{"id":"https://openalex.org/W4415841662","doi":"https://doi.org/10.1002/qre.70085","title":"Reliability Evaluation of Systems With Performance Sharing Mechanism Under Semi\u2010Markov Process","display_name":"Reliability Evaluation of Systems With Performance Sharing Mechanism Under Semi\u2010Markov Process","publication_year":2025,"publication_date":"2025-11-03","ids":{"openalex":"https://openalex.org/W4415841662","doi":"https://doi.org/10.1002/qre.70085"},"language":"en","primary_location":{"id":"doi:10.1002/qre.70085","is_oa":false,"landing_page_url":"https://doi.org/10.1002/qre.70085","pdf_url":null,"source":{"id":"https://openalex.org/S165633816","display_name":"Quality and Reliability Engineering International","issn_l":"0748-8017","issn":["0748-8017","1099-1638"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quality and Reliability Engineering International","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/A5055291708","display_name":"Lili Bai","orcid":"https://orcid.org/0000-0002-2773-0455"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lili Bai","raw_affiliation_strings":["College of Aerospace and Civil Engineering Harbin Engineering University  Harbin China","College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Aerospace and Civil Engineering Harbin Engineering University  Harbin China","institution_ids":["https://openalex.org/I151727225"]},{"raw_affiliation_string":"College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, China","institution_ids":["https://openalex.org/I151727225"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Weihai Teng","orcid":null},"institutions":[{"id":"https://openalex.org/I4210140336","display_name":"Lanzhou City University","ror":"https://ror.org/03cd4ja39","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210140336"]},{"id":"https://openalex.org/I4210159876","display_name":"Institute of Physics","ror":"https://ror.org/05cvf7v30","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210159876"]},{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weihai Teng","raw_affiliation_strings":["Lanzhou Institute of Physics CAST  Lanzhou China","Lanzhou Institute of Physics CAST, Lanzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lanzhou Institute of Physics CAST  Lanzhou China","institution_ids":["https://openalex.org/I4210140336","https://openalex.org/I76214153"]},{"raw_affiliation_string":"Lanzhou Institute of Physics CAST, Lanzhou, China","institution_ids":["https://openalex.org/I4210159876"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051602741","display_name":"Dong Li Song","orcid":"https://orcid.org/0009-0008-7885-2541"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Donghan Song","raw_affiliation_strings":["College of Aerospace and Civil Engineering Harbin Engineering University  Harbin China","College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, China"],"raw_orcid":"https://orcid.org/0009-0008-7885-2541","affiliations":[{"raw_affiliation_string":"College of Aerospace and Civil Engineering Harbin Engineering University  Harbin China","institution_ids":["https://openalex.org/I151727225"]},{"raw_affiliation_string":"College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, China","institution_ids":["https://openalex.org/I151727225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040438037","display_name":"Qiuhua Duan","orcid":"https://orcid.org/0000-0002-0937-9470"},"institutions":[{"id":"https://openalex.org/I12970578","display_name":"University of North Alabama","ror":"https://ror.org/0584fj407","country_code":"US","type":"education","lineage":["https://openalex.org/I12970578"]},{"id":"https://openalex.org/I17301866","display_name":"University of Alabama","ror":"https://ror.org/03xrrjk67","country_code":"US","type":"education","lineage":["https://openalex.org/I17301866"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qiuhua Duan","raw_affiliation_strings":["Department of Civil, Construction, and Environmental Engineering University of Alabama  Alabama USA","Department of Civil, Construction, and Environmental Engineering, University of Alabama, Alabama, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil, Construction, and Environmental Engineering University of Alabama  Alabama USA","institution_ids":["https://openalex.org/I12970578","https://openalex.org/I17301866"]},{"raw_affiliation_string":"Department of Civil, Construction, and Environmental Engineering, University of Alabama, Alabama, USA","institution_ids":["https://openalex.org/I17301866"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100403899","display_name":"Xiaoqin Wang","orcid":"https://orcid.org/0000-0003-0715-7177"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoqin Wang","raw_affiliation_strings":["College of Aerospace and Civil Engineering Harbin Engineering University  Harbin China","College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Aerospace and Civil Engineering Harbin Engineering University  Harbin China","institution_ids":["https://openalex.org/I151727225"]},{"raw_affiliation_string":"College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, China","institution_ids":["https://openalex.org/I151727225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5055291708"],"corresponding_institution_ids":["https://openalex.org/I151727225"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":1.9373,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.86147757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"42","issue":"2","first_page":"894","last_page":"910"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11941","display_name":"Power System Reliability and Maintenance","score":0.7689999938011169,"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/T11941","display_name":"Power System Reliability and Maintenance","score":0.7689999938011169,"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/T10780","display_name":"Reliability and Maintenance Optimization","score":0.1582999974489212,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.01119999960064888,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/weibull-distribution","display_name":"Weibull