Equivalence theorem of $D$-optimal equal allocation design for multiresponse mixture experiments

Abstract

The equivalence theorem is the most important theorem of experimental design. For single response, the D-optimal equivalence theorem of the continuous design and equal allocation design already exist. However, the equivalence theorem of D-optimal equal allocation design for multiresponse mixture experiments has not been investigated. In this paper, we study this problem and find that the maximize of the variance function of the equivalence theorem equal to the number of response. D-optimal designs for multiresponse are illustrated by two examples.