Statistical Tools for Chemical Process and Product Design and Improvement

数学模型对于通过设计、监控和控制来推进产品和工艺非常重要。这些模型往往在方程的数量、形式和相互关联性方面都很复杂。统计技术对于开发模型、估计参数以及确定我们在多大程度上改进了制造性能和产品特性非常重要。工程师和科学家需要统计技术来评估他们估计参数的准确度，确定哪些是重要的，检查预测的质量，并设计额外的实验来提高模型性能和物理理解。产品的改进为分析间接测量的性能(例如聚合物的强度)或复杂的特性(例如颗粒形状)带来了额外的统计需求。测量和表征产品的仪器的快速发展为统计分析提供了新的数据类型，给统计分析带来了新的挑战。 该研究计划将开发新的统计工具，用于建立数学模型，探索实验结果，开发与制造因素有关的产品质量模型，并将通过应用于工业和实验室规模的问题来测试这些统计技术的有用性。该研究计划将开发更好的方法来在过程扰动未知的情况下估计时变行为模型中的参数；开发改进的方法来测试参数估计对模型预测性能的影响；开发改进的方法来调查和建模随时间和位置变化的过程和产品行为；以及开发处理更复杂类型的数据的技术，如颗粒/细胞形状、光谱和产品性能曲线。 这些贡献将是支持化学过程和产品设计的新统计工具，并帮助大学、工业和政府科学家和工程师从他们的实验中提取更多信息和理解。

Mathematical models are important for advancing products and processes through design, monitoring, and control. These models are often complex, in the number, form and interconnectedness of equations. Statistical techniques are important for developing models, estimating parameters, and determining how much we have improved manufacturing performance and product characteristics. Engineers and scientists need statistical techniques to assess how well they can estimate parameters, to identify which are important, to check the quality of predictions, and to design additional experiments that improve model performance and physical understanding. Product improvement brings additional statistical needs for analyzing properties that are measured indirectly (e.g., strength of a polymer), or characteristics that are complex (e.g., particle shapes). Rapid advances in instruments for measuring and characterizing products have provided new kinds of data, with new challenges for statistical analysis. The research program will develop new statistical tools for building mathematical models, for exploring experimental results, for developing models relating product qualities to manufacturing factors, and will test the usefulness of these statistical techniques through application to industrial and lab-scale problems. The research program will develop better ways to estimate parameters in models of time-varying behaviour when process disturbances are unknown; develop improved ways to test the impact of parameter estimates on model prediction performance; develop improved ways for investigating and modeling process and product behaviour that changes with time and location; and develop techniques for dealing with more complex types of data such as particle/cell shapes, spectra and product performance curves. The contributions will be new statistical tools to support design of chemical processes and products, and to help university, industrial and government scientists and engineers extract more information and understanding from their experiments.