Complete enumeration of two-level orthogonal arrays of strength d with d+2 constraints

• 成果类型: Article
• 署名作者: Stufken, John; Tang, Boxin
• 署名单位: University System of Georgia; University of Georgia; Simon Fraser University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001325
• 发表日期: 2007
• 页码: 793-814
• 关键词: fractional factorial-designs; minimum; catalog; CLASSIFICATION

摘要

Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d + 2 constraints for any d and any run size n = lambda 2(d). Our results not only give the number of nonisomorphic orthogonal arrays for given d and n, but also provide a systematic way of explicitly constructing these arrays. Our approach to the problem is to make use of the recently developed theory of J-characteristics for fractional factorial designs. Besides the general theoretical results, the paper presents some results from applications of the theory to orthogonal arrays of strength two, three and four.