Construction of Saturated Designs for Mixture Experiments

DOI: 10.18805/BKAP266    | Article Id: BKAP266 | Page : 81-84
Citation :- Construction of Saturated Designs for Mixture Experiments.Bhartiya Krishi Anusandhan Patrika.2021.(36):81-84
Rahul Banerjee, Seema Jaggi, Eldho Varghese, Arpan Bhowmik, Anindita Datta, Cini Varghese arpan.stat@gmail.com
Address : ICAR-Indian Agricultural Statistics Research Institute, Library Avenue, Pusa-110 012, New Delhi, India.
Submitted Date : 26-02-2021
Accepted Date : 16-06-2021


Mixture Experiments are very common in real life experiments. Designing a mixture experiment involves selection of the proportion of the mixture components in a fashion such that a mathematical model can be fitted adequately and the parameters could be estimated. In agricultural experiments, the mixture components may be several sources of the input applied or input may be applied at different crop growth stages in splits such that total quantity applied to the crop is constant. Efficient designs for mixture experiments are useful when the response is assumed to depend on the relative proportions of the ingredients present in the mixture. A number of algorithms and heuristics are available in literature; however, a limited work has been done in the use of algorithms for mixture experiments. There is a need to develop designs for mixture experiments in smaller number of runs for a specific model for varying proportions using algorithmic approach. In this study we have developed algorithms to construct saturated designs fort mixture experiments. The algorithm provides a greater flexibility in design construction in comparison to the traditional approach in terms of models to be fitted; number of runs to be requited etc. These designs are very well suited in real life experiments. The use of algorithms in construction of designs for mixture experiments not only reduces the computational cost but also results in a more efficient search of the design in a continuous design space.


Algorithmic approach Mixture designs Mixture experiment Saturated designs


  1. Atkinson, A.C. and Donev, A.N. (1989). The Construction of Exact D-optimum Experimental Designs with Application to Blocking Response Surface Designs. Biometrika. 76(3): 515-526. 
  2. Cornell, J.A. (2002). Experiments with mixtures: Third Edition. New York, Wiley. 
  3. Khuri, A.I. and Cornell, J.A. (1996). Response Surfaces: Designs and Analyses: Second Edition, New York, Marcel Dekker, Inc.
  4. Mitchell, T.J. (1974). An Algorithm for the Construction of D-Optimal Experimental Designs. Technometrics.  16(2): 203-210. 
  5. Nigam, A.K. (1969). Contribution to design and analysis of experiments with mixtures, Ph.D. Thesis, Banaras Hindu University.
  6. Nigam, A.K. (1970). Block designs for mixture experiments. Ann. Math. Statist. 41: 1861-1869.
  7. Nigam, A.K. (1976). Corrections to blocking conditions for mixture experiments. Ann. Math. Statist. 47: 1294-1295.
  8. Nigam, A.K. (1983). A new algorithm for extreme vertices designs for linear mixture models. Technometrics. 25(4): 367-371.
  9. Scheffé, H. (1958). Experiments with mixtures. Journal of Royal Statistical Society. Series B. 20: 344- 360.
  10. Scheffé, H. (1963). Simplex-centroid designs for experiments with mixtures. Journal of Royal Statistical Society. Series B. 20: 344-360.
  11. Sinha, B.K., Mandal, N.K., Pal, M. and Das, P. (2014). Optimal Mixture Experiments, Lecture Notes in Statistics, Springer.
  12. Snee, R.D. and Marquadt, D.W. (1974). Extreme vertices designs for linear mixture models. Technometrics. 16(3): 399-408.
  13. Snee, R.D. and Rayner, A.A. (1982). Assessing the accuracy of mixture model regression calculations. J. Qual. Technol. 14: 67-79.

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