Central composite designs face-centered design

This design is similar to previous designs, but the star points are located 2 from the center, not 4 or 2 2 or 2. The star points have been brought inside the faces of the square. This design is sometimes called an inscribed central composite design . 

A possible disadvantage of the central composite design is that it requires five levels of each variable (0, 1, a). In some situations it might be necessary or preferable to have only three different settings of the variables. In this case a can be chosen to be 1 and the design is called a face-centered composite design. These designs are not rotatable. 

Inscribed central composite designs are a scaled down version of the circumcised version in that they use the factor settings as the star points and create factorial or fractional factorial design within those limits. In other words, inscribed designs are those where each factor of the circumcised version is divided by a for their generation. Face centered central composite designs occur when the star points are at the center of each face of the factorial space, where a= +1. 

In many situations, the region of interest is cuboidal rather than spherical. In these cases, a useful variation of the central composite design is the face-centered central composite design or the face-centered cube, in which OC =. ... 

This design locates the star or axial points on the centers of the faces of the cube as shown in Figure A3. This variation of the central composite design requires only three levels of each factor, and in practice it is frequently difficult to change factor levels. 

Examples of spherical designs are the central composite designs (except the face-centered central composite design), the Box-Behnken, and the Doehlert design. The three-level factorial design and the face-centered central composite design are cubic designs. 

Three types of central composite design can be constructed, namely the usual one with a > 1, called the central composite circumscribed (CCC) (Table 5), the central composite inscribed (CCI) when lal < 1, and the central composite face-centered (CCF), for which a = 1. The last results in a face-centered cube. 

Figure 13.5 Face centered central composite design. Square points 2, star points 2, = 3,...

Figure 13.21 shows the effect of adding an extra, remote star point to a small face centered central composite design. The experimental design matrix is... 

Figure 12.4 The spatial representations of four different types of experimental designs that are useful for process analyzer calibration (A) full-factorial, (B) Box-Behnken, (C) face-centered cube, and (D) central composite.

FACE-CENTERED CENTRAL COMPOSITE DESIGN FOR THREE DESIGN VARIABLES AND TWO ENVIRONMENTAL VARIABLES... 

TABLE 4.3. Central composite face-centered design matrix for method optimization for escitalopram and related substances showing the factors snlfated p-cyclodextrin (S-p-CD) concentration, buffer concentration, voltage and temperature, and the results for the g responses resolution, Rs, between the dtalopram enantiomers and between oxalate and (R)-citalopram as well as migration time, MT, and electric current (Modified from Reference 27 with permission)... 

Fractional factorial design, central composite face-centered design... 

Face-centered Draper-Lin small composite design with four central points... 

ED (BGE optimization). Box-Behnken design, central composite face-centered design, central composite circumscribed design. Eactors CD concentration, voltage, temperature. Response resolution, migration time. 

FIGURE 6.3. Representation of (a) full fractional design, (b) central composite face-centered design, and (c) Box-Behnken design models for three factors. Reprinted from Reference 65 with permission from Springer-Verlag. 

Figure A3. Face-centered central composite design for A = 3.

The face-centered central composite design is not rotatable, but it does not require as many center points as the spherical CCD =2 3 is sufficient to provide a good variance... 

CCF Central composite face-centered design Cfeed Solids content in the feed... 

A two-factor, three-level face-centered central composite design [11] was applied to construct a second-order polynomial model describing the effect of formulation factors on the product characteristics. The levels for each parameter are represented by a minus sign for the lower level, a plus sign for the higher level and by zero for the base level. 

The two-factor, three-level face-centered central composite design was apphed successfully for describing the effect of formulation factors on the product characteristics. 

The effect of selected experimental variables was studied in a multivariate way using face-centered central composite design. 

---