本研究討論了二元反應模型於混和實驗下的D型最適設計。這類的模型時常發生在許多化學以及工業的實驗上。在線性logit聯結的情況下，針對二元反應模型在給定兩個在第一象限的解釋變數時，Sitter and Torsney (1995) 與Haines et al. (2007) 已經提供了一個很好的D型最適設計架構以及數值結果。
　　首先我們提供了一個可縮減最適支撐點個數的本質完備的可行設計集合。透過這個本質完備設計集合，可使我們對D型最適設計的結構有更深入的瞭解。而此點在搜尋其他有更多限制時的設計空間時的D型最適設計會相當的有幫助。之後我們將加入由於混合實驗所產生設計的限制，並提供出在一個混合實驗的設計區間中，二元反應模型的D型最適設計。

　　In this work, D-optimal designs for binary response models in mixture experiments are discussed. This kind of model setting occurs in many chemical experiments. Under the linear logit link, D-optimal designs for binary response models with two explanatory variables on the rst quadrant as the design space have been investigated by Sitter and Torsney (1995) and Haines et al. (2007).
　　We first provide an approach to obtain an essentially complete class of designs with reduced number of optimal supports, then the D-optimal designs may also be obtained with more insights on the structure appeared there. It is helpful for the search of D-optimal designs on the other design spaces with more restrictions. Later under the design space with constraints due to the mixture restriction, we obtain the D-optimal designs for binary response models under the linear logit link in a mixture design space.

Contents
Abstract ii
1 Introduction 1
2 Preliminaries 2
3 Motivating example 4
4 D-optimal designs in the rst quadrant 9
5 D-optimal designs with mixture structure 15
6 D-optimal design for trinomial response with nested structure 18
7 Discussions and conclusions 22
References 23

References
　　Agresti, A. (2013). Categorical Data Analysis. Wiley, New York.
Atkinson, A. C., Donev, A. N., and Tobias, R. D. (2007). Optimum experimental designs, with SAS. Oxford University Press, Oxford.
　　Fedorov, V. V. (1972). Theory of Optimal Experiments. Academic Press, New York.
　　Haines, L. M., Kabera, G., Ndlovu, P., and Brien., T. E. (2007). D-optimal designs for logistic regression in two variables. In L opez-Fidalgo, J., Rodriguez-Diaz, J. M., and
Torsney, B., editors, mODa 8 - Advances in Model-Oriented Design and Analysis, pages 91-98. Springer, New York.
　　Huang, M.-N. L. and Huang, M.-K. (2009). p-optimal designs for a linear log contrast model for experiments with mixtures. Metrika, 70:239-256.
　　Karlin, S. and Studden, W. J. (1966). Tchebyche Systems with Applications in Analysis and Statistics. Wiley, New York.
　　Kiefer, J. andWolfowitz, J. (1960). The equivalence of two extremum problems. Canadian Journal of Mathematics, 12:363-366.
　　Klein, T. (2004). Optimal designs for second-degree kronecker model mixture experiments. Journal of Statistical Planning and Inference, 123:117-131.
　　Ohtani, H. (2007). Experimental study on ammability concentration areas of co/f2/n2 and sih4/cf3of/n2 mixtures. In AOFST 7.
　　Sitter, R. R. and Torsney, B. (1995). Optimal designs for binary response experiments with two design variables. Statistica Sinica, 5:405-419.
　　Yang, M. and Stufken, J. (2009). Support points of locally optimal designs for nonlinear models with two parameters. The Annals of Statistics, 37:518-541.
　　Yang, M., Zhang, B., and Huang, S. (2011). Optimal designs for generalized linear models with multiple design variables. Statistica Sinica, 21:1415-1430.