Abstract

It is very rare to conduct an experimental design with a single objective in mind. since we have uncertainties in model and its assumptions. Basically we have three approaches in literature to handle this problem, the mini-max, compound, constrained experimental design. Since Cook and Wong (1994) announced the equivalence between the compound and the constrained design, many constrained experimental design approaches have adopted the approximate design algorithm of compound experimental design. In this paper we attempt to modify the row-exchange algorithm under exact experimental design setting, not approximate experimental design one. This attempt will provide more realistic design setting for the field experiment. In this process we proposed another criterion on how to set the constrained experimental design. A graph to show the general issue of infeasibility, which occurs quite often in constrained experimental design, is suggested.

Keywords

• Exact experimental design;
• constrained optimal experimental design;
• multiple objective design

• 정확실험계획;
• 제약최적실험;
• 다중목적실험;

File

Download PDF

References

1. Box, G. E .P. and Draper, N. R. (1975). Robust design, Biometrika, 62, 347-352 https://doi.org/10.1093/biomet/62.2.347
2. Cook, R. D. and Fedorov, V. V. (1995). Constrained optimization of experimental design, Statistics, 26, 129-178 https://doi.org/10.1080/02331889508802474
3. Cook, R. D. and Nachtsheim, C. J. (1980). A comparison of algorithms for constructing exact D-optimal designs, Technometrics, 22, 315-324 https://doi.org/10.2307/1268315
4. Cook, R. D. and Wong, W. K. (1994). On the equivalence of constrained and compound optimal designs, Journal of the American Statistical Association, 89, 687-692 https://doi.org/10.2307/2290872
5. Fedorov, V. V. (1972). Theory of Optimal Experiments, Academic Press, New York
6. Gaffke, N. and Krafft, O. (1982). Exact D-optimum designs for quadratic regression, Journal of Royal Statistical Society, Series B, 44, 394-397
7. Huang, Y. C. and Wong, W. K. (1998). Sequential construction of multiple-objective optimal designs, Biometrics, 54, 1388-1397 https://doi.org/10.2307/2533665
8. Johnson, M. E. and Nachtsheim, C. J. (1983). Some guidelines for constructing exact D-optimal designs on convex design spaces, Technometrics, 25, 271-277 https://doi.org/10.2307/1268612
9. Kahng, M. W. and Kim, Y. I. (2002). Multiple constrained optimal experimental design, The Korean Communications in Statistics, 9, 619-627 https://doi.org/10.5351/CKSS.2002.9.3.619
10. Kiefer, J. (1971). The Role of Symmetry and Approximation in Exact Design Optimality, In Statistical Decision Theory and Related Topics, Academic Press, New York
11. Kiefer, J. (1974). General equivalence theory for optimal designs (approximate theory), The Annals of Statistics, 2, 849-879 https://doi.org/10.1214/aos/1176342810
12. Kim, Y. and Lim, Y. B. (2007). Hybrid approach when multiple objectives exist, The Korean Communica-tions in Statistics, 14, 531-540 https://doi.org/10.5351/CKSS.2007.14.3.531
13. Lauter, E. (1974). Experimental planning in a class of models, Mathematische Operationsforschung und Statistik, 5, 673-708
14. Lee, C. M. S. (1987). Constrained optimal designs for regression models, Communications in Statistics, Part A- Theory and Methods, 16, 765-783 https://doi.org/10.1080/03610928708829401
15. Lim, Y. B. (1991). Exact $D_{\delta}$-efficient designs for quadratic response surface model, Journal of the Korean Statistical Society, 20, 156-161
16. Meyer, R. K. and Nachtsheim, C. J. (1995). The coordinate-exchange algorithm for constructing exact optimal experimental designs, Technometrics, 37, 60-69 https://doi.org/10.2307/1269153
17. Mikulecka, J. (1983). On hybrid experimental designs, Kybernetika, 19, 1-14
18. Mitchell, T. J. (1974). An algorithm for the construction of D-optimal experimental designs, Technometrics, 16, 203-210 https://doi.org/10.2307/1267940
19. Pesotchinsky, L. L. (1975). D-optimum and quasi-D-optimum second order designs on a cube, Biometrika, 62, 335-340 https://doi.org/10.1093/biomet/62.2.335
20. Stigler, S. M. (1971). Optimal experimental design for polynomial regression, Journal of the American Statistical Association, 66, 311-318 https://doi.org/10.2307/2283928
21. Wynn, H. P. (1972). Results in the theory and construction of D-optimum experimental designs, Journal of Royal Statistical Society, Series B, 34, 133-147