21.4.3.8. Box and Behnken Design (BBD)

Box and Behnken have proposed some three-level designs for constructing response surfaces. These designs are formed by combining \({{2}^{k}}\) factorials with incomplete block designs. They are rotatable (or nearly rotatable). Box-Behnken design does not include any points at the vertices created by the upper and lower limits for each variable. This could be advantageous when the points on the corners of the cube represent factor-level combinations that are difficult or impossible to test because of physical process constraints.

Figure 21.141 A Box-Behnken design for \(k=3\).