Optimal designs for industrial and computer experimentation

这项研究致力于获得用于工业和计算机实验的最优设计。工业筛选实验经常被用来确定哪些因素在研究中的产品或过程的质量中起着统计上显著的作用。通常情况下，一些实验因素的水平比其他因素更难或更昂贵。在这样的背景下，“分裂情节设计”经常出现。这项研究考虑了只有几个游程(例如，12、16、20、24等)的分割小区设计的最佳选择。这种设计为从业者提供了比目前文献中编目的大多数分裂小区设计更灵活的游程大小，因此应该会为工业实验节省成本。近年来，对用于工业实验的最佳设计的搜索已经扩展到用于“计算机实验”的最佳设计的开发。计算机实验在实验在物理上是不可能的(或昂贵得令人望而却步或耗时)的情况下很有用。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，以模拟正在研究的物理过程，成本只需一小部分。这样的模型可能由数十个参数组成，而计算机实验的输出可能由数千个观测数据组成。本研究考虑的是功能输出环境下的计算机实验设计。此外，在这种情况下，在选择计算机实验的最佳因素水平设置时也要考虑“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.