21.4.3.7. Central Composite Design (CCD)

Composite designs for fitting second-order response surfaces were first introduced by Box and Wilson (1951) and followed up by Box and Hunter (1957). A composite design, shown in Figure 21.140, consists of a \({{2}^{k}}\) factorial or a \({{2}^{k}}\) fractional factorial portion, with runs selected from the \({{2}^{k}}\) runs \(\left( {{x}_{1}},{{x}_{2}},...,{{x}_{k}} \right)=\left( \pm 1,\pm 1,...,\pm 1 \right)\) usually of resolution V or higher, plus a set of \(2k\) axial points at a distance \(\alpha\) from the origin, plus \({{n}_{o}}\) center points. Thus, we have a total of \({{2}^{k-q}}+2k+{{n}_{o}}\) points. In general, the \({{2}^{k-q}}\) portion (or cube) may be repeated \(c\) times and the axial points (or stars) may be repeated \(s\) times. The value of \({{n}_{o}}\), \(c\) and \(s\) are to be selected by the experimenter.

However, the computer experiments do not require the repeated samplings because they have absolute repeatability. The Face Centered Central Composite Design is that all the axial points are projected on the surfaces.