A development of some systematic method of constructing statistical design of experiments and its application

这是一个为期3年的研究项目，今年是最后一年。这一期间开展的活动摘要如下。该项目的研究成果在许多会议(包括国际统计和组合数学会议)上发表，并与其他研究人员进行交流，收到了许多积极的评论或建议。这些会议和会议在日本境内的岐抚大学、庆应大学、千叶大学、筑波大学、波兰大使馆、明治大学、富士大学、美丽大学、岛根大学、京都大学、北海道大学、白滨和伊势斯地区举办，而在日本以外的纽卡斯尔大学举办。在澳大利亚，波兰的贝德勒沃，美国的波特兰，新西兰的陶波，中国的桂林。它们中的大多数都是作为特邀论文提交的。在这些经历中，我们获得了许多有用的和富有成效的评论或信息，以进一步发展我们的项目。以下是我们的一些主要结果。1.为下面的…获得了一些施工方法更多类型的区组设计和组合结构：成组可分设计、用于比较试验的双列杂交、矩形设计、差族、区组大小为4和指数3.2的框架。3.对于文献中流行的各种关于区组设计平衡性的定义，我们提出了一个统一的术语，以发展一种新的分析理论。4.阐明了平衡嵌套区组设计、平衡数组和可分解区组设计的组合结构，并给出了它们的构造。5.提出了平衡不完全区组设计的一个新性质，即加法结构，并给出了几种构造这种区组设计的方法。这个问题现在被推广到考虑双参数的情况。此外，还研究了大集的平衡不完全区组设计及其特征。较少

This is a 3-year research project and this year is final. The activity done for the period is summarized as follows. Research results on this project were presented in many conferences (including international conferences on statistics and combinatorics) to communicate with other researchers and then we have received many positive comments or suggestions. Such conferences and meetings are organized, in Japan, at Gifu Univ., Keio Univ., Chiba Univ., Univ.of Tsukuba, Embassy of Poland, Meijou Univ., Fuji.Univ., Meisei Univ., Shimane Univ., Kyoto Univ., Hokkaido Univ., Shirahama and Ise areas, while, outside Japan, at Newcastle Univ. in Australia, Bedlewo in Poland, Portland in USA, Taupo in New Zealand, Guilin in China. Most of them are presented as invited papers. We have obtained many useful and fruitful comments or information to develop our project further during such experience.Some of our main results are explained below.1.Some methods of construction are obtained for the following … More classes of block designs and combinatorial structures : group divisible designs, diallel crosses for comparative experiments, rectangular designs, difference families, frames of block size 4 and index 3.2.Systematic characterization of balanced incomplete block designs and symmetric balanced incomplete block designs are given in terms of design parameters. A characterization for certain group divisible designs are also given.3.For various popular definitions on balancedness in block designs in literature, we proposed a unified terminology to develop a new theory for analysis.4.We clarify combinatorial structures of balanced nested block designs, balanced arrays and resolvable block designs, and provide their constructions.5.We propose a new property, i.e., addition structure, of a balanced incomplete block design and present several methods of constructing such block designs. This problem is now extended to consider two-parameters' situation. Also, large sets of balanced incomplete block designs are investigated with their characterizations. Less