Minimax designs for optimum mixtures

In a mixture experiment the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffe [1958. Experiments with mixtures. Journal of Royal Statistical Society B 20, pp. 344–360; 1963. Simplex-centroid design for experiments with mixtures. Journal of Royal Statistical Society B 25, 235–263] first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal [2006. Optimum designs for optimum mixtures. Statistics and Probability Letters 76, 1369–1379] first attempted to find a solution to this problem using the trace criterion, assuming prior knowledge about the optimum mixing proportions. In this paper the minimax criterion has been employed to find a solution to the above problem.