Centered composite designs are a class of Design of Experiments (DOE) that are used to model the relationship between input variables (factors) and the output variable (response) in an experimental environment. These designs are often employed when there is a need to explore and understand a complex response surface while minimizing the number of experimental trials.
A typical centered composite plan includes the following elements:
Central points These are points where all factors are set at their central level, often represented by the number zero. These points are used to estimate the linear effects of the factors.
Axial points The "alpha" value is used to determine the distance of the axial points from the center of the factor space. More precisely, the axial points are generally positioned at an "alpha" distance from the central points along the main axes). These points are used to estimate the quadratic effects of the factors.
Axial Cube Points They are used to estimate interactions between factors. These points are located at a distance of ±1 from the origin, but along the main axes (x, y, z) in a three-factor space.
Centered composite designs are particularly useful in situations where non-linear response or significant interaction between factors is suspected. They allow more detailed characterization of the response surface, while keeping the number of trials relatively low compared with exhaustive exploration of the factor space.