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<p>The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust for the model. However, the analytical expressions of MSED and MD are currently only available in the hypercube, but both types of deviations in other studies are just approximations. Although it can obtain good approximations in the low-dimensional case, the calculation will be more complicated for an experiment with more variables. Therefore, in this paper, an algorithm based on lattice point partitioning design is proposed to obtain the analytical expression of the MSED and MD in the region covered by the lattice points. Furthermore, the design’s optimality is considered and illustrated by examples under the same uniformity.</p>

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Lattice point partition designs for experiments with mixture

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Jun-peng Li,
  • Guang-hui Li,
  • Chong-qi Zhang

摘要

The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust for the model. However, the analytical expressions of MSED and MD are currently only available in the hypercube, but both types of deviations in other studies are just approximations. Although it can obtain good approximations in the low-dimensional case, the calculation will be more complicated for an experiment with more variables. Therefore, in this paper, an algorithm based on lattice point partitioning design is proposed to obtain the analytical expression of the MSED and MD in the region covered by the lattice points. Furthermore, the design’s optimality is considered and illustrated by examples under the same uniformity.