D-optimal mixture component-amount designs for quadratic and cubic models

Abstract

When the total amount of a mixture of ingredients needs to be taken into account (in addition to the composition of its ingredients), an experimental design requires several levels of the amount. Designs for such situations are discussed, and D-optimal choices are made for fitting quadratic and cubic models, for various numbers of experimental units.

Keywords:

• component amounts
• D-optimality
• mixtures
• Scheffé models
• Scheffé designs