{"id":"https://openalex.org/W4377289110","doi":"https://doi.org/10.3390/sym15051121","title":"An Efficient Stress\u2013Strength Reliability Estimate of the Unit Gompertz Distribution Using Ranked Set Sampling","display_name":"An Efficient Stress\u2013Strength Reliability Estimate of the Unit Gompertz Distribution Using Ranked Set Sampling","publication_year":2023,"publication_date":"2023-05-20","ids":{"openalex":"https://openalex.org/W4377289110","doi":"https://doi.org/10.3390/sym15051121"},"language":"en","primary_location":{"id":"doi:10.3390/sym15051121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051121","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1121/pdf?version=1684833854","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/5/1121/pdf?version=1684833854","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072589952","display_name":"Najwan Alsadat","orcid":"https://orcid.org/0000-0001-8884-8281"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Najwan Alsadat","raw_affiliation_strings":["Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-8884-8281","affiliations":[{"raw_affiliation_string":"Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"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":true,"raw_author_name":"Amal S. Hassan","raw_affiliation_strings":["Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"],"raw_orcid":"https://orcid.org/0000-0003-4442-8458","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":[{"id":"https://openalex.org/I113643904","display_name":"Beni-Suef University","ror":"https://ror.org/05pn4yv70","country_code":"EG","type":"education","lineage":["https://openalex.org/I113643904"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Mohammed Elgarhy","raw_affiliation_strings":["Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-1333-3862","affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt","institution_ids":["https://openalex.org/I113643904"]}]},{"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":true,"raw_author_name":"Christophe Chesneau","raw_affiliation_strings":["Department of Mathematics, Campus II, Universit\u00e9 de Caen Normandie, Science 3, 14032 Caen, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Campus II, Universit\u00e9 de Caen Normandie, Science 3, 14032 Caen, France","institution_ids":["https://openalex.org/I98702875"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070056889","display_name":"Rokaya Elmorsy Mohamed","orcid":"https://orcid.org/0000-0001-8853-9868"},"institutions":[{"id":"https://openalex.org/I43424612","display_name":"Sadat Academy for Management Sciences","ror":"https://ror.org/04scnnc07","country_code":"EG","type":"education","lineage":["https://openalex.org/I43424612"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Rokaya Elmorsy Mohamed","raw_affiliation_strings":["Department of Mathematics, Statistics and Insurance, Sadat Academy for Management Sciences, Cairo 11728, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-8853-9868","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics and Insurance, Sadat Academy for Management Sciences, Cairo 11728, Egypt","institution_ids":["https://openalex.org/I43424612"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5048338546","https://openalex.org/A5083045521"],"corresponding_institution_ids":["https://openalex.org/I145487455","https://openalex.org/I98702875"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":12.105,"has_fulltext":true,"cited_by_count":39,"citation_normalized_percentile":{"value":0.99254195,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"15","issue":"5","first_page":"1121","last_page":"1121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9991999864578247,"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":0.9991999864578247,"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/T11186","display_name":"Hydrology and Drought Analysis","score":0.9850999712944031,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9794999957084656,"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/mathematics","display_name":"Mathematics","score":0.7108047604560852},{"id":"https://openalex.org/keywords/rss","display_name":"RSS","score":0.6141530871391296},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.6126396656036377},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.5357446074485779},{"id":"https://openalex.org/keywords/gompertz-function","display_name":"Gompertz function","score":0.5256223082542419},{"id":"https://openalex.org/keywords/von-mises-yield-criterion","display_name":"von Mises yield criterion","score":0.513041615486145},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4616905450820923},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27968132495880127},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.11595359444618225},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08282774686813354}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7108047604560852},{"id":"https://openalex.org/C2385561","wikidata":"https://www.wikidata.org/wiki/Q45432","display_name":"RSS","level":2,"score":0.6141530871391296},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6126396656036377},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.5357446074485779},{"id":"https://openalex.org/C134463574","wikidata":"https://www.wikidata.org/wiki/Q1011785","display_name":"Gompertz function","level":2,"score":0.5256223082542419},{"id":"https://openalex.org/C155165730","wikidata":"https://www.wikidata.org/wiki/Q1319519","display_name":"von Mises yield