Designs for Discriminating Between Two Rival Models

Abstract

In most statistical literature on the design of experiments it is assumed that the correct form of the mathematical model is known and the problem is to select the experimental conditions so that some criterion is satisfied, for example, the parameters are estimated with maximum precision. Such an approach, however, ignores one important question that often confronts experimenters who, instead of having only one model known to be correct, have a number of rival candidate models to consider. Such situations can arise, for example, at the outset of investigations on the kinetics of solid-catalyzed gas reactions in chemical engineering. Often the immediate question in these circumstances is: how should experiments be planned so that the inadequate models can be detected and hence eliminated most eliiciently? In this paper a sequential design procedure is proposed for discriminating between two rival models. The basic idea is to select for the next experimental point that at which the models differ the most. Examples are included which illustrate the application of this procedure to problems in chemical kinetics.