Example of a two-level factorial design

Expel imenr Volume of solvent salt pH Result 

For a design with three variables we would require [2 + (2 x 3) + 1] = 15 experiments. In order to obtain repeatability information it is necessary to run an experiment several times. This is done by performing the centre point experiment twice. The total number of experiments would therefore be 16. The list of experiments is shown in Table 43.3 while Fig. 43.4 shows a diagrammatic representation of the CCD. The CCD is composed of a 3 factorial design superimposed with a star design (+a, —a). In order to minimize systematic eror (bias) it is necessary randomize the experimental run order. This is shown in Table 43.4. 

Response surface methodology allows the relationship between the responses and variables to be quantified, using a mathematical model, and to be visualized. Thus the equation for a straight-line graph can be written as  

First of all we can consider how each of the variables influences the response (y) in a linear manner. However, the relationship between y and xi, X2 and xg may not be linear, so it is necessary to consider the possibility of curvature. This is done in terms of a quadratic variable, i.e. a squared dependence (xf, Xj and X3). Finally, it is also important to consider the effects of possible interactions between the variables, xi — xg — X3, i.e. xixg, X1X3 and X2X3. The overall general equation can therefore be written as  

In general, it is important to consider the following issues when earrying out an experimental design  

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