Optimal Experimental Designs and Response Surface Optimization

实验设计是新产品开发、工艺改进和优化的常用工具。优化设计以最小的成本提供可解释和准确的推断。方法和计算问题是优化设计理论面临的两个主要挑战。本研究的目标是解决后续设计、模型稳健设计和响应面优化中的各种最优性问题。分数因子设计是一种具有成本效益的实验计划，用于识别和估计多个变量对反应的重要影响。分数阶乘设计的一个基本问题是有些效应是混叠的，无法估计。后续设计是解决这一问题的方法之一。字母顺序标准是常用的选择最优设计的最优性标准。这些标准的缺点是它们依赖于预先指定的模型。这有时是不可能的，因为真正的模型在实践中是未知的。因此，根据这些准则得到的最优设计可能不是鲁棒的。响应面优化的目的是选择最优的操作设置来优化响应。这一领域的挑战在于它涉及复杂的统计建模和推理程序。这种优化的应用包括制造过程，如装配、加工和焊接，以及服务操作，如银行系统和公共交通。本研究将为后续设计、模型稳健设计和响应面优化提供新的理论和方法。将提出新的最优性准则来构建最优模型-稳健设计。我的研究计划将包括对高素质人才（HQP）的广泛培训，为他们将来在学术界和工业界的职位做准备。本研究将为工业、农业、制药、制造、工程和化学等领域的实验工作者提供新的经济可行的实验方案。

Design of experiments is a popular tool in new product development and in process improvement and optimization. Optimal design provides interpretable and accurate inference at minimal costs. Methodology and computation issues are two main challenges in optimal design theory. The goal of the proposed research is to address various optimality problems in follow-up design, model-robust design, and response surface optimization. Fractional factorial designs are cost-efficient experimental plans for identifying and estimating important effects of multiple variables on a response. A fundamental problem for fractional factorial designs is that some effects are aliased and cannot be estimated. Follow-up design is one of the methods for resolving the problem. Alphabetical criteria are popular optimality criteria used to select optimal designs. The drawback of the criteria is that they depend on a pre-specified model. This is sometimes impossible since the true model is unknown in advance in practice. Thus the optimal designs obtained by these criteria may not be robust. Response surface optimization aims to select optimal operating settings to optimize the response. The challenge in this area is that it involves complicated statistical modelling and inference procedures. The application of such optimization includes manufacturing processes, such as assembly, machining, and welding, and service operations, such as banking systems and public transportation. The proposed research will develop new theory and methods to handle these issues in follow-up design, model-robust design, and response surface optimization. New optimality criteria will be proposed to construct optimal model-robust designs. My research program will involve extensive training of highly qualified personnel (HQP) in preparing them for future positions in both academia and industry. The proposed research will advance design theory and methodology and provide new economical experimental plans for experimenters in industrial, agricultural, pharmaceutical, manufacturing, engineering, and chemical sciences.