Two-level factorial designs with extreme numbers of level changes

• 成果类型: Article
• 署名作者: Cheng, CS; Martin, RJ; Tang, BX
• 署名单位: University of California System; University of California Berkeley; University of Sheffield; University of Memphis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1522-1539
• 关键词: run order

摘要

The construction of run orders of two-level factorial designs with extreme (minimum and maximum) numbers of level changes is considered. Minimizing the number of level changes is mainly due to economic considerations, while the problem of maximizing the number of level changes arises from some recent results on trend robust designs. The construction is based on the fact that the 2(k) runs of a saturated regular fractional factorial design for 2(k) -1 factors can be ordered in such a way that the numbers of level changes of the factors consist of each integer between 1 and 2(k) - 1. Among other results, we give a systematic method of constructing designs with minimum and maximum numbers of level changes among all designs of resolution at least three and among those of resolution at least four. It is also shown that among regular fractional factorial designs of resolution at least four, the number of level changes can be maximized and minimized by different run orders of the same fraction.