Optimal designs for estimating the parameters in weighted power-mean-mixture models

Journal of Chemometrics

Volumn 24, Issue 1, 2010, Pages 34-42

  Coetzer, R L J ^a   Focke, W W ^b  

^a SASOL TECHNOLOGY PTY LTD   (South Africa)

^b UNIVERSITY OF PRETORIA   (South Africa)

Author keywords

Design efficiency; Mixture variables; Optimal designs; Power mean mixture models

Indexed keywords

OPTIMAL SYSTEMS; PARAMETER ESTIMATION;

CLUSTER PROPERTY; DESIGN EFFICIENCY; MIXTURE MODELING; MIXTURE PROPERTIES; MIXTURE VARIABLES; MOLEFRACTION; OPTIMAL DESIGN; POWER MEANS; POWER-MEAN-MIXTURE MODEL; WEIGHTED POWER MEANS;

EFFICIENCY;

EID: 74349100484     PISSN: 08869383     EISSN: 1099128X     Source Type: Journal    
DOI: 10.1002/cem.1271     Document Type: Article

References (23)

1. Focke W, Sandrock C, Kok S. Weighted-power-mean mixture model: Empirical mixing laws for liquid viscosity. Ind. Eng. Chem. Res. 2007; 46: 4660-4666.
2. Draper N, Pukelsheim F. Mixture models based on homogeneous polynomials. J. Stat. Plan. Inference 1998; 71: 303-311.
3. Cornell J. Experiments with Mixtures: Designs, Models and the Analysis of Mixture Data, 3rd edn. Wiley: New York, 2002.
4. Atkinson A, Donev A, Tobias R. Optimum Experimental Designs, with SAS. Oxford University Press Inc.: New York, 2007.
5. Snee R. Experimental designs for quadratic models in constrained mixture spaces. Technometrics 1975; 17: 399-408.
6. Snee R. Experimental designs for mixture systems with multicomponent constraints. Commun. Stat. Theory Methods 1979; A8(4): 303-326.
7. Draper N, Pukelsheim F. Kiefer ordering of simplex designs for first-and second-degree mixture models. J. Stat. Plan. Inference 1999; 79: 325-348.
8. Atkinson A, Bogacka B, Bogacki M. D-and t-optimum designs for the kinetics of a reversible chemical reaction. Chemometr. Intell. Lab. Syst. 1998; 43: 185-198.
9. Atkinson A, Bogacka B. Compound and other optimum designs for systems of nonlinear differential equation sarising in chemical kinetics. Chemometr. Intell. Lab. Syst. 2002; 61: 17-33.
10. Kiefer J, Wolfowitz J. The equivalence of two extremum problems. Can. J. Math. 1960; 12: 363-366.
11. Atkinson A, Haines L. Designs for nonlinear and generalised linear models. In Handbook of Statistics, Vol. 13, Ghosh S, Rhao CR (eds). North-Holland, Amsterdam, 1996, pp. 437-475.
12. Federov V. Theory of Optimal Experiments. Academic Press: New York, 1972.
13. Scheffé H. Experiments with mixtures. J. R. Stat. Soc. Series B 1958; 20: 344-360.
14. Grunberg L, Nissan A. Mixing law for viscosity. Nature 1949; 164: 799.
15. Wilson G. Vapor-liquid equilibrium. xi. a new expression for the excess free energy of mixing. J. Am. Chem. Assoc. 1964; 86: 127.
16. Walas S. Phase Equilibrium in Chemical Engineering. Butterworth: Boston, 1985.
17. Prausnitz J, Lichtenthalern R, de Azevedo E. Molecularthermodynamics of fluid-phase equilibria. Prentice Hall: Upper Saddle River, NJ, 1999.
18. Hamad E. Exact limits of mixture properties and excess thermodyamic functions. Fluid Phase Equilib. 1998; 142: 163.
19. Miller AJ, Nguyen N-K. Algorithm AS 295: a federov exchange algorithm for d-optimal design. Applied Statistics 1994; 43(4): 669-677.
20. Mitchell T. An algorithm for the construction of 'd-optimal' experimental designs. Technometrics 1974a; 16: 203-210.
21. Mitchell T. Computer construction of 'd-optimal' first-order designs. Technometrics 1974b; 16(2): 211-220.
22. Galil Z, Kiefer J. Timeand space-saving computer methods, related to mitchell's detmax, for finding d-optimum designs. Technometrics 1980; 22(3): 301-313.
23. Welch WJ. Computer-aided design of experiments for response estimation. Technometrics 1984; 26(3): 217-224.