Central Composite Design (CCD): Second-Order Response Surface Experiments
The Structure of CCD
A CCD has three parts: 2 to the k corner points (the plus or minus 1 levels of the factorial design), 2k axial points (each factor at plus or minus alpha with the others at 0) and several center points (all at 0). The total number of runs is 2 to the k + 2k + n0, for example 4 + 4 + 3 = 11 runs for two factors and 8 + 6 + 3 = 17 for three. This structure fits a complete second-order model with squared and interaction terms using relatively few runs, and the corner and axial points together determine rotatability and prediction accuracy.
The Advantage of Sequential Experimentation
CCD naturally supports a sequential approach: run the 2 to the k factorial design with center points first, and if the center-point check shows significant curvature, add the axial points to upgrade to a full CCD without repeating existing runs. This is very practical on the shop floor: use the cheap factorial design to confirm the key factors, then add axial points to refine the surface, accumulating information without waste. The tool supports sequential mode, outputting the factorial part first and generating the axial run plan after curvature is confirmed.
How to Set the Axial Distance Alpha
Alpha fixes the axial point positions: for a rotatable design alpha = (2 to the k) to the 1/4 (1.414 for two factors, 1.682 for three, 2 for four), giving isotropic prediction variance on the sphere; alpha = 1 gives a face-centered design where factors only take -1, 0 or +1, suited to constrained ranges; or you can set a custom value from the practically operable range. The tool defaults to the rotatable alpha and allows manual adjustment; the choice of alpha directly determines the spherical range covered by the experimental points.
Analysis and Usage Steps
After the experiment the tool fits the second-order model, tests the significance of linear, quadratic and interaction terms and lack of fit, and outputs contour and surface plots. It solves for the stationary point, classifies the optimum type, and gives the optimal factor settings with the predicted response confidence interval. The workflow: enter factor count and levels, generate the plan, run and fill in data, review the model, find the optimum and verify with confirmation runs. If the stationary point lies outside the experimental range or the interval is too wide, extend factor levels or add center point replicates.