Computation of Confidence Regions for Optimal Factor Levels in Constrained Response Surface Problems

This article presents an improved approach for computing the confidence regions for the optimal factor settings obtained from optimizing a general response surface model. The approach has a better computational efficiency and improved accuracy compared to existing methodology. A three-factor mixture experiment was used for the performance comparison. The coverage rate properties of the resulting confidence regions were assessed through an extensive simulation study.

[1]  G. Derringer,et al.  Simultaneous Optimization of Several Response Variables , 1980 .

[2]  John J. Peterson,et al.  A General Approach to Confidence Regions for Optimal Factor Levels of Response Surfaces , 2002, Biometrics.

[3]  Virgil L. Anderson,et al.  Extreme Vertices Design of Mixture Experiments , 1966 .

[4]  J. Sneddon Sequential simplex optimization , 1992 .

[5]  Anthony V. Fiacco,et al.  The Sequential Unconstrained Minimization Technique for Nonlinear Programing, a Primal-Dual Method , 1964 .

[6]  Enrique Del Castillo,et al.  A Tool for Computing Confidence Regions on the Stationary Point of a Response Surface , 2001 .

[7]  George E. P. Box,et al.  A CONFIDENCE REGION FOR THE SOLUTION OF A SET OF SIMULTANEOUS EQUATIONS WITH AN APPLICATION TO EXPERIMENTAL DESIGN , 1954 .

[8]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[9]  Glen D. Camp Letter to the Editor - Inequality-Constrained Stationary-Value Problems , 1955, Oper. Res..

[10]  R. H. Myers,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[11]  J. Mcginity,et al.  Influence of nonionic surfactants on the physical and chemical properties of a biodegradable psuedolatex , 1994 .

[12]  K. I. M. McKinnon,et al.  Convergence of the Nelder-Mead Simplex Method to a Nonstationary Point , 1998, SIAM J. Optim..

[13]  E D Campbell,et al.  Drug activity and therapeutic synergism in cancer treatment. , 1982, Cancer research.

[14]  Margaret H. Wright,et al.  Direct search methods: Once scorned, now respectable , 1996 .

[15]  Daniel John Woods,et al.  An interactive approach for solving multi-objective optimization problems (interactive computer, nelder-mead simplex algorithm, graphics) , 1985 .

[16]  Enrique Del Castillo,et al.  Multiresponse Process Optimization via Constrained Confidence Regions , 1996 .

[17]  Anthony V. Fiacco,et al.  Computational Algorithm for the Sequential Unconstrained Minimization Technique for Nonlinear Programming , 1964 .

[18]  J. W. Gorman,et al.  On the Detection of an Additive Blending Component in Multicomponent Mixtures , 1978 .

[19]  John J. Peterson A General Approach to Ridge Analysis With Confidence Intervals , 1993 .

[20]  W. H. Carter,et al.  Confidence regions for constrained optima in response-surface experiments. , 1983, Biometrics.

[21]  Raymond H. Myers,et al.  Confidence intervals and an improved ridge analysis of response surfaces , 1986 .

[22]  N. G. Becker Models for the Response of a Mixture , 1968 .

[23]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..