Simplex Centroid n 4 components for fitting quadratic model
Run X1 (%) X2 (%) X3 (%) X4 (%)
1 100 0 0 0
2 0 100 0 0
3 0 0 100 0
4 0 0 0 100
5 0 0 50 50
6 0 50 0 50
7 0 50 50 0
8 50 50 0 0
9 50 0 0 50
10 50 0 50 0
11 0 33.33 33.33 33.33
12 33.33 33.33 0 33.33
13 33.33 33.33 33.33 0
14 33.33 0 33.33 33.33
15 25 25 25 25
Basically the simplex centroid designs are improved version of the simplex latices - both are introduced by Henry Scheffe in sixties. The centroid designs are composite in terms of adding new components, they are useful for more complicated regression models. Also they are D-optimal.
The Simplex-Lattice can estimate a full cubic model, whereas the Simplex-Centroid cannot - it can estimate the special cubic. Thus, the Simplex-Lattice would only be better if you suspect that the response(s) you are measuring might require a full cubic.
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