{"id":"https://openalex.org/W2810307377","doi":"https://doi.org/10.1109/tr.2018.2837080","title":"On Reliability Analysis of $k$ -Out-of-$n$ Systems Consisting of Heterogeneous Components With Discrete Lifetimes","display_name":"On Reliability Analysis of $k$ -Out-of-$n$ Systems Consisting of Heterogeneous Components With Discrete Lifetimes","publication_year":2018,"publication_date":"2018-06-25","ids":{"openalex":"https://openalex.org/W2810307377","doi":"https://doi.org/10.1109/tr.2018.2837080","mag":"2810307377"},"language":"en","primary_location":{"id":"doi:10.1109/tr.2018.2837080","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2018.2837080","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/A5033405013","display_name":"Anna Dembi\u0144ska","orcid":"https://orcid.org/0000-0001-7946-8818"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Anna Dembinska","raw_affiliation_strings":["Politechnika Warszawska, Warszawa, PL"],"raw_orcid":"https://orcid.org/0000-0001-7946-8818","affiliations":[{"raw_affiliation_string":"Politechnika Warszawska, Warszawa, PL","institution_ids":["https://openalex.org/I108403487"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033405013"],"corresponding_institution_ids":["https://openalex.org/I108403487"],"apc_list":null,"apc_paid":null,"fwci":3.6566,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.94243449,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"67","issue":"3","first_page":"1071","last_page":"1083"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9976999759674072,"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":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.7761542201042175},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.516584038734436},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.48491746187210083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4540468454360962},{"id":"https://openalex.org/keywords/mathematical-notation","display_name":"Mathematical notation","score":0.43989020586013794},{"id":"https://openalex.org/keywords/reliability-theory","display_name":"Reliability theory","score":0.4113371670246124},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39713990688323975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33561599254608154},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33089885115623474},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23033612966537476},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.22331982851028442},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.13388848304748535},{"id":"https://openalex.org/keywords/failure-rate","display_name":"Failure rate","score":0.10226607322692871},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06581670045852661}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7761542201042175},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.516584038734436},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.48491746187210083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4540468454360962},{"id":"https://openalex.org/C24457124","wikidata":"https://www.wikidata.org/wiki/Q1140046","display_name":"Mathematical notation","level":3,"score":0.43989020586013794},{"id":"https://openalex.org/C201729545","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability theory","level":3,"score":0.4113371670246124},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39713990688323975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33561599254608154},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33089885115623474},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23033612966537476},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.22331982851028442},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.13388848304748535},{"id":"https://openalex.org/C163164238","wikidata":"https://www.wikidata.org/wiki/Q2737027","display_name":"Failure rate","level":2,"score":0.10226607322692871},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06581670045852661},{"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/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.2018.2837080","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2018.2837080","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/G8388491102","display_name":null,"funder_award_id":"2015/19/B/ST1/03100","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"}],"funders":[{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W961491129","https://openalex.org/W1508202123","https://openalex.org/W1602581640","https://openalex.org/W1859574785","https://openalex.org/W1969594794","https://openalex.org/W2002387515","https://openalex.org/W2017567481","https://openalex.org/W2023984295","https://openalex.org/W2044535134","https://openalex.org/W2046404566","https://openalex.org/W2050395507","https://openalex.org/W2058588258","https://openalex.org/W2062712414","https://openalex.org/W2064051692","https://openalex.org/W2073855294","https://openalex.org/W2074041516","https://openalex.org/W2083215154","https://openalex.org/W2121230460","https://openalex.org/W2122188798","https://openalex.org/W2142645298","https://openalex.org/W2153540526","https://openalex.org/W2180240107","https://openalex.org/W2293024501","https://openalex.org/W2293952659","https://openalex.org/W2344766374","https://openalex.org/W2344936681","https://openalex.org/W2466663912","https://openalex.org/W2607002408","https://openalex.org/W2610613723","https://openalex.org/W2744160819","https://openalex.org/W2904683338","https://openalex.org/W4298545761","https://openalex.org/W6630357635","https://openalex.org/W6638945058"],"related_works":["https://openalex.org/W1968256718","https://openalex.org/W2393607213","https://openalex.org/W2495832077","https://openalex.org/W2278797713","https://openalex.org/W98357545","https://openalex.org/W977407476","https://openalex.org/W4249487612","https://openalex.org/W2624682093","https://openalex.org/W4280602899","https://openalex.org/W4239038871"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,39],"study":[4],"reliability":[5],"of":[6,29,52,55,86,89,109,112,115],"<inline-formula":[7,12,91,96],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8,13,92,97],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[9,14,93],"notation=\"LaTeX\">$k$</tex-math></inline-formula>":[10,94],"-out-of-":[11,95],"notation=\"LaTeX\">$n$</tex-math></inline-formula>":[15,100],"systems":[16],"with":[17],"possibly":[18],"heterogeneous":[19],"components.":[20],"We":[21],"focus":[22],"on":[23],"the":[24,27,47,90],"case":[25],"when":[26],"lifetimes":[28,114],"components":[30],"have":[31],"a":[32,42,87,116],"joint":[33,48],"discrete":[34,66],"distribution.":[35],"The":[36],"basic":[37],"tool":[38],"use":[40],"is":[41],"new":[43],"closed-form":[44],"formula":[45,69],"describing":[46,106],"probability":[49],"mass":[50],"function":[51],"any":[53],"subset":[54],"order":[56],"statistics":[57],"arising":[58],"from":[59],"not":[60],"necessarily":[61],"independent":[62],"nor":[63],"identically":[64],"distributed":[65],"variates.":[67],"This":[68],"and":[70,82],"some":[71,83],"its":[72],"modifications":[73],"enable":[74],"us":[75],"to":[76],"establish":[77],"explicit":[78],"expressions":[79,105],"for":[80],"unconditional":[81],"conditional":[84],"probabilities":[85],"failure":[88],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[98],"<tex-math":[99],"system":[101],"as":[102,104],"well":[103],"survival":[107],"functions":[108],"various":[110],"types":[111],"residual":[113],"used":[117],"system.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}