R-Optimal Designs for Canonical Polynomial Models with Mixture Experiments

Abstract

The concept of R-optimality was introduced in the literature as an alternative to the commonly used D-optimality criteria when the objective is to construct rectangular confidence regions. This present article aspires to extend the notion of R-optimality in mixture experiments. In this study, we obtain saturated R-optimal designs for quadratic canonical polynomial for[Formula: see text]mixture components as well as for different forms of cubic polynomial mixture models, that is, full cubic, cubic without 3-way effect, and special cubic mixture models in three mixture components. The optimality of the proposed designs is confirmed by the equivalence theorem. AMS subject classification: 62K05