{"id":"https://openalex.org/W2114904755","doi":"https://doi.org/10.1109/tr.2011.2161701","title":"Optimal Reliability Demonstration Test Plans for $k$-out-of-$n$ Systems of Gamma Distributed Components","display_name":"Optimal Reliability Demonstration Test Plans for $k$-out-of-$n$ Systems of Gamma Distributed Components","publication_year":2011,"publication_date":"2011-07-26","ids":{"openalex":"https://openalex.org/W2114904755","doi":"https://doi.org/10.1109/tr.2011.2161701","mag":"2114904755"},"language":"en","primary_location":{"id":"doi:10.1109/tr.2011.2161701","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2011.2161701","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/A5045225985","display_name":"Arturo J. Fern\u00e1ndez","orcid":"https://orcid.org/0000-0003-2646-0905"},"institutions":[{"id":"https://openalex.org/I158438070","display_name":"Universidad de La Laguna","ror":"https://ror.org/01r9z8p25","country_code":"ES","type":"education","lineage":["https://openalex.org/I158438070"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Arturo J. Fern\u00e1ndez","raw_affiliation_strings":["Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universidad de La Laguna, La Laguna, Tenerife, Spain","Dept. de Estadistica e Investig. Operativa, Univ. de La Laguna, La Laguna, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universidad de La Laguna, La Laguna, Tenerife, Spain","institution_ids":["https://openalex.org/I158438070"]},{"raw_affiliation_string":"Dept. de Estadistica e Investig. Operativa, Univ. de La Laguna, La Laguna, Spain","institution_ids":["https://openalex.org/I158438070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045225985"],"corresponding_institution_ids":["https://openalex.org/I158438070"],"apc_list":null,"apc_paid":null,"fwci":2.4798,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.90654206,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"60","issue":"4","first_page":"833","last_page":"844"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9988999962806702,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9980000257492065,"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/notation","display_name":"Notation","score":0.5656200051307678},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.4992520809173584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4585326910018921},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43799862265586853},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40845394134521484},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36887383460998535},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12143489718437195}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5656200051307678},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.4992520809173584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4585326910018921},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43799862265586853},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40845394134521484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36887383460998535},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12143489718437195},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":1,"locations":[{"id":"doi:10.1109/tr.2011.2161701","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2011.2161701","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":[{"id":"https://metadata.un.org/sdg/16","score":0.550000011920929,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W635907678","https://openalex.org/W1969503705","https://openalex.org/W1971805336","https://openalex.org/W2057313310","https://openalex.org/W2061207866","https://openalex.org/W2073326092","https://openalex.org/W2080107567","https://openalex.org/W2082515638","https://openalex.org/W2086074691","https://openalex.org/W2091686287","https://openalex.org/W2096731208","https://openalex.org/W2101042137","https://openalex.org/W2105849708","https://openalex.org/W2110226580","https://openalex.org/W2111569007","https://openalex.org/W2116418320","https://openalex.org/W2121230460","https://openalex.org/W2122188798","https://openalex.org/W2124384532","https://openalex.org/W2129761538","https://openalex.org/W2133941993","https://openalex.org/W2140435148","https://openalex.org/W2156099708","https://openalex.org/W2158654036","https://openalex.org/W2167790180","https://openalex.org/W2220335249","https://openalex.org/W4285719527","https://openalex.org/W6684864437"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2504004674","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Constrained":[0],"optimization":[1,186],"problems":[2],"are":[3,36,65,139,164,219],"solved":[4],"to":[5,38,78,120,223,276],"determine":[6],"the":[7,34,39,44,47,50,56,83,87,122,153,185,194,201,227,232],"best":[8],"reliability":[9,60,195],"sampling":[10,257],"plans":[11,258],"for":[12,183,245,251,262],"<formula":[13,20,90,102,126],"formulatype=\"inline\"":[14,21,91,103,127],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[15,22,92,104,128],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[16,23,93,105],"Notation=\"TeX\">$k$</tex>":[17],"</formula>":[18,25,107],"-out-of-":[19],"Notation=\"TeX\">$n$</tex>":[24],":F":[26],"systems":[27],"of":[28,125,190,200,241],"gamma":[29,228],"distributed":[30],"components.":[31],"As":[32],"usual,":[33],"constraints":[35],"related":[37],"quality":[40],"levels":[41],"required":[42],"by":[43,141],"producer":[45],"and":[46,136,149,204,207,213,231],"consumer,":[48],"whereas":[49],"decision":[51],"criterion":[52],"is":[53,76,96,118,181,249,270],"based":[54],"on":[55,86,101,152],"uniformly":[57],"most":[58,178],"powerful":[59],"test.":[61],"Excellent":[62],"approximate":[63],"solutions":[64,218],"derived":[66],"in":[67,81,177,210,226,264],"closed-forms":[68],"assuming":[69],"a":[70,110,114,160,174,238,247,278],"frequentist":[71],"perspective.":[72],"This":[73],"classical":[74],"methodology":[75],"generalized":[77],"those":[79],"situations":[80],"which":[82,171],"prior":[84,99,191,233],"information":[85],"fraction":[88],"effective,":[89],"Notation=\"TeX\">$r$</tex></formula>":[94,131],",":[95],"appreciable.":[97],"Because":[98],"knowledge":[100,192],"Notation=\"TeX\">$r$</tex>":[106],"often":[108],"suggests":[109],"restricted":[111],"parameter":[112,230],"interval,":[113],"limited":[115],"beta":[116],"distribution":[117],"used":[119],"describe":[121],"probabilistic":[123],"behavior":[124],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[129],"<tex":[130],".":[132],"Optimal":[133],"sample":[134,155,211],"sizes":[135],"acceptance":[137],"factors":[138],"obtained":[140],"solving":[142,184],"mixed":[143],"integer":[144],"nonlinear":[145],"programming":[146],"problems.":[147],"Lower":[148],"upper":[150],"bounds":[151],"smallest":[154],"size,":[156],"as":[157,159],"well":[158],"quite":[161,221],"accurate":[162],"approximation,":[163],"also":[165],"provided.":[166],"An":[167,235],"efficient":[168],"step-by-step":[169],"procedure,":[170],"only":[172],"needs":[173],"few":[175],"iterations":[176],"practical":[179,265],"cases,":[180],"proposed":[182,254],"problem.":[187],"The":[188,216,253],"incorporation":[189],"into":[193],"analysis":[196],"provides":[197],"better":[198],"assessment":[199],"true":[202],"producer's":[203],"consumer's":[205],"risks,":[206],"considerable":[208],"savings":[209],"size":[212],"test":[214,256,277],"duration.":[215],"optimal":[217],"usually":[220],"robust":[222],"small":[224],"variations":[225],"shape":[229],"information.":[234],"example":[236],"concerning":[237],"system":[239],"composed":[240],"five":[242],"water":[243],"pumps":[244],"cooling":[246],"reactor":[248],"included":[250],"illustration.":[252],"component":[255],"can":[259],"be":[260],"recommended":[261],"use":[263],"applications,":[266],"particularly":[267],"when":[268],"it":[269],"economically":[271],"infeasible,":[272],"or":[273],"even":[274],"impossible,":[275],"whole":[279],"system.":[280]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
