Crossover Designs and Orthogonal Arrays

-----------------------------------------------------------------------提案编号：DMS 9803684 PI: John Stufken机构：爱荷华州立大学项目：交叉设计和正交阵列摘要：本研究进一步了解了两种最有用的统计设计类型：交叉设计和正交阵列。在交叉设计中，几个受试者中的每一个接受多种治疗，在几个时间段中的每一个。设计问题包括选择要使用的处理序列，以及决定使用这些序列的频率。虽然实际考虑因素起着主要作用，但基于统计考虑因素的答案会根据对测量的统计模型的假设而有所不同。本研究涉及在各种现实模型假设下寻找有效的实用设计。我们使用这些结果来识别大多数模型具有良好性能的设计。在正交阵列方面，本研究提供了构建混合正交阵列的新方法，并建立了丰富的混合正交阵列库。此外，还研究了复合正交阵列在析因实验中同时检测位置和色散效应时的性能。设计好的实验是科学研究、工业产品开发和改进的一个组成部分。交叉设计和正交阵列发挥了特别突出的作用。交叉设计以其在医学研究和临床试验中的作用而闻名，在这些研究中，它们被用于比较两种或两种以上的治疗，可能包括安慰剂。正交阵列在所有制造业的质量改进和评价研究中起着至关重要的作用。除其他外，它们被用于研究，以确定制造过程中的变化对最终产品质量的可能影响。这项研究通过确定更好的设计并使这些设计广泛使用，有助于提高此类试验和研究的效率。

----------------------------------------------------------------------- Proposal Number: DMS 9803684 PI: John Stufken Institution: Iowa State University Project: Crossover Designs and Orthogonal Arrays Abstract: This research furthers the understanding of two of the most useful types of statistical designs: crossover designs and orthogonal arrays. In a crossover design each of several subjects receives multiple treatments, one at each of several time periods. The design problem consists of selecting the sequences of treatments to be used, and of deciding how often to use each of these sequences. While practical considerations play a major role, answers based on statistical considerations differ depending on the assumptions about the statistical model for the measurements. This research involves finding efficient practical designs under various realistic model assumptions. We use these results to identify designs with good properties for most models. Concerning orthogonal arrays, this research provides new methods for the construction of mixed orthogonal arrays, as well as an extensive library of such arrays. In addition, compound orthogonal arrays are studied for their properties when used in a factorial experiment to detect location and dispersion effects simultaneously. Designed experiments are an integral part of scientific research and of product development and improvement in industry. Crossover designs and orthogonal arrays play a particularly prominent role. Crossover designs are best known for their role in medical research and in clinical trials, where they are used in studies to compare two or more treatments, possibly including a placebo. Orthogonal arrays play a crucial role in quality improvement and assessment studies in all of manufacturing. They are, among others, used in studies to determine the possible effect that changes in a manufacturing process have on the quality of the final product. This research helps to improve the efficiency of such trials and studies by identifying better designs and by making such designs widely available.