D-optimal designs for mixture experiments with various correlation structures

Mixture experimental designs have been in widespread use in agricultural, pharmaceutical, and other industrial research for many years. Much of the previous work mainly focuses on optimal design for mixture experiments when observations are uncorrelated, in large part because of the intractability of the optimal mixture experimental design on correlated case. When observations have certain correlation structures within each block, the order of the observations in each block matters and this order impacts the optimality of the design. Thus, there is need of research into construction of these useful designs when correlation structures might exist within blocks. In this paper, we propose D-optimal minimum support designs for Scheffe’s quadratic mixture model with odd number of components when observations in blocks are circulant correlated and hub correlated respectively, and Scheffe’s mixture model with any components when observations are in block-structured correlation.