Full Factorial Design
Factorial design experiment is an experiment whose design consists of two or more variables, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. Such an experiment allows studying the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.
The whole number of the experiment is very high. If n is the number of k variables, then the number of model calculations is kn. The picture below demonstrate the factorial design of 3 variables with 3 levels:
Central Composite Design
Central Composite Design contains an imbedded 2n factorial design with center points that is augmented with a group of 2n star points that allow estimation of curvature. The distance from the center of the design space to a factorial point is ±1 unit for each factor. If n is the number variables, then the number of model calculations is 2n+2n. The picture below demonstrate the CCD of 3 variables:
