# Mixture Designs in orthogonal blocks using F-squares

## Abstract

John (1984) used latin squares for the construction of orthogonal block designs for the Scheffé's quadratic model in mixture experiments. Draper et al. (1993) discussed mixture designs for four components in orthogonal blocks, which were extended by Prescott et al. (1993) for five components. Lewis et al. (1994) generalized it for q components and gave general methods of constructing designs for q ≥3 mixture components in two or more orthogonal blocks. In this paper, we consider the case of equal volume fractions and construct orthogonal blocks of blends using F-squares. We present a general algorithm for obtaining mates of F-squares that are required for constructing orthogonal blocks. Moreover for four components, we obtain the D-, A- and E-optimal designs for the class of orthogonal block designs obtained using F-squares for Scheffé's quadratic mixture model.

## Publication Title

Metron

## Recommended Citation

Aggarwal, M., Singh, P., Sarin, V., & Husain, B.
(2009). Mixture Designs in orthogonal blocks using F-squares.* Metron**, 67* (2), 105-128.
Retrieved from https://digitalcommons.memphis.edu/facpubs/5129