Box-Benhken design of experiments
H = scidoe_bbdesign(nbvar) H = scidoe_bbdesign(nbvar,"center",nbcenter)
a 1-by-1 matrix of doubles, integer value, nbvar >= 3. The number of variables of the experiment
a 1-by-1 matrix of doubles, integer value, positive. The number of repetitions of the central point in the design (default nbcenter depends on nbvar).
a m-by-nbvar matrix of doubles, the design of experiments in the range [-1,1], where m=nbvar*4+nbcenter
Creates a Box-Benkhen Design of Experiments. This type of design is sufficient for quadratic models.
This is a three-level design, where each variable can only have one of the following values: -1, 0, +1.
By default, scidoe_bbdesign produces a number of center points which depends on nbvar. If nbvar>16, then nbcenter is equal to nbvar. If nbvar<=16, the nbcenter = T(nbvar), where T is from the following table:
[0 0 3 3 6 6 6 8 9 10 12 12 13 14 15 16]
To have only one center point, use the
H=scidoe_bbdesign(nbvar,"center",1)
calling sequence.
In this design, there is no point at the corners of the cube [-1,+1]. This property can be advantageous when the corners of the cube are too expensive, or even impossible, to compute.
On output, the rows in H are sorted in increasing order.
This function does not entirely reproduce Matlab's bbdesign. For nbvar = 9,16, the function gives different results than the known bibliography.
// Create a Box-Benkhen Design with three // variables one repetition of center: H = scidoe_bbdesign(3) // Plot the design h = scf(); param3d(H(:,1),H(:,2),H(:,3)) h.children.children.mark_mode="on"; h.children.children.line_mode="off"; h.children.children.mark_size=1; scidoe_plotcube(3) xtitle("Box-Benkhen Design","X1","X2","X3") // With three variables and the // center repeated two times: H = scidoe_bbdesign(3,2) // Print the number of experiments for nbvar = 3 : 10 H = scidoe_bbdesign(nbvar); m = size(H,"r"); mprintf("nbvar=%d, Num. Experiments=%d\n",.. nbvar,m) end | ![]() | ![]() |
http://en.wikipedia.org/wiki/Box%E2%80%93Behnken_design
Design and analysis of experiments, Montgomery, 5th Edition, Wiley, 2001
Plans d'expériences Applications à l'entreprise, Gilbert Saporta, Jean-Jacques Droesbeke, Jeanne Fine, Editions Technip, 1997