Incomplete three-level factorial designs

Another alternative to the 3 full factorial is the Box-Behnken design (Box and Behnken [19]). These designs are a class of incomplete three-level factorial designs that either meet, or approximately meet, the criterion of rotatability. A Box-Behnken design for p=3 variables is shown in Table 2.7. This design will estimate the ten coefficients of the second-order... 

In the introduction to this chapter, it was said that complete three-level factorial designs with more than two variables would give too many runs to be convenient for response surface modelling. It is, however, possible to select a limited number of runs from such designs to obtain incomplete 3 designs which can be used to fit quadratic models. 

The Box-Behnken is considered an efficient option in response surface methodology and an ideal alternative to central composite designs. It has three levels per factoi but avoids the corners of the space, and fills in the combinations of center and extreme levels (Figure 5). It combines a fractional factorial with incomplete block designs in such a way as to avoid the... 

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