Mixture Experiments: Geometry and Pseudocomponents

Abstract

Constraints, in the form of upper and lower bounds, are often placed on the components of mixtures. These constraints restrict the size of the experimental region and may alter its shape. A transformation from the original components to new variables, called pseudocomponents, is typically used to reduce the ill conditioning created by the restricted size of the experimental region. If the experimental region is a simplex, the pseudocomponent transformation is also used to adapt standard designs to the experimental region. A new pseudocomponent transformation is introduced, and the conditions under which it is preferable to the usual pseudocomponent transformation are given. The effect of changing the constraints on both the size and shape of the experimental region is discussed.

KEY WORDS:

• Mixtures
• Constrained mixture experiments
• Consistent mixture constraints