Open Access Open Access  Restricted Access Subscription Access

Construction of Mixture Designs Based on Taguchi’s Fixed Element Orthogonal Arrays

Poonam Singh, Vandana Sarin, Neha Midha


McLean and Anderson (1966) developed extreme vertices designs for mixture experiments where components are restricted by lower and upper bounds. Murthy and Murty (1983) discussed a method of construction of mixture designs for the exploration of the restricted regionusing factorials. Saxena and Nigam (1977) explored the restricted mixture region using symmetric-simplex design. This paper proposes a new algorithm for constructing mixture designs usingTaguchi’s fixed elementorthogonal arrays. The motivation is to reduce the number of design points to lower the experimentation time and cost. These designs facilitateexploration of the restricted factor space with much less computational effort.

Full Text:



C. R. Rao; Hypercubes of strength "d" leading to confounded designs in factorial experiments, Bulletin of the Calcutta Mathematical Society, 38 67-78 (1946).

C. R. Rao; Factorial Experiments derivable from combinatorial arrangements of arrays, Journal of Royal Statistical Society (Suppl.), 9(1) 128-139 (1947).

G. E. P. Box; C. J. Gardiner; Constrained Designs-Part I, First-order designs, University of Wisconsin Department of Statistics, Technical Report No. 89 (1966).

G. Taguchi; Orthogonal Arrays and Linear Graphs. American Supplier Institute, Inc., Dearborn, MI, (1986).

H. Scheffé; Experiments with Mixtures, Journal of the Royal Statistical Society Series B (Methodological), 20(2) 344-360 (1958).

H. Scheffé; The Simplex-Centroid Design for Experiments with Mixtures, Journal of the Royal Statistical Society Series B (Methodological), 25(2) 235-263 (1963).

J. A. Cornell; I. J. Good; The mixture problem for categorized components, Journal of American Statistical Association, 65(329) 339-355 (1970).

J. A. Cornell; Experiments with Mixtures: Designs, Models and the Analysis of Mixture Data, 3rd edition. New York, John Wiley, (2002).

J. Kiefer; J. Wolfowitz; The equivalence of two extremum problems, Canadian Journal of Mathematics, 12(3) 363-366 (1960).

M. S. R. Murthy; J. S. Murty; Restricted Region Simplex design for Mixture Experiments. Communication in Statistics-Theory and Methods, 12(22) 2605-2615 (1983).

R. A. McLean; V. L. Anderson; Extreme vertices design of mixture experiments, Technometrics, 8(3) 447-454 (1966).

R. C. Bose; Mathematical Theory of the Symmetrical Factorial Designs, Sankhya, 8(2) 107-166 (1947).

R. D. Snee; D. W. Marquardt; Extreme Vertices Designs for Linear Mixture Models, Technometrics, 16(3) 399-408 (1974).

R. D. Snee; Experimental designs for quadratic models in constrained mixture spaces, Technometrics, 17(2) 149-159 (1975).

R. E. Wheeler; Efficient experimental design presented at the Annual Meeting of the American Statistical Association, Montreal (August 1972).

R. N. Kacker; E. S. Lagergren; J. J. Filliben; Taguchi’s Orthogonal Arrays Are Classical Designs of Experiments, Journal of Research of the National Institute of Standards and Technology, 96(5) 577-591 (1991).

S. K. Saxena; A. K. Nigam; Restricted Exploration of mixtures by Symmetric Simplex Design, Technometrics, 19(1) 47-52 (1977).

W. C. Thompson; R. H. Myers; Response surface designs for experiments with mixtures, Technometrics, 10(4) 739-756 (1968).


  • There are currently no refbacks.



© 2015 IARS. All right reserved.