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In statistics, a central composite design is an experimental design, useful in response surface methodology, for building a second order (quadratic) model for the response variable without needing to use a complete three-level factorial experiment.

After the designed experiment is performed, linear regression is used, sometimes iteratively, to obtain results. Coded variables are often used when constructing this design.

A central composite design is an experimental design used in Response Surface Modeling design where star points and center points may be added to a factorial experiment, providing three or five levels for each factor.

#### Implementation

Central composite design consists of three distinct sets of experimental runs:

1. factorial (perhaps fractional) design in the factors studied, each having two levels;
2. A set of center points, experimental runs whose values of each factor are the medians of the values used in the factorial portion. This point is often replicated in order to improve the precision of the experiment;
3. A set of axial points, experimental runs identical to the center points except for one factor, which will take on values both below and above the median of the two factorial levels, and typically both outside their range. All factors are varied in this way.

#### Application of central composite designs for optimization

Statistical approaches such as Response Surface Methodology can be employed to maximize the production of a special substance by optimization of operational factors. In contrast to conventional methods, the interaction among process variables can be determined by statistical techniques. For instance, in a study, a central composite design was employed to investigate the effect of critical parameters of pretreatment of rice straw including temperature, time, and ethanol concentration. The residual solid, lignin recovery, and hydrogen yield were selected as the response variables.

#### References

Wikipedia. Central composite design. https://en.wikipedia.org/wiki/Central_composite_design