Fig. 4

Examples of experimental designs with two and three factors. Factorial designs are constructed by testing every factor at each level, and can lead to large numbers of experimental runs as the number of factors increases. Box-Behnken designs reduce the number of experimental runs, but interactions between factors at ‘extreme’ levels are not included (i.e., the ‘corners’). Box-Wilson or Central composite designs (CCDs) combine factorial designs with ‘star points’ (shown in blue) to estimate second-order (quadratic effects). Modifications to the CCD result in face-centred (CCF) or inscribed (CCI) designs when the design space must be constrained