V-optimal mixture designs for the qth degree model

• This paper discusses V-optimal designs for mixture experiments.
• The focus is on the qth degree model.
• The paper identifies some conflicting results in the literature.
• V-optimal designs are presented and verified using the general equivalence theorem.

This paper revisits the problem of finding continuous V-optimal mixture designs for the qth degree model. For this problem, Liu and Neudecker [10] present general analytical expressions for the weights of the points of the simplex-centroid design and claim that the resulting designs are V-optimal. For a problem involving three mixture ingredients, Liu and Neudecker's results are in conflict with those of Laake [6]. We find that Laake's design for three ingredients is superior to that of Liu and Neudecker, and we establish the V-optimality of Laake's design and report V-optimal weights for the points of the simplex-centroid design for cases involving more than three ingredients. All newly proposed designs are superior to those of Liu and Neudecker.