Title: Robust design for mixture experiments: An efficient class of exchangeable designs for Scheff polynomials
Authors: Irene Garcia-Camacha Gutierrez - University of Castilla-La Mancha (Spain) [presenting]
Raul Martin-Martin - University of Castilla-La Mancha (Spain)
Jose Luis Polo Sanz - University of Castilla-La Mancha (Spain)
Angela Sebastia Bargues - University of Castilla-La Mancha (Spain)
Abstract: Modern industry, engineering, and science are interested in exploring new methods to determine the composition which optimally describes certain features of their products. The aim of mixture design is to identify the proportions of different blends over a simplex-shape experimental region which suitably describes the property under study. Designs obtained using Optimal Experimental Design (OED) theory are extremely model-dependent, and practitioners vaguely know the model form prior to run their experiments. Theory and methods are provided to address the mixture design problem of model robustness for Scheffe polynomials. Asymptotic designs are obtained by optimizing a function that assumes a potential model subject to a class of unknown contaminating functions. Theoretical results are proven for binary blends, whereas two strategies are provided for ternary blends: (i) an analytical solution for the continuous problem under strict assumptions on both the design region and the designs, and (ii) a numerical alternative for the general case, which involves the discretization of the problem. The geometrical properties observed in the obtained designs encouraged the investigation of a class of restricted designs named exchangeable designs. They keep the natural structure of symmetry in the simplex through medians. Results reveal that this class of restricted designs may be widely recommended for its simplicity, well performance and computational saving.