{"id":"https://openalex.org/W3090219667","doi":"https://doi.org/10.1109/tr.2020.3020597","title":"A Prime-Logarithmic Method for Optimal Reliability Design","display_name":"A Prime-Logarithmic Method for Optimal Reliability Design","publication_year":2020,"publication_date":"2020-09-29","ids":{"openalex":"https://openalex.org/W3090219667","doi":"https://doi.org/10.1109/tr.2020.3020597","mag":"3090219667"},"language":"en","primary_location":{"id":"doi:10.1109/tr.2020.3020597","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2020.3020597","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/A5100777492","display_name":"Han-Lin Li","orcid":"https://orcid.org/0000-0002-3053-2409"},"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":"Han-Lin Li","raw_affiliation_strings":["College of Business, City University of Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"College of Business, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032119311","display_name":"Yao\u2010Huei Huang","orcid":"https://orcid.org/0000-0003-0562-5117"},"institutions":[{"id":"https://openalex.org/I114150738","display_name":"Fu Jen Catholic University","ror":"https://ror.org/04je98850","country_code":"TW","type":"education","lineage":["https://openalex.org/I114150738"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yao-Huei Huang","raw_affiliation_strings":["Department of Information Management, Fu Jen Catholic University, New Taipei City, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Information Management, Fu Jen Catholic University, New Taipei City, Taiwan","institution_ids":["https://openalex.org/I114150738"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027860626","display_name":"Shu\u2010Cherng Fang","orcid":"https://orcid.org/0000-0001-5087-3262"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shu-Cherng Fang","raw_affiliation_strings":["Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","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":false,"raw_author_name":"Way Kuo","raw_affiliation_strings":["City University of Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100777492"],"corresponding_institution_ids":["https://openalex.org/I168719708"],"apc_list":null,"apc_paid":null,"fwci":0.9325,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.73747599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"70","issue":"1","first_page":"146","last_page":"162"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9977999925613403,"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":0.9977999925613403,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9635000228881836,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.961899995803833,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6929186582565308},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6276280879974365},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.6036317944526672},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5682089924812317},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5554524064064026},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5352082848548889},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.49832892417907715},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4960092008113861},{"id":"https://openalex.org/keywords/reliability-theory","display_name":"Reliability theory","score":0.46741247177124023},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46119192242622375},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.4413221478462219},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4107152223587036},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3494431972503662},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3224528729915619},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26823270320892334},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18627643585205078},{"id":"https://openalex.org/keywords/failure-rate","display_name":"Failure rate","score":0.13594406843185425},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1251668632030487},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12142667174339294}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6929186582565308},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6276280879974365},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.6036317944526672},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5682089924812317},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5554524064064026},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5352082848548889},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.49832892417907715},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4960092008113861},{"id":"https://openalex.org/C201729545","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability theory","level":3,"score":0.46741247177124023},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46119192242622375},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.4413221478462219},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4107152223587036},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3494431972503662},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3224528729915619},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26823270320892334},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18627643585205078},{"id":"https://openalex.org/C163164238","wikidata":"https://www.wikidata.org/wiki/Q2737027","display_name":"Failure