5.
Process Improvement
5.3. Choosing an experimental design 5.3.3. How do you select an experimental design? 5.3.3.6. Response surface designs


An alternate choice for fitting quadratic models that requires 3 levels of each factor and is rotatable (or "nearly" rotatable) 
The BoxBehnken design is an independent quadratic design in that it
does not contain an embedded factorial or fractional factorial design.
In this design the treatment combinations are at the midpoints of
edges of the process space and at the center. These designs are
rotatable (or near rotatable) and require 3 levels of each factor.
The designs have limited capability for orthogonal blocking compared
to the central composite designs.
Figure 3.22 illustrates a BoxBehnken design for three factors. 

BoxBehnken design for 3 factors 


Geometry of the design 
The geometry of this design suggests a sphere within the process space
such that the surface of the sphere protrudes through each face with the
surface of the sphere tangential to the midpoint of each edge of the
space.
Examples of BoxBehnken designs are given on the next page. 