Circular designs balanced for neighbours at distances one and two

• 成果类型: Article
• 署名作者: Aldred, R. E. L.; Bailey, R. A.; Mckay, Brendan D.; Wanless, Ian M.
• 署名单位: University of Otago; University of St Andrews; Australian National University; Monash University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asu036
• 发表日期: 2014
• 页码: 943956
• 关键词: latin squares; sets

摘要

We define three types of neighbour-balanced designs for experiments where the units are arranged in a circle or single line in space or time. The designs are balanced with respect to neighbours at distance one and at distance two. The variants come from allowing or forbidding self-neighbours, and from considering neighbours to be directed or undirected. For two of the variants, we give a method of constructing a design for all values of the number of treatments, except for some small values where it is impossible. In the third case, we give a partial solution that covers all sizes likely to be used in practice.