Uniform mixture designs using designs in 2-dimensional spherical region

Practitioners who are working with mixture experiments often found that the existing mixture designs fail to provide the mixture combinations in a true sense. This problem can be overcomed by using the concept of uniform designs with mixture experiments. Uniform designs aim at scattering the points uniformly in the experimental region. Uniform mixture design can be applied in the fields like material science, chemical engineering, food science, agriculture and in many other areas where the composition of the mixtures is required to obtain response/outcome. In this paper, an attempt has been made to construct uniform mixture designs for s component mixtures using the uniform design in s-dimensional spherical region. A transformation is proposed for constructing uniform designs in s-dimensional spherical region by using the existing designs in 2-dimensional spherical region. The uniformity of the constructed designs is measured by distance-based approach and the uniformity of the mixture designs is measured by DM2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{DM}}_{2}$$\end{document}-discrepancy.