Title page for ETD etd-08252006-133010


Type of Document Dissertation
Author Wang, Li
Author's Email Address liwang4@vt.edu
URN etd-08252006-133010
Title Recommendations for Design Parameters for Central Composite Designs with Restricted Randomization
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Vining, G. Geoffrey Committee Chair
Kowalski, Scott M. Committee Co-Chair
Morgan, John P. Committee Member
Spitzner, Dan J. Committee Member
Ye, Keying Committee Member
Keywords
  • response surface designs
  • orthogonal blocking
  • rotatability
  • split-plot designs
  • central composite designs
Date of Defense 2006-08-15
Availability unrestricted
Abstract
In 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.

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