distribution","score":0.7006999850273132},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.6866999864578247},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.6431000232696533},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.597599983215332},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5590000152587891},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5400000214576721},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5329999923706055},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5013999938964844},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.4839000105857849}],"concepts":[{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.7006999850273132},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6866999864578247},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.6431000232696533},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.597599983215332},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5590000152587891},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5523999929428101},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5400000214576721},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5329999923706055},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5013999938964844},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4839000105857849},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46860000491142273},{"id":"https://openalex.org/C113608303","wikidata":"https://www.wikidata.org/wiki/Q1056835","display_name":"Transmission system","level":3,"score":0.4462999999523163},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.44530001282691956},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4377000033855438},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.4339999854564667},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.41940000653266907},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.3718999922275543},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.3610999882221222},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3131999969482422},{"id":"https://openalex.org/C140311924","wikidata":"https://www.wikidata.org/wiki/Q200928","display_name":"Electric power transmission","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C92018576","wikidata":"https://www.wikidata.org/wiki/Q3242194","display_name":"Power transmission","level":3,"score":0.2797999978065491},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.26489999890327454},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.25760000944137573}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/qre.70085","is_oa":false,"landing_page_url":"https://doi.org/10.1002/qre.70085","pdf_url":null,"source":{"id":"https://openalex.org/S165633816","display_name":"Quality and Reliability Engineering International","issn_l":"0748-8017","issn":["0748-8017","1099-1638"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quality and Reliability Engineering International","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":32,"referenced_works":["https://openalex.org/W1999203685","https://openalex.org/W1999622254","https://openalex.org/W2008331720","https://openalex.org/W2013578738","https://openalex.org/W2032754167","https://openalex.org/W2048993427","https://openalex.org/W2090661672","https://openalex.org/W2090714087","https://openalex.org/W2115105639","https://openalex.org/W2313940623","https://openalex.org/W2793532928","https://openalex.org/W2794430751","https://openalex.org/W2884441493","https://openalex.org/W2943899942","https://openalex.org/W2947844719","https://openalex.org/W3011834709","https://openalex.org/W3024868887","https://openalex.org/W3118294669","https://openalex.org/W3125048175","https://openalex.org/W3150115479","https://openalex.org/W3165202843","https://openalex.org/W3176595721","https://openalex.org/W3176750987","https://openalex.org/W3191934128","https://openalex.org/W3196997366","https://openalex.org/W3204492588","https://openalex.org/W3211077771","https://openalex.org/W3214403694","https://openalex.org/W3215054966","https://openalex.org/W4206023438","https://openalex.org/W4379878697","https://openalex.org/W4386295287"],"related_works":[],"abstract_inverted_index":{"ABSTRACT":[0],"A":[1,146],"new":[2,41],"performance\u2010sharing":[3],"system":[4,42,117,144,185,216],"is":[5,29,123,139,155,169,186,232],"proposed":[6,179],"in":[7,10,48,217],"this":[8,193],"paper,":[9],"which":[11],"the":[12,17,24,51,94,100,115,127,134,143,152,165,173,178,190,214,224,227],"states":[13],"of":[14,26,54,97,103,130,161,177,192],"units":[15,33,74,78,84,106],"follow":[16],"general":[18],"distribution":[19,65,236],"like":[20],"semi\u2010Markov":[21,121,210],"process,":[22],"and":[23,50,66,81,99,133,164,175,209,222],"transmission":[25,95,105],"surplus":[27,86],"performance":[28,73,82,87,104,229],"restricted":[30],"to":[31,125,141,157,171,188,234],"adjacent":[32,89],"for":[34],"some":[35],"reason.":[36],"First,":[37],"we":[38],"establish":[39],"a":[40,71,120,131,182,199],"that":[43,198,226],"n\u2010":[44],"subsystems":[45,90,113],"are":[46,107],"connected":[47],"series,":[49],"state":[52,128,162,201],"transition":[53],"components":[55],"not":[56],"only":[57],"obeys":[58,63],"exponential":[59,235],"distribution,":[60],"but":[61],"also":[62],"Weibull":[64],"normal":[67],"distribution.":[68],"In":[69],"such":[70],"system,":[72,132],"generate":[75],"performance,":[76,80],"demand":[77],"consume":[79],"transfer":[83],"share":[85],"between":[88],"via":[91],"lines,":[92],"where":[93],"loss":[96],"lines":[98],"capacity":[101],"limitation":[102,225],"considered.":[108],"When":[109],"one":[110],"or":[111],"more":[112,220],"fail,":[114],"whole":[116],"fails.":[118],"Meanwhile,":[119],"process":[122,211],"used":[124],"reflect":[126,189],"probability":[129,202],"universal":[135],"generating":[136],"function":[137],"technique":[138],"applied":[140,170],"solve":[142,223],"reliability.":[145],"high\u2010precision":[147,200],"calculation":[148,203],"method":[149,204],"based":[150,205],"on":[151,206],"Simpson":[153,207],"formula":[154,208],"raised":[156],"access":[158],"analytical":[159],"solution":[160],"probability,":[163],"Monte":[166],"Carlo":[167],"algorithm":[168],"verify":[172],"correctness":[174],"efficiency":[176],"method.":[180],"Finally,":[181],"wind":[183],"power":[184],"employed":[187],"application":[191],"model.":[194],"The":[195],"results":[196],"show":[197],"can":[212],"describe":[213],"complex":[215],"practical":[218],"engineering":[219],"accurately":[221],"current":[228],"sharing":[230],"model":[231],"limited":[233],"assumption.":[237]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-11-04T00:00:00"}