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

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 Scheffe'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 Scheffe's quadratic, Becker's models, Darroch and Waller's quadratic, and K-mixture models.