SMALLCOMPOSITEDESIGNS

The compositedesignsfor fitting second-ordermodelsin k factorsall contain

cube portionsof resolutionat leastV, plus axial points,plus centerpoints.

Of

course there must be at least 1/2(k + 1)(k + 2) points in the design, this being the

number of coefficients to estimate.

Hartley (1959) pointed out that the cube

portion of the composite design need not be of resolution V.

It could, in fact, be

of resolution as low as III, provided that two-factor interactions were not aliased

with two-factor interactions.

(Two-factor interactions could be aliased with main

effects, because the star portion provides additional information on the main

effects.)

This idea permitted much smaller cubes to be used.

Westlake (1965)

5, 7, and 9 cases.

took this idea further by finding even smaller cubes for the k

=

The following table shows the numbers of points in the various designs

suggested, for 2 <= k <= 9 .