Central composite designs
main topic 

You can create blocked or unblocked central composite designs. Central composite designs consist of

·    2K or 2K-1 factorial points (also called cube points), where K is the number of factors

·    axial points (also called star points)

·    center points

A central composite design with two factors is shown below. Points on the diagrams represent the experimental runs that are performed:

     image\CCD1.gif

image\CCD2.gif

image\CCD3.gif

The points in the factorial portion of the design are coded to be -1 and +1.

The points in the axial (star) portion of the design are at:(+ a, 0), (-a, 0), (0,+ a), (0,- a)

Here, the factorial and axial portions along with the center point are shown. The design center is at (0,0).

Central composite designs are often recommended when the design plan calls for sequential experimentation because these designs can incorporate information from a properly planned factorial experiment. The factorial and center points may serve as a preliminary stage where you can fit a first-order (linear) model, but still provide evidence regarding the importance of a second-order contribution or curvature.

You can then build the factorial portion of the design up into a central composite design to fit a second-degree model by adding axial and center points. Central composite designs allow for efficient estimation of the quadratic terms in the second-order model, and it is also easy to obtain the desirable design properties of orthogonal blocking and rotatability.

More

Orthogonally blocked designs allow for model terms and block effects to be estimated independently and minimize the variation in the regression coefficients. Rotatable designs provide the desirable property of constant prediction variance at all points that are equidistant from the design center, thus improving the quality of the prediction.