{"id":"https://openalex.org/W3210074729","doi":"https://doi.org/10.1155/2021/2404997","title":"A New Estimation Study of the Stress-Strength Reliability for the Topp\u2013Leone Distribution Using Advanced Sampling Methods","display_name":"A New Estimation Study of the Stress-Strength Reliability for the Topp\u2013Leone Distribution Using Advanced Sampling Methods","publication_year":2021,"publication_date":"2021-10-28","ids":{"openalex":"https://openalex.org/W3210074729","doi":"https://doi.org/10.1155/2021/2404997","mag":"3210074729"},"language":"en","primary_location":{"id":"doi:10.1155/2021/2404997","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/2404997","pdf_url":"https://downloads.hindawi.com/journals/sp/2021/2404997.pdf","source":{"id":"https://openalex.org/S166774750","display_name":"Scientific Programming","issn_l":"1058-9244","issn":["1058-9244","1875-919X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/sp/2021/2404997.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065692874","display_name":"Abdullah M. Almarashi","orcid":"https://orcid.org/0000-0003-3201-8961"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Abdullah M. Almarashi","raw_affiliation_strings":["Faculty of Science, Department of Statistis, King Abdulaziz University, Jeddah, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science, Department of Statistis, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053087213","display_name":"Ali Algarni","orcid":"https://orcid.org/0000-0001-5994-1073"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ali Algarni","raw_affiliation_strings":["Faculty of Science, Department of Statistis, King Abdulaziz University, Jeddah, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science, Department of Statistis, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048338546","display_name":"Amal S. Hassan","orcid":"https://orcid.org/0000-0003-4442-8458"},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Amal S. Hassan","raw_affiliation_strings":["Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt","institution_ids":["https://openalex.org/I145487455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026468035","display_name":"Mohammed Elgarhy","orcid":"https://orcid.org/0000-0002-1333-3862"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Elgarhy","raw_affiliation_strings":["The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, Algarbia, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-1333-3862","affiliations":[{"raw_affiliation_string":"The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, Algarbia, Egypt","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010653691","display_name":"Farrukh Jamal","orcid":"https://orcid.org/0000-0001-6192-9890"},"institutions":[{"id":"https://openalex.org/I174731842","display_name":"Islamia University of Bahawalpur","ror":"https://ror.org/002rc4w13","country_code":"PK","type":"education","lineage":["https://openalex.org/I174731842"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Farrukh Jamal","raw_affiliation_strings":["Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-6192-9890","affiliations":[{"raw_affiliation_string":"Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan","institution_ids":["https://openalex.org/I174731842"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083045521","display_name":"Christophe Chesneau","orcid":"https://orcid.org/0000-0002-1522-9292"},"institutions":[{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christophe Chesneau","raw_affiliation_strings":["Universit\u00b4e de Caen, LMNO, Campus II, Science 3, 14032, Caen, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00b4e de Caen, LMNO, Campus II, Science 3, 14032, Caen, France","institution_ids":["https://openalex.org/I98702875"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057666980","display_name":"Khudir Alrashidi","orcid":null},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Khudir Alrashidi","raw_affiliation_strings":["Faculty of Science, Department of Statistis, King Abdulaziz University, Jeddah, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science, Department of Statistis, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082956031","display_name":"Wali Khan Mashwani","orcid":"https://orcid.org/0000-0002-5081-741X"},"institutions":[{"id":"https://openalex.org/I178777954","display_name":"Kohat University of Science and Technology","ror":"https://ror.org/057d2v504","country_code":"PK","type":"education","lineage":["https://openalex.org/I178777954"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Wali Khan Mashwani","raw_affiliation_strings":["Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat 26000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-5081-741X","affiliations":[{"raw_affiliation_string":"Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat 26000, Pakistan","institution_ids":["https://openalex.org/I178777954"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085453380","display_name":"Heba F. Nagy","orcid":"https://orcid.org/0000-0003-0262-205X"},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Heba F. Nagy","raw_affiliation_strings":["Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt","institution_ids":["https://openalex.org/I145487455"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":9,"corresponding_author_ids":["https://openalex.org/A5082956031"],"corresponding_institution_ids":["https://openalex.org/I178777954"],"apc_list":{"value":1800,"currency":"USD","value_usd":1800},"apc_paid":{"value":1800,"currency":"USD","value_usd":1800},"fwci":1.87,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.87677451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2021","issue":null,"first_page":"1","last_page":"13"},"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":0.998199999332428,"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":0.98089998960495,"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/simple-random-sample","display_name":"Simple random