Abstract
We introduce a very rich class of mixture designs in the interior of the simplex, which are useful when all experiments must constitute a complete mixture, that is, when none of the components is absent from the mixture. These designs are called yantram designs, as they are directly derivable from the Hindu yantrams, which are certain numerical configurations of positive integers having certain properties. Not only do these designs work well within the interior of the simplex, they can also be easily refined to satisfy the constraints, if there are any, on the mixture components. Leverage values for such designs are more evenly distributed among interior points compared to simplex-lattice or simplex-centroid designs, which tend to place higher leverages on the vertices or edge design points where the experiments may not be feasible.
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References
Anik, S. T., and L. Sukumar. 1981. Extreme vertexes design in formulation development: Solubility of butoconazole nitrate in a multicomponent system. J. Pharm. Sci., 70, 897–900.
Box, G. E. P., and N. R. Draper. 2007. Response surfaces, mixtures and ridge analyses. Hoboken, NJ: Wiley.
Cornell, J. A. 1986. A comparison between two ten-point designs for studying three-component mixture systems. J. Qual. Technol., 18, 1–15.
Cornell, J. A. 2002. Experiments with mixtures: Design, models and analysis of mixture data. Wiley.
Cornell, J. A., and L. Ott. 1975. The use of gradients to aid in the interpretation of mixture response surfaces. Technometrics, 17, 409–424.
Gorman, J. W., and J. E. Hinman. 1962. Simplex-lattice designs for multi-component systems. Technometrics, 4, 463–487.
Khattree, R. 2001. On the calculation of antieigenvalues and antieigenvectors. J. Interdiscip. Math. 4, 195–199.
Khattree, R. 2003. Antieigenvalues and antieigenvectors in statistics. J. Stat. Plan. Inference, 114, 13–144.
Khattree, R. 2010. Antieigenvalues provide a bound on realized signal to noise ratio. J. Stat. Plan. Inference, 140, 2846–2848.
Khattree, R. 2014a. A class of designs for mixture experiments implied by the numerical configurations in Hindu yantram. Preprint.
Khattree, R. 2014b. An alternative to extreme vertices designs for constrained mixture experiments: QP-procrustated designs. J. Indian Society Agr. Res. (in press).
Khuri, A. I. 1996. Response surfaces, designs and analyses. New York, NY: Marcel Dekker.
Lawson, J. 2010. Design and analysis of experiments with SAS. Boca Raton, FL: CRC Press.
Mclean, R. A., and V. L. Anderson. 1966. Extreme vertices design of mixture experiments. Technometrics, 8, 447–457.
Myers, R. H., D. C. Montgomery, and C. M. Anderson-Cook. 2009. Response surface methodology and product optimization using designed experiments. Hoboken, NJ: Wiley.
Sinha, B. K., N. K. Mandal, M. Pal, and P. Das. 2014. Optimal mixture experiments. India: Springer.
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Khattree, R. Mixture experiments in the interior: Yantram designs. J Stat Theory Pract 9, 797–822 (2015). https://doi.org/10.1080/15598608.2015.1029148
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DOI: https://doi.org/10.1080/15598608.2015.1029148