rate","level":2,"score":0.13594406843185425},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1251668632030487},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12142667174339294},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tr.2020.3020597","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2020.3020597","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/G2399332790","display_name":null,"funder_award_id":"MOST 103-2221-E-009-082-MY2","funder_id":"https://openalex.org/F4320321040","funder_display_name":"National Science Council"},{"id":"https://openalex.org/G3424881406","display_name":null,"funder_award_id":"MOST 109-2410-H-030-037-MY3","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"},{"id":"https://openalex.org/G3978337388","display_name":null,"funder_award_id":"MOST 107-2410-H-030-031-707-MY2","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"},{"id":"https://openalex.org/G6493723399","display_name":null,"funder_award_id":"W911NF-15-1-0223.","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6861691842","display_name":null,"funder_award_id":"MOST 102-2221-E-009-089-MY2","funder_id":"https://openalex.org/F4320321040","funder_display_name":"National Science Council"},{"id":"https://openalex.org/G7271898509","display_name":null,"funder_award_id":"MOST 105-2221-E-009-123","funder_id":"https://openalex.org/F4320321040","funder_display_name":"National Science Council"},{"id":"https://openalex.org/G859210714","display_name":null,"funder_award_id":"MOST 104-2221-E-009-095","funder_id":"https://openalex.org/F4320321040","funder_display_name":"National Science Council"}],"funders":[{"id":"https://openalex.org/F4320321040","display_name":"National Science Council","ror":"https://ror.org/02kv4zf79"},{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1531340371","https://openalex.org/W1586313000","https://openalex.org/W1965071897","https://openalex.org/W1968050691","https://openalex.org/W1971738442","https://openalex.org/W1975903957","https://openalex.org/W2001729361","https://openalex.org/W2008389133","https://openalex.org/W2009702080","https://openalex.org/W2011039300","https://openalex.org/W2034629430","https://openalex.org/W2036206719","https://openalex.org/W2043549502","https://openalex.org/W2064836078","https://openalex.org/W2098425563","https://openalex.org/W2100906919","https://openalex.org/W2108834246","https://openalex.org/W2109202810","https://openalex.org/W2114209383","https://openalex.org/W2114621702","https://openalex.org/W2118590037","https://openalex.org/W2118643058","https://openalex.org/W2125697860","https://openalex.org/W2132032636","https://openalex.org/W2142372217","https://openalex.org/W2156439985","https://openalex.org/W2157874048","https://openalex.org/W2160184257","https://openalex.org/W2161116097","https://openalex.org/W2316039394","https://openalex.org/W2415377241","https://openalex.org/W2564627491","https://openalex.org/W2762723962","https://openalex.org/W2799390115","https://openalex.org/W2936036540","https://openalex.org/W3144672859"],"related_works":["https://openalex.org/W2794559785","https://openalex.org/W2950281908","https://openalex.org/W1754499339","https://openalex.org/W2013873776","https://openalex.org/W2952185452","https://openalex.org/W2583828359","https://openalex.org/W2963117165","https://openalex.org/W2046736294","https://openalex.org/W2963720107","https://openalex.org/W2084977674"],"abstract_inverted_index":{"Optimal":[0],"reliability":[1,31],"design":[2],"(ORD)":[3],"problem":[4,39,83],"is":[5],"challenging":[6],"and":[7,64,93,103],"fundamental":[8],"to":[9,107],"the":[10,58,66,81,118],"study":[11],"of":[12,23,37,61,80],"system":[13,17],"reliability.":[14],"For":[15],"a":[16,75],"with":[18,48],"u":[19],"components/stages":[20],"where":[21],"each":[22],"them":[24],"can":[25,105],"be":[26],"set":[27],"in":[28,70,101,110,121,128],"m":[29],"possible":[30],"levels,":[32],"state-of-the-art":[33],"linear":[34,77,96],"reformulation":[35,78],"models":[36],"ORD":[38,82,126],"require":[40],"O(um)":[41,54,85],"binary":[42,86],"variables,":[43,87,92],"O(mn)":[44,50],"continuous":[45,91],"variables":[46,102],"together":[47],"either":[49],"inequality":[51],"constraints":[52,104],"or":[53],"equality":[55],"constraints.":[56,97],"Using":[57],"special":[59],"property":[60],"prime":[62],"factorization":[63],"adopting":[65],"logarithmic":[67],"expression":[68],"technique,":[69],"this":[71],"article,":[72],"we":[73],"propose":[74],"novel":[76],"model":[79],"requiring":[84],"O(mn":[88],"n!":[89],")":[90],"very":[94],"few":[95],"This":[98],"theoretic":[99],"reduction":[100,120],"lead":[106],"significant":[108],"savings":[109],"computational":[111,122],"efforts.":[112],"Our":[113],"numerical":[114],"experiments":[115],"further":[116],"confirm":[117],"drastic":[119],"time":[123],"for":[124],"solving":[125],"problems":[127],"large":[129],"size.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}