The Divergence Design Criterion

If the structure of the models is more complex and we have more than one independent variable or we have more than two rival models, selection of the best experimental conditions may not be as obvious as in the above example. A straightforward design to obtain the best experimental conditions is based on the divergence criterion. 

Hunter and Reimer (1965) proposed the simple Divergence criterion that can readily be extended to multi-response situations. In general, if we have performed N experiments the experimental conditions xN+] for the next one are obtained by maximizing the weighted Divergence between the rival models, defined as 

Box and Hill (1967) proposed a criterion that incorporates the uncertainties associated with model predictions. For two rival single-response models the proposed divergence expression takes the form, 

Buzzi-Ferraris et al., (1983, 1984) proposed the use of a more powerful statistic for the discrimination among rival models however, computationally it is more intensive as it requires the calculation of the sensitivity coefficients at each grid point of the operability region. Thus, the simple divergence criterion of Hunter and Reimer (1965) appears to be the most attractive. 

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