Inscribed central composite designs

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 . 

Figure 13.21 An inscribed central composite design with distantly located extra star point. DF = 4, DF = 3.

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. 

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. 

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