Abstract
Optimal orthogonal block designs for Scheffé’s quadratic model are discussed by Czitrom(1988, 1989, 1992), Draper et al.(1993), Prescott et al.(1993, 1997), Lewis et al.(1994), Chan and Sandhu (1999), and Ghosh and Liu(1999). In this paper, we construct a class of orthogonal block designs in t=(q-1) blocks for Darroch and Waller’s additive quadratic models in q(≤50) components when q is prime or a prime power and obtain D-, A- and E-optimal designs in this class with the restriction of only two non-zero components. Conditions required for orthogonality are also given.
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References
Chan, L. Y., and Sandhu, M. K., 1999. Optimal orthogonal block designs for a quadratic mixture model for three components, Journal of Applied Statistics, 26, 19–34.
Chan, L. Y., Guan, Y. N. and Zhang C. Q.,1998 a. A-optimal designs for an additive quadratic mixture model, Statistica Sinica, 8, 979–990.
Chan, L. Y., Meng, J. H., Jiang, Y. C. and Guan, Y. N.,,1998 b. D-optimal axial designs for quadratic and cubic additive mixture model, Australian and New Zealand Journal of Statistics, 40, 359–371.
Cornell, J. A., 2002. Experiments with mixtures, Third Edition, Wiley, New York
Czitrom, V., 1988. Mixture experiments with process variables: D-optimal orthogonal experimental designs, Communications in Statistics-Theory and Methods, 17, 105–121.
Czitrom, V., 1989. Experimental designs for four mixture components with process variables, Communications in Statistics — Theory and Methods, 18, 4561–4581.
Czitrom, V., 1992. Note on mixture experiments with process variables, Communications in Statistics-Simulation and Computation, 21, 493–498.
Darroch, J. N. and Waller, J., 1985. Additivity and interactions in three-components experiments with mixtures, Biometrika, 72, 153–163.
Draper, N. R., Prescott, P., Lewis, S. M, Dean, A. M., John, P. W. M. and Tuck, M. G., 1993. Mixture designs for four components in orthogonal blocks, Technometrics, 35, 268–276.
Ghosh, S. and Liu, T., 1999. Optimal mixture designs for four components in two orthogonal blocks, Journal of Statistical Planning and Inference, 78, 219–228.
John, P. W. M., 1984. Experiments with Mixture Involving Process Variables, Technical Report 8, Center for Statistical Sciences, University of Texas, Austin, TX, 1–17.
Lewis, S. M., Dean, A. M., Draper, N. R. and Prescott, P., 1994. Mixture designs for q components in orthogonal blocks. Journal of the Royal Statistical Society, Series B, 56, 457–467.
Nigam, A. K., 1970. Block designs for mixture experiments, Annals of Mathematical Statistics, 41, 1861–1869.
Prescott, P., Draper, N. R., Dean, A. M., Lewis, S. M., 1993. Mixture designs for five components in orthogonal blocks, Journal of Applied Statistics, 20, 105–117.
Prescott, P., Draper, N. R., Lewis, S. M., and Dean, A. M., 1997. Further properties of mixture designs for five components in orthogonal blocks, Journal of Applied Statistics, 24, 147–156.
Scheffé, H., 1958. Experiments with Mixtures, Journal of Royal Statistical Society, Series B, 20, 344–360.
Scheffé, H., 1963. Simplex-centroid designs for experiments with Mixtures, Journal of Royal Statistical Society, Series B, 25, 235–263.
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Aggarwal, M.L., Singh, P. & Chan, L.Y. Optimal Designs in (q-1) Orthogonal Blocks for Darroch And Waller’s Quadratic Mixture Model In q Components. J Stat Theory Pract 1, 465–477 (2007). https://doi.org/10.1080/15598608.2007.10411852
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DOI: https://doi.org/10.1080/15598608.2007.10411852