Nearly Optimal Orthogonally Blocked Designs for Four Mixture Components Based on F-Squares

Abstract

Prescott (1998) discussed nearly optimal orthogonally blocked designs based on latin squares for mixtures involving three and four components. Aggarwal et al. (2009a) studied orthogonal blocking of blends for Scheffé's quadratic model using F-squares for the case when some components assume equal volume fractions and presented a general method for obtaining mates that are required to construct orthogonal blocks using F-squares. In this article, we obtain nearly D-, A-, and E-optimal orthogonally blocked designs in two blocks based on F-squares for four component mixtures for Scheffé's quadratic, Becker's models, Darroch and Waller's quadratic, and K-mixture models.

Keywords:

• A-optimality
• Becker's models
• Darroch and Waller's model
• D-optimality
• E-optimality
• F-squares
• K-model
• Mixture experiments
• Orthogonal blocking
• Scheffé model

Mathematics Subject Classification:

• 62K10
• 62K15

Acknowledgments

The authors are very grateful to the Editor and the referees for making extremely useful suggestions and comments which resulted in considerable improvement in the presentation of the article.