DUAL-OBJECTIVE OPTIMAL MIXTURE DESIGNS: DUAL-OBJECTIVE OPTIMAL MIXTURE DESIGNS

Summary Mixture experiments are widely used in many industries and particularly in the manufacture of consumer products. Almost all work to date assumes a single study objective, which is unrealistic. Researchers may want to estimate model parameters and make predictions or extrapolations at the same time. We discuss design issues for determining the optimal proportions of the mixture components when there are two or more objectives in the study and there is a large sample size. We present a general methodology for constructing two types of dual-objective optimal design for mixture experiments and discuss the general applicability of the design strategy to more complicated types of mixture design problems, including mixture experiments.

[1]  Christopher J. Nachtsheim,et al.  Model Robust, Linear-Optimal Designs , 1982 .

[2]  H. Dette,et al.  A Generalization of $D$- and $D_1$-Optimal Designs in Polynomial Regression , 1990 .

[3]  A new nonlinear mixture response surface paradigm for the study of synergism: a three drug example. , 2003, Current drug metabolism.

[4]  John A. Cornell,et al.  Models for Mixture Experiments When the Response Depends on the Total Amount , 1985 .

[5]  Corwin L. Atwood,et al.  Optimal and Efficient Designs of Experiments , 1969 .

[6]  Weng Kee Wong,et al.  An algorithmic construction of optimal minimax designs for heteroscedastic linear models , 2000 .

[7]  W. J. Studden.  $D_s$-Optimal Designs for Polynomial Regression Using Continued Fractions , 1980 .

[8]  W K Wong,et al.  Multiple-objective optimal designs. , 1998, Journal of biopharmaceutical statistics.

[9]  E. Läuter,et al.  Optimal multipurpose designs for regression models , 1976 .

[10]  Carl Lee,et al.  Constrained optimal designs , 1988 .

[11]  Ray-Bing Chen,et al.  Optimal minimax designs over a prespecified interval in a heteroscedastic polynomial model. , 2008, Statistics & probability letters.

[12]  H. Scheffé.  The Simplex‐Centroid Design for Experiments with Mixtures , 1963 .

[13]  H. Scheffé.  Experiments with Mixtures , 1958 .

[14]  K. Chaloner,et al.  The Equivalence of Constrained and Weighted Designs in Multiple Objective Design Problems , 1996 .

[15]  Douglas C. Montgomery,et al.  OPTIMIZATION OF A HOUSEHOLD PRODUCT FORMULATION USING A MIXTURE EXPERIMENT , 1995 .

[16]  Y C Huang,et al.  Sequential construction of multiple-objective optimal designs. , 1998, Biometrics.

[17]  Hongshik Ahn,et al.  Multiple-objective optimal designs for the logit model , 1998 .

[18]  Stephen M. Stigler,et al.  Optimal Experimental Design for Polynomial Regression , 1971 .

[19]  Carl Lee,et al.  Constrained optimal designs for regressiom models , 1987 .

[20]  Combinations of optimality criteria and optimum designs , 1989 .

[21]  W. Wong.  A graphical approach for the construction of constrained a and l-optimal designs using efficiency plots , 1995 .

[22]  S Furlanetto,et al.  Mixture experiment methods in the development and optimization of microemulsion formulations. , 2011, Journal of pharmaceutical and biomedical analysis.

[23]  W. Wong,et al.  Optimal minimax designs for prediction in heteroscedastic models , 1998 .

[24]  Weng Kee Wong,et al.  On the Equivalence of Constrained and Compound Optimal Designs , 1994 .

[25]  James J. Chen,et al.  ANALYSIS OF QUANTAL RESPONSE DATA FROM MIXTURE EXPERIMENTS , 1996 .

[26]  Barbara Bogacka,et al.  Compound D - and D S -optimum designs for determining the order of a chemical reaction , 1997 .