Sequential Design for Optimal Discrimination between

1 Sequential Design for Optimal Discrimination between Rival Models 

Suppose one has to discriminate between two models = ax + b and = ax, where / is a dependent variable that can be conversion or rate. It is logical to design an experiment where a maximum difference or divergence can be expected between the two models. From Fig. 2.7.1.1-1, this would be for values of the independent variable x close to zero and Xj, but surely not in the vicinity of 

Suppose n- experiments have been performed at / - 1 settings of x, so that estimates for a and b can be obtained. These are the preliminary experiments, carried out at values of the independent variable that are chosen with common sense or by making use of an a priori method. To select the setting of X for the first sequentially designed experiment, the operability region on the x axis is divided into a certain number of intervals. 

Design Criterion. The design criterion is based upon the divergence defined, for example, as follows  

A design criterion of the type given in (2.7.1.1-1) was used by Hunter and Reiner [1965]. It may occur that the confidence intervals on the responses (Xy) and (Xy) overlap as shown in Fig. 2.7.1.1-1 for large x . Therefore, Box and Hill [1967] proposed a criterion that accounts for the variances of the predicted response values. It has been experienced, however, that the optimal settings predicted by this formula frequently agree with the simpler expression (2.7.1.1-1). 

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