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Recommendations for Design Parameters for Central Composite Designs with Restricted Randomization

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dc.contributor.authorWang, Lien
dc.contributor.committeechairVining, Gordon Geoffreyen
dc.contributor.committeecochairKowalski, Scott M.en
dc.contributor.committeememberYe, Keyingen
dc.contributor.committeememberMorgan, John P.en
dc.contributor.committeememberSpitzner, Dan J.en
dc.contributor.departmentStatisticsen
dc.date.accessioned2014-03-14T20:15:41Zen
dc.date.adate2006-09-26en
dc.date.available2014-03-14T20:15:41Zen
dc.date.issued2006-08-15en
dc.date.rdate2008-09-26en
dc.date.sdate2006-08-25en
dc.description.abstractIn response surface methodology, the central composite design is the most popular choice for fitting a second order model. The choice of the distance for the axial runs, alpha, in a central composite design is very crucial to the performance of the design. In the literature, there are plenty of discussions and recommendations for the choice of alpha, among which a rotatable alpha and an orthogonal blocking alpha receive the greatest attention. Box and Hunter (1957) discuss and calculate the values for alpha that achieve rotatability, which is a way to stabilize prediction variance of the design. They also give the values for alpha that make the design orthogonally blocked, where the estimates of the model coefficients remain the same even when the block effects are added to the model. In the last ten years, people have begun to realize the importance of a split-plot structure in industrial experiments. Constructing response surface designs with a split-plot structure is a hot research area now. In this dissertation, Box and Hunters' choice of alpha for rotatablity and orthogonal blocking is extended to central composite designs with a split-plot structure. By assigning different values to the axial run distances of the whole plot factors and the subplot factors, we propose two-strata rotatable splitplot central composite designs and orthogonally blocked split-plot central composite designs. Since the construction of the two-strata rotatable split-plot central composite design involves an unknown variance components ratio d, we further study the robustness of the two-strata rotatability on d through simulation. Our goal is to provide practical recommendations for the value of the design parameter alpha based on the philosophy of traditional response surface methodology.en
dc.description.degreePh. D.en
dc.identifier.otheretd-08252006-133010en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-08252006-133010/en
dc.identifier.urihttp://hdl.handle.net/10919/28794en
dc.publisherVirginia Techen
dc.relation.haspartdissertationLiWangrevised.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectresponse surface designsen
dc.subjectorthogonal blockingen
dc.subjectrotatabilityen
dc.subjectsplit-plot designsen
dc.subjectcentral composite designsen
dc.titleRecommendations for Design Parameters for Central Composite Designs with Restricted Randomizationen
dc.typeDissertationen
thesis.degree.disciplineStatisticsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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