Mixture experiment alternatives to the slack variable approach

Quality Engineering

Volumn 21, Issue 3, 2009, Pages 262-276

  Piepel, Greg F ^a   Landmesser, Samantha M ^b  

^a PACIFIC NORTHWEST NATIONAL LABORATORY   (United States)

^b Arsenal Capital Partners   (United States)

Author keywords

Experimental design; Mixture components; Model reduction; Partial quadratic mixture models; Variable selection

Indexed keywords

EXPERIMENTAL DESIGN; MIXTURE COMPONENTS; MIXTURE MODEL; MODEL REDUCTION; VARIABLE SELECTION;

DESIGN; EXPERIMENTS; STATISTICS;

MIXTURES;

EID: 70749089501     PISSN: 08982112     EISSN: 15324222     Source Type: Journal    
DOI: 10.1080/08982110902862095     Document Type: Article

References (26)

1. Abdullah, A., Resurreccion, A. V. A., Beuchat, L. R. (1993). Formulation and evaluation of a peanut milk based whipped topping using response surface methodology. Lebensmittel-Wissenschaft und- Technologie (Food Sci. and Technol.), 26(2):162-166.
2. Becker, N. G. (1968). Models for the response of a mixture. Journal of the Royal Statistical Society, Series B, 30(2):349-358.
3. Cain, M., Price, M. L. R. (1986). Optimal mixture choice. Applied Statistics, 35(1):1-7.
4. Chan, K. Y., Kavanagh, P. E. (1992). Application of plackett-burman design and linear programming to light-duty liquid detergent formulation. Journal of the American Oil Chemists Society, 69(7):690-694.
5. Cornell, J. A. (2000). Fitting a slack-variable model to mixture data: some questions raised. Journal of Quality Technology, 32(2):133-147.
6. Cornell, J. A. (2002). Experiments with Mixtures: Designs, Models and the Analysis of Mixture Data, 3rd ed. New York: John Wiley and Sons.
7. Fonner, D. E., Buck, J. R., Banker, G. S. (1970). Mathematical optimization techniques in drug product design and process analysis. Journal of Pharmaceutical Sciences, 59(11):1587-1596.
8. Goh, T. N., Roy, S. K. (1989). Application of taguchi's orthogonal array in a material screening experiment. Quality Assurance, 15(1 ):10-13.
9. Guillou, A. A., Floros, J. D. (1993). Multiresponse optimization minimizes salt in natural cucumber fermentation and storage. Journal of Food Sciences, 58(6):1381-1389.
10. Khuri, A. I. (2005). Slack-variable models versus Scheffé's mixture models. Journal of Applied Statistics, 32(9):887-908.
11. Landmesser, S. M., Piepel, G. F. (2007). Comparison of slack variable and mixture experiment approaches. Proceedings of the 2007 Joint Statistical Meetings, 1711-1717.
12. Levison, K. K., Takayama, K., Isowa, K., Okabe, K., Nagai, T. (1994). Formulation optimization of indomethacin gels containing a combination of three kinds of cyclic monoterpenes as percutaneous penetration enhancers. Journal of Pharmaceutical Sciences, 83(9):1367-1372.
13. MacDonald, I. A., Bly, D. A. (1966). Determination of optimal levels of several emulsifiers in cake mix shortenings. Cereal Chemistry, 43:571-584.
14. Marquardt, D. W., Snee, R. D. (1974). Test statistics for mixture models. Technometrics, 16(4):533-537.
15. Myers, R. H., Montgomery, D. C., Anderson-Cook, C.M. (2009). Response Surface Methodology: Process Optimization Using Designed Experiments, 3rd ed. New York: John Wiley and Sons.
16. Piepel, G. F. (2006a). 50 years of mixture experiment research: 1955-2004. In: Khuri, A. I., et al., Ed. Response Surface Methodology and Related Topics, Chapter 12, Singapore: World Scientific Press, 283-327.
17. Piepel, G.F. (2006b). A note comparing component-slope, scheffé, and cox parameterizations of the linear mixture experiment model. Journal of Applied Statsistics, 33(4):397-403.
18. Piepel, G. F. (2007). A component slope linear model for mixture experiments. Quality Technology and Quantitative Management., 4(3):331-343.
19. Piepel, G. F., Cornell, J. A. (1994). Mixture experiment approaches: examples, discussion, and recommendations. Journal of Quality Technology, 26(3):177-196.
20. Piepel, G. F., Cooley, S. K. (2009). Automated method for reducing Scheffé linear mixture experiment models. Quality Technology and Quantitative Management, Special Issue on Response Surface Methodology September 2009, in press.
21. Piepel, G. F., Szychowski, J. M., Loeppky, J. L. (2002). Augmenting Scheffé linear mixture models with squared and/or crossproduct terms. Journal of Quality Technology, 34(3):297-314.
22. Setz, S., Semling, M., Mülhaupt, R. (1997). Fuzzy set approach for fitting a continuous response surface in adhesion formulation. Journal of Chemometrics, 11(5):403-418.
23. Smith, W. F. (2005). Experimental Design for Formulation. ASA-SIAM Series on Statistics and Applied Probability, SIAM, Philadelphia, PA and ASA, Alexandria, VA.
24. Snee, R. D. (1973). Techniques for the analysis of mixture data. Technometrics, 15(3):517-528.
25. Snee, R. D., Rayner, A. A. (1982), Assessing the accuracy of mixture model regression calculations. Journal of Quality Technology, 14(2): 67-79.
26. Takayama, K., Nagai, T. (1991). Simultaneous optimization for several characteristics concerning percutaneous absorption and skin damage of ketoprofen hydrogels containing d-limonene. International Journal of Pharmaceutics, 74(2-3):115-126.