sample","score":0.8145552277565002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7466189861297607},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.7271122932434082},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7002596259117126},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.49271920323371887},{"id":"https://openalex.org/keywords/stratified-sampling","display_name":"Stratified sampling","score":0.476526141166687},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.4509553015232086},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.43781647086143494},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.41067203879356384},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14394733309745789}],"concepts":[{"id":"https://openalex.org/C20353970","wikidata":"https://www.wikidata.org/wiki/Q1056998","display_name":"Simple random sample","level":3,"score":0.8145552277565002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7466189861297607},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.7271122932434082},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7002596259117126},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.49271920323371887},{"id":"https://openalex.org/C49898467","wikidata":"https://www.wikidata.org/wiki/Q1517706","display_name":"Stratified sampling","level":2,"score":0.476526141166687},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.4509553015232086},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.43781647086143494},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41067203879356384},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14394733309745789},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","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/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2021/2404997","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/2404997","pdf_url":"https://downloads.hindawi.com/journals/sp/2021/2404997.pdf","source":{"id":"https://openalex.org/S166774750","display_name":"Scientific Programming","issn_l":"1058-9244","issn":["1058-9244","1875-919X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Programming","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5bcc77acdb4448ed84941bd3b020abe7","is_oa":true,"landing_page_url":"https://doaj.org/article/5bcc77acdb4448ed84941bd3b020abe7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scientific Programming, Vol 2021 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/2404997","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/2404997","pdf_url":"https://downloads.hindawi.com/journals/sp/2021/2404997.pdf","source":{"id":"https://openalex.org/S166774750","display_name":"Scientific Programming","issn_l":"1058-9244","issn":["1058-9244","1875-919X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3781986735","display_name":null,"funder_award_id":"KEP\u2013PhD-69-130-42","funder_id":"https://openalex.org/F4320322322","funder_display_name":"King Abdulaziz University"}],"funders":[{"id":"https://openalex.org/F4320322322","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3210074729.pdf","grobid_xml":"https://content.openalex.org/works/W3210074729.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1579724198","https://openalex.org/W1583532667","https://openalex.org/W1971568850","https://openalex.org/W1972577016","https://openalex.org/W1977196204","https://openalex.org/W1986049907","https://openalex.org/W1998726217","https://openalex.org/W2008408176","https://openalex.org/W2051734881","https://openalex.org/W2062584721","https://openalex.org/W2079424310","https://openalex.org/W2084502335","https://openalex.org/W2093736296","https://openalex.org/W2148527884","https://openalex.org/W2507139530","https://openalex.org/W2542861852","https://openalex.org/W2737577858","https://openalex.org/W2883969005","https://openalex.org/W3120346508","https://openalex.org/W4231739827","https://openalex.org/W4234406918"],"related_works":["https://openalex.org/W2370014976","https://openalex.org/W2350399852","https://openalex.org/W3047864323","https://openalex.org/W4238714840","https://openalex.org/W2383809451","https://openalex.org/W4297686948","https://openalex.org/W2381368487","https://openalex.org/W2994963386","https://openalex.org/W2367020632","https://openalex.org/W4230157703"],"abstract_inverted_index":{"In":[0],"this":[1],"manuscript,":[2],"we":[3,62],"investigate":[4],"the":[5,8,19,34,59,70,73,80,92,95,102,114,124,128,131,138,147,164,167,194],"estimation":[6],"of":[7,67,72,94,118,166,186,196],"unknown":[9],"reliability":[10],"measure":[11],"R":[12,68,119],"=":[13],"P":[14],"[Y":[15],"<":[16],"X],":[17],"in":[18,122],"case":[20],"where":[21],"Y":[22],"and":[23,51,173],"X":[24],"are":[25,41,46,77,99,135,144,151],"two":[26,74,96,132,142,149],"independent":[27],"random":[28,75,83,97,133,181],"variables":[29,76,98,134],"with":[30,178],"Topp\u2013Leone":[31],"distributions.":[32],"As":[33],"main":[35],"contribution,":[36],"various":[37],"advanced":[38],"sampling":[39,105,182],"strategies":[40,45],"studied.":[42],"The":[43,184],"suggested":[44],"simple":[47,82,180],"random,":[48],"ranked":[49,53,103,111,175],"set,":[50],"median":[52,110,174],"set":[54,104,112,140,155,176],"samplings.":[55],"Firstly,":[56],"based":[57,108,170],"on":[58,109,171],"maximum":[60,115],"likelihood,":[61],"give":[63],"an":[64,87],"efficient":[65],"estimator":[66,88,117],"when":[69,91],"observations":[71,93,129],"selected":[78,100,136],"from":[79,101,130,137],"same":[81,139],"sample.":[84],"Secondly,":[85],"such":[86],"is":[89,120,160,190],"addressed":[90,121],"method.":[106],"Then,":[107],"sampling,":[113],"likelihood":[116],"all":[123],"four":[125],"cases.":[126],"When":[127],"size,":[141],"cases":[143,150],"considered,":[145],"while":[146],"other":[148],"considered":[152],"at":[153],"different":[154],"sizes.":[156],"A":[157],"simulation":[158],"research":[159],"developed":[161],"to":[162,192],"evaluate":[163],"behavior":[165],"obtained":[168],"estimates":[169],"standard":[172],"samplings":[177],"their":[179],"equivalents.":[183],"ratio":[185],"mean":[187],"square":[188],"error":[189],"used":[191],"assess":[193],"effectiveness":[195],"these":[197],"estimates.":[198]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}