= Central composite design
{wiki}
A <central composite design> combines a <factorial> portion with axial points $\pm\alpha e_j$ and center runs. For a full $2^d$ <factorial design>, $d$ quantitative <factors> and $n_0\geq1$ center runs, its run count is $2^d+2d+n_0$. The <factorial> portion supplies <main effects> and <interaction terms>, while the axial runs allow the individual squared terms of a full <quadratic regression> model to be estimated. Additional center <replicates> estimate <pure error>.
For two <factors> and $n_0=5$, this gives $4+4+5=13$ runs. The four corners are $(\pm1,\pm1)$, the four axial points are $(\pm\alpha,0)$ and $(0,\pm\alpha)$, and the remaining five runs repeat $(0,0)$. Choosing $\alpha=\sqrt2$ makes this full-factorial design <rotatable>. Choosing $\alpha=1$ keeps the axial points on the faces and uses only three levels per <factor>, but does not give that rotatability in dimension at least two.
Circumscribed designs place the axial points outside the original <factorial> cube; inscribed designs rescale the cube inward to respect physical <factor> limits. A fractional <factorial> portion can reduce runs, but must retain sufficient <resolution of a fractional factorial design> to estimate the desired interactions: axial points have zero cross-products and cannot separate interactions that remain aliased in the <factorial> portion. The institutional handbook describes augmentation from a full or resolution V <factorial> portion.<NIST and SEMATECH e-Handbook of Statistical Methods/5.3.3.6.1. Central Composite Designs (CCD)>[Table 3.22 and its preceding construction]{ref}
Back to article page
