Abstract
The variations of the Face-centered Central Composite Design under partial replications of design points are studied. The experimental conditions include replicating the cube points while the star points and center point are held fixed or not replicated, replicating the star points while the cube points and the center point are held fixed or not replicated and replicating the center point while the cube points and the star points are held fixed or not replicated. As a measure of goodness of the designs, D- and G-efficiency criteria are utilized. Results show that for the two- and three-variable quadratic models considered, the Face-centered Central Composite Design comprising of two cube portions, one star portion and a center point performed better than other variations under D-optimality criterion as well as G-optimality criterion. When compared with the traditional method of replicating the center point, the two cube portions, one star portion and a center point variation was relatively better in terms of design efficiency.
Highlights
Unreplicated designs are very widely used in experimental situations
The variation of the Central Composite Design (CCD) is studied when (i) The cube points are replicated while the star points and center point are held fixed or not replicated; (ii) The star points are replicated while the cube points and the center point are held fixed or not replicated; (iii) The center point is replicated while the cube points and the star points are held fixed or not replicated
Using the second-order polynomial model in equation (1), the partial replications of the factorial points and the star points with respect to replicating the center point are investigated with the following results
Summary
Fitting full model for unreplicated designs results in zero degrees of freedom for error and tests about main and interaction effects of factors cannot be carried out. This constitutes a potential problem in statistical testing (Farrukh, 2014). Designs with factors that are set at two levels implicitly assume that the effect of the factors on the response variable is linear and one would usually anticipate fitting the first-order model. When it is suspected that the relationship between the factors in the design and the response variable is not linear, there is the need to include one or more experimental runs. In some cases, the curvature in the response function is not adequately modeled and the need to consider the second-order model for better representation
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