Uniform designs of experiments with mixtures under the mean L₁-distance criterion and a new approach to Scheffé-type designs

We introduce a criterion, named the mean (Formula presented.) -distance (ML1D) criterion, to construct uniform designs in experiments with mixtures. This criterion allows for a flexible number of design points and produces a more uniform pattern within the experimental region, in terms of representative points of the uniform distribution across that region. We further explore the optimal Scheffé-type simplex-lattice designs under the ML1D criterion and show that a connection exists between uniform mixture designs and optimal Scheffé-type simplex-lattice designs. An efficient algorithm is proposed to generate uniform designs under the ML1D criterion. Simulations and applications highlight the advantages of the proposed designs, supporting their use for modelling and prediction in mixture experiments. Our method combines model-based and uniform design principles to enable flexible and efficient mixture experiments.