Statistics Toolbox

Box-Behnken Designs

Like central composite designs, Box-Behnken designs are response surface designs that can fit a full quadratic model. Unlike most central composite designs, Box-Behnken designs use just three levels of each factor. This makes them appealing when the factors are quantitative but the set of achievable values is small.

Central composite faced (CCF) designs also use just three factor levels. However, they are not rotatable as Box-Behnken designs are. On the other hand, Box-Behnken designs can be expected to have poorer prediction ability in the corners of the cube that encloses the design, because unlike CCF designs they do not include points at the corners of that cube.

The figure below shows a Box-Behnken design for three factors, with the circled point appearing at the origin and possibly repeated for several runs. A repeated center point makes it possible to compute an estimate of the error term that does not depend on the fitted model. For this design all points except the center point appear at a distance from the origin. That doesn't hold true for Box-Behnken designs with different numbers of factors.

Central Composite Designs

D-Optimal Designs