Other designs for quadratic models

In this section, some designs are given by which it is possible to fit a quadratic response surface model with fewer runs than what is needed for the composite designs. However, there is always a price to pay for being lazy, and with a reduced number of experiments, the quality of the predictions firom the model becomes poorer. 

In some cases it would be inconvenient to use more than three levels for the variation of the experimental variables. In the composite rotatable designs, five levels are used. In this section, some examples of three-level response surface designs are also given. 

The equiradial designs are useful when two experimental variables are studied. The coded experimental settings are evenly distributed on the periphery of the unit circle, and with at least one experiment at the center point. Without the center point the X X matrix will be singular. The designs are defined by the following relations  

There should be at least one experiment at the center point, Xj = Xj = 0, and m experiment on the periphery, defined by 

A quadratic model in two variables contains six parameters, and the smallest design which can be used must therefore contain six experiments. This wiU correspond to an equiradial design in which the experiments on the periphery (m = 5) define a regular pentagon, see Fig. 12.17a. 

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