Recommendations for Design Parameters for Central Composite Designs with Restricted Randomization
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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- Doctoral Dissertations [13049]
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