Functions > Design of Experiments > Design Matrices > Box-Behnken and Box-Wilson Designs
Box-Behnken and Box-Wilson Designs
Box-Behnken and Box-Wilson designs are used for modeling quantitative factors. Box-Behnken is a 3-level design and Box-Wilson is a second-order design.
boxbehnken(n)—Returns an n factor Box-Behnken design matrix.
This function is limited to designs with 3 ≤ n ≤ 7.
boxwilson(n, [nc, α])—Returns an n factor Box-Wilson design matrix (also called Center Composite Design, CCD). The optional arguments nc and α can be added to specify the number of center points and the value of the real axial point distance from the center of the design.
This function is limited to designs with 2 ≤ n ≤ 9.
The boxwilson function uses the ordering specified by NIST — the National Institute of Standards and Technology.
Arguments
n is an integer specifying the number of factors.
nc (optional) is an integer specifying the number of center points. The default number of center points is nc = 4 ∙ √(nf + 1) − 2n, where nf is the number of runs for the factorial portion of the Box-Wilson design.
α (optional) is a real number specifying the real axial point distance from the center of the design. The default value for α is nf1/4, where nf is the number of runs for the factorial portion of the Box-Wilson design. To satisfy rotatability, α > 1.