criterion","level":3,"score":0.513041615486145},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4616905450820923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27968132495880127},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.11595359444618225},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08282774686813354},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15051121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051121","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1121/pdf?version=1684833854","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b24227f733c14975b5b3cb11617cf09c","is_oa":false,"landing_page_url":"https://doaj.org/article/b24227f733c14975b5b3cb11617cf09c","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 5, p 1121 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/5/1121/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15051121","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15051121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051121","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1121/pdf?version=1684833854","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1968062351","display_name":null,"funder_award_id":"RSPD2023R548","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"}],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4377289110.pdf"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W612010249","https://openalex.org/W1184090414","https://openalex.org/W1976061970","https://openalex.org/W1976749402","https://openalex.org/W1978468296","https://openalex.org/W1983486623","https://openalex.org/W1986049907","https://openalex.org/W1990204932","https://openalex.org/W1999027478","https://openalex.org/W2008408176","https://openalex.org/W2034422039","https://openalex.org/W2046262695","https://openalex.org/W2055057204","https://openalex.org/W2063842416","https://openalex.org/W2080515301","https://openalex.org/W2084502335","https://openalex.org/W2084872827","https://openalex.org/W2152485919","https://openalex.org/W2428472680","https://openalex.org/W2467305554","https://openalex.org/W2507139530","https://openalex.org/W2883969005","https://openalex.org/W2900560033","https://openalex.org/W2936337024","https://openalex.org/W2954461242","https://openalex.org/W2971089215","https://openalex.org/W2991888559","https://openalex.org/W2997728557","https://openalex.org/W3000173489","https://openalex.org/W3000561553","https://openalex.org/W3042463579","https://openalex.org/W3088640440","https://openalex.org/W3120346508","https://openalex.org/W3122754428","https://openalex.org/W3165096265","https://openalex.org/W3173682655","https://openalex.org/W3179447081","https://openalex.org/W3192034825","https://openalex.org/W3198876371","https://openalex.org/W3214552377","https://openalex.org/W4200450619","https://openalex.org/W4220975733","https://openalex.org/W4294308554","https://openalex.org/W4308099316","https://openalex.org/W4308475336","https://openalex.org/W4316662232","https://openalex.org/W4317243158","https://openalex.org/W4324360588","https://openalex.org/W4327621739","https://openalex.org/W4361275202","https://openalex.org/W6627637888","https://openalex.org/W6644280126","https://openalex.org/W6644940711","https://openalex.org/W6717494615","https://openalex.org/W6765657330","https://openalex.org/W6780473085","https://openalex.org/W6849687121","https://openalex.org/W6850381640"],"related_works":["https://openalex.org/W426968574","https://openalex.org/W2365639220","https://openalex.org/W2382520895","https://openalex.org/W2393709043","https://openalex.org/W2080567403","https://openalex.org/W2539387137","https://openalex.org/W2374952201","https://openalex.org/W2374808384","https://openalex.org/W2385449752","https://openalex.org/W2619844325"],"abstract_inverted_index":{"In":[0,142],"this":[1,36],"paper,":[2],"the":[3,6,14,31,56,59,69,83,109,112,122,125,129,135,147,171],"estimation":[4],"of":[5,30,40,111,174],"stress\u2013strength":[7],"reliability":[8,60,126],"is":[9,38,62],"taken":[10],"into":[11],"account":[12],"when":[13],"stress":[15],"and":[16,44,74,97,176],"strength":[17],"variables":[18],"have":[19,134],"unit":[20,32],"Gompertz":[21,33],"distributions":[22],"with":[23],"a":[24,104,156],"similar":[25],"scale":[26],"parameter.":[27],"The":[28,79],"consideration":[29],"distribution":[34],"in":[35,128],"context":[37],"because":[39],"its":[41],"intriguing":[42],"symmetric":[43],"asymmetric":[45],"properties":[46],"that":[47,124,146,169],"can":[48],"accommodate":[49],"various":[50],"histogram":[51],"proportional-type":[52],"data":[53,167],"shapes.":[54],"As":[55],"main":[57],"contribution,":[58],"estimate":[61],"determined":[63],"via":[64],"seven":[65],"frequentist":[66],"techniques":[67],"using":[68,117,164],"ranked":[70],"set":[71],"sampling":[72,77],"(RSS)":[73],"simple":[75],"random":[76],"(SRS).":[78],"proposed":[80],"methods":[81],"are":[82,150,162],"maximum":[84,91,130],"likelihood,":[85],"least":[86,89],"squares,":[87,90],"weighted":[88],"product":[92,131],"spacing,":[93],"Cram\u00e9r\u2013von":[94],"Mises,":[95],"Anderson\u2013Darling,":[96],"right":[98],"tail":[99],"Anderson\u2013Darling":[100],"methods.":[101],"We":[102,120],"perform":[103],"simulation":[105],"work":[106],"to":[107,139,152],"evaluate":[108],"effectiveness":[110],"recommended":[113],"RSS-based":[114,148],"estimates":[115,127,149],"by":[116,155],"accuracy":[118],"metrics.":[119],"draw":[121],"conclusion":[123],"spacing":[132],"approach":[133],"lowest":[136],"value":[137],"compared":[138],"other":[140],"approaches.":[141],"addition,":[143],"we":[144],"note":[145],"superior":[151],"those":[153],"obtained":[154,163],"comparable":[157],"SRS":[158],"approach.":[159],"Additional":[160],"results":[161],"two":[165],"genuine":[166],"sets":[168],"reflect":[170],"survival":[172],"periods":[173],"head":[175],"neck":[177],"cancer":[178],"patients.":[179]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":7}],"updated_date":"2026-06-09T15:46:55.921056","created_date":"2023-05-23T00:00:00"}