Crossover Designs and Orthogonal Arrays

- 建议编号：DMS 9803684 PI： John Stufken研究所： 爱荷华州州立大学项目： 交叉设计与正交表 摘要： 本研究进一步了解两种最有用的统计设计类型：交叉设计和正交表。在交叉设计中，多名受试者中的每一名接受多种治疗，在多个时间段中的每一个时间段接受一种治疗。设计问题包括选择要使用的治疗序列，以及决定使用这些序列中的每一个的频率。虽然实际考虑因素起着重要作用，但基于统计考虑的答案因测量统计模型的假设而异。这项研究涉及在各种现实的模型假设下找到有效的实用设计。我们使用这些结果来确定大多数模型具有良好性能的设计。在正交表方面，本研究为混合正交表的构造提供了新的方法，并提供了一个广泛的混合正交表库。 此外，本文还研究了复合正交表在析因实验中用于位置检测时的性质 和分散效应。 设计实验是科学研究和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着特别突出的作用。 交叉设计以其在医学研究和临床试验中的作用而闻名，在临床试验中，它们用于比较两种或多种治疗方法的研究，可能包括安慰剂。正交表在所有制造业的质量改进和评估研究中发挥着至关重要的作用。除其他外，它们用于研究，以确定制造过程中的变化对最终产品质量的可能影响。 这项研究有助于通过确定更好的设计和广泛使用这些设计来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.