":"https://openalex.org/keywords/reliability-engineering","display_name":"Reliability engineering","score":0.4662403464317322},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3278042674064636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3059368133544922},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24272871017456055},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.14937254786491394},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08177736401557922}],"concepts":[{"id":"https://openalex.org/C17618745","wikidata":"https://www.wikidata.org/wiki/Q207509","display_name":"Copula (linguistics)","level":2,"score":0.7875826358795166},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.6345906257629395},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.5199345946311951},{"id":"https://openalex.org/C2779679103","wikidata":"https://www.wikidata.org/wiki/Q5251805","display_name":"Degradation (telecommunications)","level":2,"score":0.511991560459137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5100467801094055},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.4662403464317322},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3278042674064636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3059368133544922},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24272871017456055},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.14937254786491394},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08177736401557922},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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":3,"locations":[{"id":"doi:10.3390/sym16010057","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym16010057","pdf_url":"https://www.mdpi.com/2073-8994/16/1/57/pdf?version=1704101080","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:50e641b9dadb453bbad424cc9ef2d6d4","is_oa":false,"landing_page_url":"https://doaj.org/article/50e641b9dadb453bbad424cc9ef2d6d4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 1, p 57 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/16/1/57/","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16010057","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym16010057","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym16010057","pdf_url":"https://www.mdpi.com/2073-8994/16/1/57/pdf?version=1704101080","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322720","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390479422.pdf","grobid_xml":"https://content.openalex.org/works/W4390479422.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1969638528","https://openalex.org/W1988286714","https://openalex.org/W1988482885","https://openalex.org/W1988603015","https://openalex.org/W2013641085","https://openalex.org/W2013896079","https://openalex.org/W2033370164","https://openalex.org/W2041966621","https://openalex.org/W2088078669","https://openalex.org/W2088555868","https://openalex.org/W2090749763","https://openalex.org/W2114087231","https://openalex.org/W2127264253","https://openalex.org/W2132049856","https://openalex.org/W2137951154","https://openalex.org/W2196347524","https://openalex.org/W2515834243","https://openalex.org/W2620003726","https://openalex.org/W2625517649","https://openalex.org/W2895715583","https://openalex.org/W6647729547"],"related_works":["https://openalex.org/W2990837948","https://openalex.org/W3127236696","https://openalex.org/W2202466617","https://openalex.org/W2080551413","https://openalex.org/W2756923888","https://openalex.org/W2767176313","https://openalex.org/W4287838929","https://openalex.org/W2359012312","https://openalex.org/W2800558361","https://openalex.org/W3177005804"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigated":[2],"reliability":[3],"modeling":[4],"for":[5,121],"systems":[6],"subject":[7],"to":[8,80,113],"dependent":[9],"competing":[10,26],"risks":[11],"considering":[12],"that":[13],"variation":[14,31,41],"of":[15,32,42,57,67,117,129],"the":[16,30,40,43,51,55,58,100,115,118,125,130],"failure":[17,27],"threshold":[18,44],"is":[19,70],"not":[20],"considered":[21,46,99],"in":[22],"most":[23],"studies":[24],"on":[25,47,92],"reliability.":[28],"Firstly,":[29],"degradation":[33,53,83,88,105],"quantity":[34],"under":[35,54],"shocks":[36],"was":[37,45,62,78,96,111],"analyzed,":[38],"and":[39,85,127],"this":[48],"basis.":[49],"Secondly,":[50],"cumulative":[52],"influence":[56],"random":[59],"shock":[60],"process":[61,76],"analyzed.":[63],"The":[64],"attractive":[65],"property":[66],"Copula":[68,94],"functions":[69],"symmetry.":[71],"Then,":[72],"a":[73,86,93,108],"linear":[74],"Wiener":[75],"model":[77,81,90,120],"applied":[79],"performance":[82],"failure,":[84],"multi-performance":[87,104],"correlated-competition":[89],"based":[91],"function":[95],"constructed,":[97],"which":[98],"correlated":[101],"competition":[102],"between":[103],"failures.":[106],"Lastly,":[107],"micromotor":[109],"system":[110],"used":[112],"analyze":[114],"applicability":[116],"proposed":[119,131],"bivariate":[122],"instances,":[123],"demonstrating":[124],"rationality":[126],"effectiveness":[128],"model.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}