An Evaluation of the Performances of Central Composite Designs with Factorial and Axial Points Replications

An Evaluation of the Performances of Central Composite Designs with Factorial and Axial Points Replications | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article An Evaluation of the Performances of Central Composite Designs with Factorial and Axial Points Replications Prof. Waheed Babatunde Yahya, Oluwafemi Paul Adeyemi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6473198/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract An optimal design is most desirable when an experimenter has a number of alternative designs for his experiment. This study evaluates the performances of Central Composite Designs (CCDs) for k = 3, 4, 5, 6 with replicated portions (given a fixed number of experimental runs) used to fit full second-order models, with respect to the A-, D-, D s -, E- and G-optimality criteria and the FDS plot. The results show that the full second order CCDs experience an improvement in performance when either the factorial or axial portion or both are replicated under the D- and G-optimality criteria whereas the CCDs experience variation in their performances under the A-, D s - and E-optimality criteria. The FDS plots show that for k = 3 and 4, there is an improvement in the performance of the Slope-Rotatable Composite Design (SRCD) when either the factorial or axial portion or both are replicated. Hence, the performance of each CCD depends on the optimality criterion used and the number of factors being considered. Applied Statistics Central Composite Designs Factorial Points Axial Points Fraction of Design Space Optimality Criteria Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6473198","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":444500185,"identity":"5e774746-df0d-49c9-964e-a6d6e99a505a","order_by":0,"name":"Prof. Waheed Babatunde Yahya","email":"","orcid":"","institution":"University of Ilorin","correspondingAuthor":false,"prefix":"","firstName":"Prof.","middleName":"Waheed Babatunde","lastName":"Yahya","suffix":""},{"id":444500575,"identity":"36763c97-2303-4dbd-8436-4ba68c3d81a0","order_by":1,"name":"Oluwafemi Paul Adeyemi","email":"data:image/png;base64,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","orcid":"","institution":"University of Ilorin","correspondingAuthor":true,"prefix":"","firstName":"Oluwafemi","middleName":"Paul","lastName":"Adeyemi","suffix":""}],"badges":[],"createdAt":"2025-04-17 15:43:03","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6473198/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6473198/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80994738,"identity":"13480513-923f-439c-8bbf-76d6ae6c106d","added_by":"auto","created_at":"2025-04-21 04:50:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":662334,"visible":true,"origin":"","legend":"","description":"","filename":"paper1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6473198/v1_covered_f5c49789-6c7e-4e20-bda1-2f1ff787d2de.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eAn Evaluation of the Performances of Central Composite Designs with Factorial and Axial Points Replications\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Central Composite Designs, Factorial Points, Axial Points, Fraction of Design Space, Optimality Criteria","lastPublishedDoi":"10.21203/rs.3.rs-6473198/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6473198/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAn optimal design is most desirable when an experimenter has a number of alternative designs for his experiment. This study evaluates the performances of Central Composite Designs (CCDs) for k\u0026thinsp;=\u0026thinsp;3, 4, 5, 6 with replicated portions (given a fixed number of experimental runs) used to fit full second-order models, with respect to the A-, D-, D\u003csub\u003es\u003c/sub\u003e-, E- and G-optimality criteria and the FDS plot. The results show that the full second order CCDs experience an improvement in performance when either the factorial or axial portion or both are replicated under the D- and G-optimality criteria whereas the CCDs experience variation in their performances under the A-, D\u003csub\u003es\u003c/sub\u003e- and E-optimality criteria. The FDS plots show that for k\u0026thinsp;=\u0026thinsp;3 and 4, there is an improvement in the performance of the Slope-Rotatable Composite Design (SRCD) when either the factorial or axial portion or both are replicated. 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