## Central composite design: Response Surface methodology

Response surface methodology (RSM) is a collection of statistical and mathematical techniques used to study the relationships between a response variable and multiple predictor variables. One of the popular designs in RSM is the Central Composite Design (CCD), which is a type of experimental design that allows for the estimation of the curvature of the response surface.

The following are the steps involved in Central Composite Design:

- Identify the factors: Determine the predictor variables that are likely to affect the response variable.
- Choose the levels of the factors: The levels of the factors should be chosen based on prior knowledge, experience or experimentation. CCD typically requires at least five levels (-α, -1, 0, +1, +α) for each factor, where α is the distance between the center point and the high or low level.
- Determine the number of experimental runs: CCD involves three sets of runs: factorial, axial and center points. The number of experimental runs is determined by the number of factors and the number of levels chosen for each factor. The total number of runs for a CCD is (2k + 2k + n) where k is the number of factors and n is the number of center points.
- Conduct the experiment: Conduct the experiments according to the design matrix generated by the CCD.
- Analyze the data: Analyze the data using statistical software to estimate the response surface and determine the optimal settings of the predictor variables.
- Validate the model: Validate the model by comparing the predicted values with the actual values obtained in the experiment. If the model fits well, it can be used for optimization.

CCD is a useful experimental design technique for exploring the relationship between multiple predictor variables and the response variable. By using CCD, it is possible to estimate the curvature of the response surface and identify the optimal settings of the predictor variables. It is important to check that the assumptions of CCD are met before analyzing the data.

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