复杂响应曲面试验的设计与分析研究

Response surface experiment has been widely applied into the area of industry, agriculture and medicine. And it also plays an important role in the research and development of high-tech products. In the practice of response surface methodology, the experimenters often are in puzzle about how to choose a good design and how to obtain a good design which can meet the requirements of them. Besides, in practice, the experimenters often encounter complex response surface, such as, the response with missing value and blocking. This project will study the problem about the design and analysis of complex response surface. We will carry out research about the response surface with quantitative and qualitative factors simultaneously, the response surface with block structure, the response surface with missing value and multiple responses. We will explore some new evaluation and comparison criteria, which not only can effectively depict the extent of fitting a model to the data, but also take the robustness into consideration. And the combinatorial methods, efficient algorithms will be adopted to construct good designs under these criteria. In addition, we will study deeply the robust, reliable and efficient screening methods of response surface modelling, which will provide a sound support to the analysis of response surface experiments.

响应曲面试验在工业、农业、医学等领域被广泛采用，并在高新技术产品的研发中发挥重要作用。在响应曲面方法的应用实践中，试验者常常会困惑于选择什么样的设计较好，以及怎样获得满足自己需求的优良设计。此外，在实践中，试验者常常会遇到带有响应缺失以及区组结构等复杂的响应曲面。本项目将研究复杂的响应曲面的设计与分析问题，围绕着同时含有定性定量因子的响应曲面，带有区组结构的响应曲面，带有缺失值的响应曲面以及存在多个响应的响应曲面的设计与分析问题开展研究。通过寻求既能很好地刻画模型对数据的拟合程度，同时又兼顾稳健性的评价准则，采用组合方法、设计高效算法构造出好的设计，为响应曲面试验提供理论指导以及大量优良的设计。同时，深入研究稳健可靠有效的响应曲面因子筛选方法，为响应曲面的分析提供有力依据。

试验设计在科学技术进步、揭示科学规律和发现新的科学知识方面发挥了重要作用。科学的不断发展和日新月异的实践进一步要求进行复杂试验设计，比如设计带有不同属性因子，带有区组结构和多个响应。当目前为止，本项目开展了如下研究：（1）考虑到序惯试验的自然分区组属性，研究了拓展设计；（2）考虑到多个响应试验，且系统环境相对稳定时，研究广义折叠翻转设计；（3）考虑到不同属性因子情形，引入边际配对偏差.项目研究进一步扩充均匀设计的内容，提供了一些性质良好的设计表。