Optimal orthogonal block designs for four-mixture components in two blocks based on F-squares for Becker's models and K-model

Abstract

Orthogonal block designs in mixture experiments have been extensively studied by various authors. Aggarwal et al. [M.L. Aggarwal, P. Singh, V. Sarin, and B. Husain, Mixture designs in orthogonal blocks using F-squares, METRON – Int. J. Statist. LXVII(2) (2009), pp. 105–128] considered the case of components assuming the same volume fractions and obtained mixture designs in orthogonal blocks using F-squares. In this paper, we have used the class of designs presented by Aggarwal et al. and have obtained D-, A- and E-optimal orthogonal block designs for four components in two blocks for Becker's mixture models and K-model, respectively. Orthogonality conditions for the considered models are also given.

Keywords:

• mixture experiments
• orthogonal blocking
• Becker's models
• K-model
• F-squares
• D-optimality
• A-optimality
• E-optimality

Acknowledgements

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 paper.