{"id":"https://openalex.org/W2044694860","doi":"https://doi.org/10.1109/tr.2012.2208302","title":"Relations and Generalizations of Importance Measures in Reliability","display_name":"Relations and Generalizations of Importance Measures in Reliability","publication_year":2012,"publication_date":"2012-07-21","ids":{"openalex":"https://openalex.org/W2044694860","doi":"https://doi.org/10.1109/tr.2012.2208302","mag":"2044694860"},"language":"en","primary_location":{"id":"doi:10.1109/tr.2012.2208302","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2012.2208302","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/A5078941517","display_name":"Way Kuo","orcid":"https://orcid.org/0000-0002-8845-1708"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Way Kuo","raw_affiliation_strings":["City University of Hong Kong, Hong Kong, China","City Univ. of Hong Kong, Kowloon, China"],"affiliations":[{"raw_affiliation_string":"City University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"City Univ. of Hong Kong, Kowloon, China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100671241","display_name":"Xiaoyan Zhu","orcid":"https://orcid.org/0000-0002-1574-8762"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaoyan Zhu","raw_affiliation_strings":["Department of Industrial and Information Engineering, University of Tennessee, Knoxville, TN, USA","Dept. of Ind. & Inf. Eng., Univ. of Tennessee, Knoxville, TN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Information Engineering, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Dept. of Ind. & Inf. Eng., Univ. of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078941517"],"corresponding_institution_ids":["https://openalex.org/I168719708"],"apc_list":null,"apc_paid":null,"fwci":8.3146,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.98127966,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"61","issue":"3","first_page":"659","last_page":"674"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998000264167786,"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":0.9998000264167786,"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/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9994999766349792,"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/T11357","display_name":"Risk and Safety Analysis","score":0.9983999729156494,"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.6535595655441284},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.603044331073761},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5858369469642639},{"id":"https://openalex.org/keywords/reliability-theory","display_name":"Reliability theory","score":0.5651269555091858},{"id":"https://openalex.org/keywords/reliability-engineering","display_name":"Reliability engineering","score":0.5043781995773315},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.488988995552063},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.4763662815093994},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.431460440158844},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4293973743915558},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4278271496295929},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24698874354362488},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.20337218046188354},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1956653594970703},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17296764254570007},{"id":"https://openalex.org/keywords/failure-rate","display_name":"Failure rate","score":0.10669338703155518}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6535595655441284},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.603044331073761},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5858369469642639},{"id":"https://openalex.org/C201729545","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability theory","level":3,"score":0.5651269555091858},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.5043781995773315},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.488988995552063},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.4763662815093994},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.431460440158844},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4293973743915558},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4278271496295929},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24698874354362488},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.20337218046188354},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1956653594970703},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17296764254570007},{"id":"https://openalex.org/C163164238","wikidata":"https://www.wikidata.org/wiki/Q2737027","display_name":"Failure