Developing mixture models, are we done

Abstract

Forty-one years ago, Scheffé’s pioneering article “Experiments With Mixtures”, was the impetus for much of the research on mixture experiments performed during the next three decades and into the 1990’s. That article introduced the simplex lattice designs and the associated canonical polynomials, the latter often referred to as Scheffé’s models. Over the years, alternative designs and models have been developed mainly to deal with such modifications to the standard mixture problem as the placing of additional constraints on the mixture component proportions and the inclusion of nonmixture factors called process variables or the amount of the mixture. As we move into the 21st century and think about future research on models for mixture experiments, we are tempted to ask, “Are there additional challenges facing us or are we done” To answer this question truthfully we must look back to see where we’ve been and look to the future at what it is we want to accomplish. This paper is the beginning of this process.

Keywords:

• Component proportion
• Scheffé-type models
• multiple constraints
• process variables