Crossover Designs and Orthogonal Arrays

交叉设计和正交阵列

• 批准号: 9803684
• 负责人: Dean Isaacson
• 金额: $ 5.08万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-15 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803684&HistoricalAwards=false
• 关键词: Crossover; Designs; Orthogonal; Arrays

----------------------------------------------------------------------- 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.

------------------------------------------------------------------- 提案编号：DMS 9803684 PI：John Stufken 机构：爱荷华州立大学 项目：交叉设计和正交数组 摘要：这项研究进一步加深了对两种最有用的统计设计类型的理解：交叉设计和正交数组。在交叉设计中，多个受试者中的每一个都接受多种治疗，在几个时间段中的每个时间段进行一次治疗。设计问题包括选择要使用的治疗序列，以及决定使用每个序列的频率。虽然实际考虑起着重要作用，但基于统计考虑的答案会根据测量统计模型的假设而有所不同。这项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确定大多数模型具有良好特性的设计。关于正交阵列，这项研究提供了构建混合正交阵列的新方法，以及此类阵列的广泛库。 此外，还研究了复合正交阵列在阶乘实验中使用时的特性，以同时检测位置和色散效应。 设计实验是科学研究以及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。 交叉设计因其在医学研究和临床试验中的作用而闻名，它们用于比较两种或多种治疗方法（可能包括安慰剂）的研究。正交阵列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，它们还用于研究以确定制造过程的变化对最终产品质量可能产生的影响。 这项研究通过确定更好的设计并使此类设计广泛可用，有助于提高此类试验和研究的效率。