rate","level":2,"score":0.10669338703155518},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tr.2012.2208302","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2012.2208302","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":93,"referenced_works":["https://openalex.org/W116212983","https://openalex.org/W1494274901","https://openalex.org/W1574534240","https://openalex.org/W1963555921","https://openalex.org/W1964285013","https://openalex.org/W1965047962","https://openalex.org/W1966470202","https://openalex.org/W1968936541","https://openalex.org/W1973018842","https://openalex.org/W1987824485","https://openalex.org/W1989599254","https://openalex.org/W1992574757","https://openalex.org/W1994080277","https://openalex.org/W1999142322","https://openalex.org/W2000530291","https://openalex.org/W2000930147","https://openalex.org/W2001669742","https://openalex.org/W2004811305","https://openalex.org/W2006458258","https://openalex.org/W2011151964","https://openalex.org/W2012513855","https://openalex.org/W2014707363","https://openalex.org/W2016208870","https://openalex.org/W2018625634","https://openalex.org/W2019006256","https://openalex.org/W2020599601","https://openalex.org/W2021374909","https://openalex.org/W2021490058","https://openalex.org/W2022480359","https://openalex.org/W2023086733","https://openalex.org/W2025657386","https://openalex.org/W2027062622","https://openalex.org/W2028335380","https://openalex.org/W2031070862","https://openalex.org/W2032123850","https://openalex.org/W2032882708","https://openalex.org/W2042089001","https://openalex.org/W2048993427","https://openalex.org/W2051046706","https://openalex.org/W2052392909","https://openalex.org/W2053629506","https://openalex.org/W2058213225","https://openalex.org/W2058576362","https://openalex.org/W2058706155","https://openalex.org/W2059773160","https://openalex.org/W2059900422","https://openalex.org/W2060603488","https://openalex.org/W2065447203","https://openalex.org/W2068850555","https://openalex.org/W2073327558","https://openalex.org/W2075476573","https://openalex.org/W2079258339","https://openalex.org/W2081528897","https://openalex.org/W2082280551","https://openalex.org/W2084700596","https://openalex.org/W2085775185","https://openalex.org/W2089752315","https://openalex.org/W2091761699","https://openalex.org/W2102660190","https://openalex.org/W2103742469","https://openalex.org/W2105513771","https://openalex.org/W2106351801","https://openalex.org/W2118512362","https://openalex.org/W2121127123","https://openalex.org/W2123733250","https://openalex.org/W2126484023","https://openalex.org/W2127368091","https://openalex.org/W2130516480","https://openalex.org/W2132082404","https://openalex.org/W2142194347","https://openalex.org/W2147455959","https://openalex.org/W2148510882","https://openalex.org/W2149335246","https://openalex.org/W2151773255","https://openalex.org/W2153950669","https://openalex.org/W2155326466","https://openalex.org/W2158596264","https://openalex.org/W2159854031","https://openalex.org/W2162222625","https://openalex.org/W2162251767","https://openalex.org/W2163472086","https://openalex.org/W2316039394","https://openalex.org/W2321977520","https://openalex.org/W2405854861","https://openalex.org/W2496248666","https://openalex.org/W2802034669","https://openalex.org/W2936036540","https://openalex.org/W4229535831","https://openalex.org/W4229829378","https://openalex.org/W4241814927","https://openalex.org/W4245535854","https://openalex.org/W6634463089","https://openalex.org/W6653732668"],"related_works":["https://openalex.org/W2494523064","https://openalex.org/W2943623134","https://openalex.org/W2588219639","https://openalex.org/W2030292806","https://openalex.org/W2215759665","https://openalex.org/W2960358116","https://openalex.org/W2156982617","https://openalex.org/W3041172967","https://openalex.org/W2379390860","https://openalex.org/W2063338624"],"abstract_inverted_index":{"To":[0],"identify":[1],"the":[2,41,58,60,65,80,89,103],"critical":[3],"components":[4,8],"or":[5],"sets":[6],"of":[7,25,79,98,105],"in":[9,35,44,70,108],"a":[10],"system,":[11],"various":[12],"importance":[13,27,42,81,106],"measures":[14,28,43,82,107],"have":[15],"been":[16],"proposed":[17],"with":[18],"different":[19],"probabilistic":[20],"perspectives":[21],"and":[22,46,49,73,115],"applications.":[23],"Many":[24],"these":[26],"are":[29,83],"actually":[30],"related":[31],"to":[32,57,95],"each":[33],"other":[34],"some":[36],"ways.":[37],"This":[38,100],"paper":[39,101],"summarizes":[40],"reliability,":[45],"presents":[47],"relations":[48,62],"comparisons":[50],"among":[51,63],"them,":[52,64],"focusing":[53],"on":[54],"their":[55,68,74],"interrelations":[56],"B-importance,":[59],"dominant":[61],"dual":[66],"relations,":[67],"performances":[69],"typical":[71],"systems,":[72,87,110,112,114],"computations.":[75],"The":[76],"early":[77],"versions":[78],"for":[84],"binary":[85],"coherent":[86],"while":[88],"recent":[90],"research":[91],"is":[92],"not":[93],"limited":[94],"this":[96],"type":[97],"system.":[99],"investigates":[102],"extensions":[104],"noncoherent":[109],"multistate":[111],"continuum":[113],"repairable":[116],"systems.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
