TWO-LEVEL PARALLEL FLATS DESIGNS

• 成果类型: Article
• 署名作者: Wang, Chunyan; Mee, Robert W.
• 署名单位: Nankai University; Nankai University; University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2071
• 发表日期: 2021
• 页码: 3015-3042
• 关键词: quaternary code designs; nonregular designs; factorial; CONSTRUCTION; RESOLUTION; fractions; one-8th

摘要

Regular 2(n-P) designs are also known as single flat designs. Parallel flats designs (PFDs) consisting of three parallel flats (3-PFDs) are the most frequently utilized PFDs, due to their simple structure. Generalizing to f-PFD with f > 3 is more challenging. This paper aims to study the general theory for the f-PFD for any f >= 3. We propose a method for obtaining the confounding frequency vectors for all nonequivalent f-PFDs, and to find the least G-aberration (or highest D-efficiency) f-PFD constructed from any single flat. PFDs are particularly useful for constructing nonregular fraction, split-plot or randomized block designs. We also characterize the quaternary code design series as PFDs. Finally, we show how designs constructed by concatenating regular fractions from different families may also have a parallel flats structure. Examples are given throughout to illustrate the results.