Abstract
An easy method to construct efficient blocked mixture experiments in the presence of fixed and/or random blocks is presented. The method can be used when qualitative variables are involved in a mixture experiment as well. The resulting designs are \(\mathcal{D}\)-optimal in the class of minimum support designs. It is illustrated that the minimum support designs are more efficient than orthogonally blocked mixture experiments presented in the literature and only slightly less efficient than \(\mathcal{D}\)-optimal designs.
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References
Atkinson AC, Donev AN (1992) Optimum experimental designs. Clarendon Press, Oxford
Cornell JA (2002) Experiments with mixtures: designs, models, and the analysis of mixture data. Wiley, New York
Donev AN (1989) Design of experiments with both mixture and qualitative factors. J R Stat Soc Ser B 51:297–302
Draper NR, Prescott P, Lewis S, Dean A, John P, Tuck M (1993) Mixture designs for four components in orthogonal blocks. Technometrics 35:268–276, Correction (1994) Technometrics 36:234
Goos P, Donev AN (2006a) Blocking response surface designs. Comput Stat Data Anal (to appear)
Goos P, Donev AN (2006b) The D-optimal design of blocked experiments with mixture components. J Qual Technol (to appear)
John PWM (1984) Experiments with mixtures involving process variables. Technical Report 8, Center for Statistical Sciences, University of Texas, Austin, Texas
Khuri AI (1992) Response surface models with random block effects. Technometrics 34:26–37
Lewis SM, Dean AM, Draper NR, Prescott P (1994) Mixture designs for q components in orthogonal blocks. J R Stat Soc Ser B 56:457–467
Nigam AK (1976) Corrections to blocking conditions for mixture experiments. Ann Stat 47:1294–1295
Prescott P (2000) Projection designs for mixture experiments in orthogonal blocks. Commun Stat Theory Methods 29:2229–2253
Prescott P, Draper NR (1998) Mixture designs for constrained components in orthogonal blocks. J Appl Stat 25:613–638
Prescott P, Draper NR, Dean AM, Lewis SM (1993) Mixture designs for five components in orthogonal blocks. J Appl Stat 20:105–117
Prescott P, Draper NR, Lewis SM, Dean AM (1997) Further properties of mixture designs for five components in orthogonal blocks. J Appl Stat 24:147–156
Scheffé H (1958) Experiments with mixtures. J R Stat Soc Ser B 20:344–360
Trinca LA, Gilmour SG (2000) An algorithm for arranging response surface designs in small blocks. Comput Stat Data Anal 33:25–43
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Goos, P., Donev, A.N. \(\mathcal{D}\)-optimal Minimum Support Mixture Designs in Blocks. Metrika 65, 53–68 (2007). https://doi.org/10.1007/s00184-006-0059-6
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DOI: https://doi.org/10.1007/s00184-006-0059-6