# Central Composite Design

The most popular response surface method (RSM) design is the central composite design (CCD).

A CCD has three groups of design points:

1. two-level factorial or fractional factorial design points

2. axial points (sometimes called “star” points)

3. center points

CCD’s are designed to estimate the coefficients of a quadratic model. All point descriptions will be in terms of coded values of the factors.

# Factorial Points

The two-level factorial part of the design consists of all possible combinations of the +1 and -1 levels of the factors. For the two factor case there are four design points:

(-1, -1) (+1, -1) (-1, +1) (+1, +1)

# Star or Axial Points

The star points have all of the factors set to 0, the midpoint, except one factor, which has the value +/- Alpha. For a two-factor problem, the star points are:

(-Alpha, 0) (+Alpha, 0) (0, -Alpha) (0, +Alpha)

The value for Alpha is calculated in each design for both rotatability and orthogonality of blocks. The experimenter can choose between these values or enter a different one. The default value is set to the rotatable value.

Another position for the star points is at the face of the cube portion on the design. This is commonly referred to as a face-centered central composite design. You can create this by setting the alpha distance to one, or choosing the Face Centered option. This design only requires three levels for each factor.

# Center Points

Center points, as implied by the name, are points with all levels set to coded level 0 - the midpoint of each factor range: (0, 0)

Center points are usually repeated 4-6 times to get a good estimate of experimental error (pure error). For example, with two factors the design will be created with five center points by default. These runs can be identified in the design layout by doing a right mouse click on the Select button and choosing Point Type.

To summarize, central composite designs require 5 levels of each factor: -Alpha, -1, 0, 1, and +Alpha. One of the commendable attributes of the central composite design is that its structure lends itself to sequential experimentation. Central composite designs can be carried out in blocks.

# Categorical Factors

You may also add categorical factors to this design. This will cause the number of runs generated to be multiplied by the number of combinations of the categorical factor levels.