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scidoe_bbdesign

Box-Benhken design of experiments

Calling Sequence

H = scidoe_bbdesign(nbvar)
H = scidoe_bbdesign(nbvar,"center",nbcenter)

Parameters

nbvar :

a 1-by-1 matrix of doubles, integer value, nbvar >= 3. The number of variables of the experiment

nbcenter :

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).

H :

a m-by-nbvar matrix of doubles, the design of experiments in the range [-1,1], where m=nbvar*4+nbcenter

Description

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.

Examples

// 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

Bibliography

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

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