Optimal designs for industrial and computer experimentation

本研究的目的是获得用于工业和计算机实验的最佳设计。工业筛选实验经常用于确定哪些因素在所研究的产品或过程的质量中起统计学意义上的重要作用。通常情况下，改变某些实验因素的水平比改变其他因素更困难或更昂贵。在这种情况下，“分裂情节设计”经常出现。本研究考虑了仅由少量运行（例如，12、16、20、24等）组成的分块设计的最佳选择。这种设计为实践者提供了比目前文献中列出的大多数分块设计更灵活的运行规模，因此应该为工业实验节省成本。近年来，寻找用于工业实验的最佳设计已经扩展到开发用于“计算机实验”的最佳设计。计算机实验在物理上不可能（或昂贵或耗时）的情况下是有用的。在这种情况下，可以开发复杂的数学模型，通过计算机代码实现，以模拟所研究的物理过程，成本只是其中的一小部分。这样的模型可能由几十个参数组成，而计算机实验的输出可能由数千个观测结果组成。本研究考虑在功能输出发生的设定中设计计算机实验。此外，在这种情况下，在选择计算机实验的最佳因子水平设置时，也考虑了“噪声”或不可控因素的影响。

This research is concerned with obtaining optimal designs for use in industrial and computer experimentation. Industrial screening experiments are frequently used to ascertain which factors play a statistically significant role in the quality of a product or process under study. It is often the case that the levels of some of the experimental factors are more difficult, or expensive, to vary than the rest. In such settings "split-plot designs" often arise. This research considers the optimal choice of split-plot designs consisting of only a few runs (for example, 12, 16, 20, 24, etc). Such designs offer practitioners more flexible run sizes than most split-plot designs presently cataloged in the literature and as such should result in cost-savings for industrial experimenters.In recent years, the search for optimal designs for use in industrial experimentation has expanded to the development of optimal designs for use in "computer experiments". Computer experiments are useful in situations where experimentation is physically impossible (or prohibitively expensive or time-consuming). In such settings complex mathematical models, implemented via computer code, may be developed to mimic the physical process under study for a fraction of the cost. Such models may consist of dozens of parameters, and the output from the computer experiment may consist of thousands of observations. This research considers the design of computer experiments in the setting where functional output occurs. Furthermore, in this context, the effect of "noise", or uncontrollable factors, is also considered in the choice of optimal factor level settings for computer experiments.