{"id":"https://openalex.org/W7130408601","doi":"https://doi.org/10.3390/axioms15020149","title":"Reliability Improvement of a Parallel\u2013Series System via Duplication and Reduction Strategies Under the Akshaya Distribution","display_name":"Reliability Improvement of a Parallel\u2013Series System via Duplication and Reduction Strategies Under the Akshaya Distribution","publication_year":2026,"publication_date":"2026-02-18","ids":{"openalex":"https://openalex.org/W7130408601","doi":"https://doi.org/10.3390/axioms15020149"},"language":"en","primary_location":{"id":"doi:10.3390/axioms15020149","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15020149","pdf_url":"https://www.mdpi.com/2075-1680/15/2/149/pdf?version=1771407425","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/15/2/149/pdf?version=1771407425","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109656213","display_name":"Ahmed T. Ramadan","orcid":null},"institutions":[{"id":"https://openalex.org/I130009713","display_name":"Suez University","ror":"https://ror.org/00ndhrx30","country_code":"EG","type":"education","lineage":["https://openalex.org/I130009713"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ahmed T. Ramadan","raw_affiliation_strings":["Department of Mathematics, Faculty of Basic Science, Galala University, Suez 43713, Egypt"],"raw_orcid":"https://orcid.org/0000-0003-2485-6287","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Basic Science, Galala University, Suez 43713, Egypt","institution_ids":["https://openalex.org/I130009713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126309924","display_name":"Ahmed R. El-Saeed","orcid":null},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahmed R. El-Saeed","raw_affiliation_strings":["Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-8303-1782","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123335814","display_name":"Norah D. Alshahrani","orcid":null},"institutions":[{"id":"https://openalex.org/I4210136004","display_name":"University of Bisha","ror":"https://ror.org/040548g92","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210136004"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Norah D. Alshahrani","raw_affiliation_strings":["Department of Mathematics, College of Sciences, University of Bisha, Bisha 61922, Saudi Arabia"],"raw_orcid":"https://orcid.org/0009-0003-9992-6398","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Sciences, University of Bisha, Bisha 61922, Saudi Arabia","institution_ids":["https://openalex.org/I4210136004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060040866","display_name":"Ahlam H. Tolba","orcid":"https://orcid.org/0000-0001-8938-9187"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Ahlam H. Tolba","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-8938-9187","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5060040866"],"corresponding_institution_ids":["https://openalex.org/I159247623"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.32698244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"2","first_page":"149","last_page":"149"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.6137999892234802,"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":0.6137999892234802,"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/T10780","display_name":"Reliability and Maintenance Optimization","score":0.2922999858856201,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.022099999710917473,"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/redundancy","display_name":"Redundancy (engineering)","score":0.7186999917030334},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.640999972820282},{"id":"https://openalex.org/keywords/imperfect","display_name":"Imperfect","score":0.5},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4361000061035156},{"id":"https://openalex.org/keywords/failure-mode-and-effects-analysis","display_name":"Failure mode and effects analysis","score":0.4050999879837036},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4047999978065491},{"id":"https://openalex.org/keywords/bridging","display_name":"Bridging (networking)","score":0.3343999981880188}],"concepts":[{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.7760000228881836},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.7186999917030334},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.640999972820282},{"id":"https://openalex.org/C2780310539","wikidata":"https://www.wikidata.org/wiki/Q12547192","display_name":"Imperfect","level":2,"score":0.5},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4936000108718872},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4361000061035156},{"id":"https://openalex.org/C66283442","wikidata":"https://www.wikidata.org/wiki/Q1389268","display_name":"Failure mode and effects analysis","level":2,"score":0.4050999879837036},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4047999978065491},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C32587265","wikidata":"https://www.wikidata.org/wiki/Q1182260","display_name":"Data deduplication","level":2,"score":0.3264000117778778},{"id":"https://openalex.org/C201729545","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability theory","level":3,"score":0.3000999987125397},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.29899999499320984},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.29170000553131104},{"id":"https://openalex.org/C94361409","wikidata":"https://www.wikidata.org/wiki/Q7882500","display_name":"Uncertainty reduction theory","level":2,"score":0.29089999198913574},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.28940001130104065},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.2685000002384186}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms15020149","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15020149","pdf_url":"https://www.mdpi.com/2075-1680/15/2/149/pdf?version=1771407425","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f00ce4b25cac473d8b77c22aa5b412ba","is_oa":false,"landing_page_url":"https://doaj.org/article/f00ce4b25cac473d8b77c22aa5b412ba","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":"Axioms, Vol 15, Iss 2, p 149 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms15020149","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15020149","pdf_url":"https://www.mdpi.com/2075-1680/15/2/149/pdf?version=1771407425","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.42293864488601685,"display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320325415","display_name":"Al-Imam Muhammad Ibn Saud Islamic University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7130408601.pdf","grobid_xml":"https://content.openalex.org/works/W7130408601.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Parallel\u2013series":[0],"systems":[1],"are":[2,87],"fundamental":[3],"in":[4],"many":[5],"industrial":[6],"and":[7,14,78,89,102,118,140,167],"engineering":[8],"applications,":[9],"yet":[10],"their":[11],"reliability":[12,62,67,74,138,157],"assessment":[13],"improvement":[15,85],"remain":[16],"challenging,":[17],"particularly":[18],"when":[19],"components":[20,37],"exhibit":[21],"non-constant":[22],"failure":[23,72],"rates.":[24],"This":[25,154],"study":[26,113],"addresses":[27],"this":[28,53],"challenge":[29],"by":[30],"modeling":[31],"a":[32,43,99,132,145,160],"hybrid":[33],"parallel\u2013series":[34],"system":[35,66,82],"whose":[36],"follow":[38],"the":[39,65,115,120,136,141,165],"Akshaya":[40],"lifetime":[41],"distribution,":[42],"flexible":[44],"model":[45],"that":[46,128],"can":[47],"capture":[48],"various":[49],"hazard-rate":[50],"shapes.":[51],"For":[52],"system,":[54],"we":[55],"derive":[56],"closed-form":[57],"analytical":[58,162],"expressions":[59],"for":[60,148,164],"key":[61],"indices,":[63],"including":[64],"function,":[68],"mean":[69],"time":[70],"to":[71],"(MTTF),":[73],"equivalence":[75],"factors":[76],"(REFs),":[77],"\u03b4-fractiles.":[79],"To":[80],"enhance":[81],"performance,":[83],"four":[84],"strategies":[86],"formulated":[88],"analytically":[90],"compared:":[91],"failure-rate":[92],"reduction,":[93],"hot":[94],"duplication,":[95],"cold":[96,103,129],"duplication":[97,104,130],"with":[98,105,131,159],"perfect":[100,133],"switch,":[101],"an":[106],"imperfect":[107],"switch.":[108],"A":[109],"comprehensive":[110,161],"numerical":[111],"case":[112],"validates":[114],"theoretical":[116],"derivations":[117],"demonstrates":[119],"effectiveness":[121],"of":[122,169],"each":[123],"strategy.":[124],"The":[125],"results":[126],"show":[127],"switch":[134],"yields":[135],"highest":[137],"gain,":[139],"computed":[142],"REFs":[143],"provide":[144],"quantitative":[146],"tool":[147],"balancing":[149],"redundancy":[150],"against":[151],"component-level":[152],"improvements.":[153],"work":[155],"provides":[156],"engineers":[158],"framework":[163],"design":[166],"enhancement":[168],"complex":[170],"parallel-series":[171],"systems.":[172]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2026-02-19T00:00:00"}
