Central composite designs with fractional factorials

The Box-Behnken is considered an efficient option in response surface methodology and an ideal alternative to central composite designs. It has three levels per factoi but avoids the corners of the space, and fills in the combinations of center and extreme levels (Figure 5). It combines a fractional factorial with incomplete block designs in such a way as to avoid the... 

One limitation of two-level factorial designs is the assumption of linearity of the effects. If it is possible that the effect of one or more of the factors is nonlinear, a response surface design may be selected. A central composite response surface design is a full factorial or fractional factorial design that is supplemented with additional trials to allow for estimation of curvature from the factors of interest. For each factor of interest to be studied for curvature, two additional trials are performed (1) one trial with all of the factors at their middle level except for... 

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