D-Optimal Designs for Second-Order Response Surface Models with Qualitative Factors
D-Optimal Designs for Second-Order Response Surface Models with Qualitative Factors
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DOI：
10.6339/jds.2011.09(2).921
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发表时间：
2011-04
期刊：
影响因子：
--
通讯作者：
Chuan-Pin Lee;Mong-Na Lo Huang
中科院分区：
文献类型：
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作者：
Chuan-Pin Lee;Mong-Na Lo Huang
中心组合设计（Central Composite Design，CCD）是一种应用广泛的二阶响应面模型，可以通过定量因子来提高模型的精度。当实验中还包括定性因素时，应考虑定量因素和定性因素之间的影响。在本文中，D-最优设计的模型中的定性因素相互作用，分别与线性效应，或线性效应和2-因子相互作用或二次效应的定量因素。结果表明，在每一个定性水平上，相应的D-最优设计也由三个部分组成，即立方体设计、轴向设计和中心点，但权重不同。通过一个化学实验的实例，说明了本文所得到的D-最优设计如何有助于更有效地设计既有定量因素又有定性因素的实验。
Central composite design (CCD) is widely applied in many fields to construct a second-order response surface model with quantitative factors to help to increase the precision of the estimated model. When an experiment also includes qualitative factors, the effects between the quantitative and qualitative factors should be taken into consideration. In the present paper, D-optimal designs are investigated for models where the qualitative factors interact with, respectively, the linear effects, or the linear effects and 2-factor interactions or quadratic effects of the quantitative factors. It is shown that, at each qualitative level, the corresponding D-optimal design also consists of three portions as CCD, i.e. the cube design, the axial design and center points, but with different weights. An example about a chemical study is used to demonstrate how the D-optimal design obtained here may help to design an experiment with both quantitative and qualitative factors more efficiently.