Simulation studies for design selection in a simplex space with edge effects on some mixture components

Abstract

This work proposes an evaluation – through data simulations – of optimality criteria A and D in mixture designs built from a rotational design, considering a normal model and exploring the edge of zero in parts of simplex components, in addition to the analysis of the use of inverse terms in such components. As a function of the mathematical restrictions imposed on such designs, rotationality is obtained by following a specific algebraic procedure, thus preserving the constant prediction variance in all experimental points. When it comes to mixture problems, a response may show extreme alterations when a part of such components tends to the edge of zero and the models may not be suitable to deal with that. The adequate alternative to deal with such response alterations is to include inverse terms into the models. Given the assessed scenarios, the optimum designs were more robust and more promising than the rotational ones, when evaluating the precision of residual mean squares (RMS) in all such scenarios. When a part of the components tends to the edge of zero, RMS was more precise under the D-optimum designs with inverse terms in the components of the normal lineal model.