Study on construction and analysis of balanced fractional3^m factorial designs-main effects being estimable

平衡分式3^m因子设计的构建与分析研究——主效应可估计

• 批准号: 17500181
• 负责人: KUWADA Masahide
• 金额: $ 2.05万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17500181/
• 关键词: Balanced designs; Resolution; Simple arrays; Matrix equations; Information matrices; Relationship algebras; Index set; Factorial effects; 釣合い型2次計画; 制約された単純配列

In this study, we obtain similar results to the (partially) balanced fractional ((P) BFF) designs for the 2 levels whose research was partially supported by Grand-in-Aid for Scientific Research (C) of the JSPS under contract number 14580348. In the 2 levels case, the irreducible representation of the information matrix w.r.t. the ideals of some algebra can be described by the product of the Gram matrix. The linearly independent column vectors of the Gram matrix concerned with an index of a simple array (SA) are only one for the 2 levels SA, but for 3 levels SA, one or two.1. Construction of designs : (1) Balanced second-order (3^m-BSO) designs : Under the second-order model, if the linear component of the main effect are estimable, then a design is said to be of resolutions R({10}∪S|Ω). An SA with indices whose suffices have at least one zero is called a "restricted SA (RSA)". A 3^-BSO design of resolutions R({10}∪S|Ω) is constructed by an RSA with N<v(m) except for only one design, wh … More ere N is the total number of the experimental units and v(m) is the number of non-negligible factorial effects.(2) 3^m-BFF designs of resolution IV: Using the similar method mentioned (1), we can obtain 3^m-BFF designs of resolution IV derived from an SA with N<v(m). In the BFF design class, there are generally fourteen kinds of resolution IV designs.2. Optimality criterion: The GA-optimal criterion was introduced by the previous research mentioned above. The confounding (or aliasing) relations among the 2-factor interactions (some case include the general mean) are expressed as plural formulas. Thus we introduce new optimality criterion, which is called "GA^*-optimality criterion". It is an improvement of the GA-optimality criterion.3. Optimal designs : (1) 3"-BSO designs : Optimal 3^m-BSO designs derived from an SA with N<v(m) w.r.t. the GA"-optimality criterion are obtained for 4〓m〓6.(2) 3^m-BFF designs : In this case, optimal designs derived from an SA with SA with N<v(m) w.r.t. the GA*-optimality criterion are not obtained yet. Less

在本研究中，我们获得了与2个水平的（部分）平衡部分（（P）BFF）设计相似的结果，其研究部分得到了JSPS科学研究补助金（C）（合同号14580348）的支持。在2层情况下，信息矩阵的不可约表示w.r.t.某些代数的理想可以用格拉姆矩阵的乘积来描述。对于简单数组（SA）的2层SA，与其下标有关的Gram矩阵的线性无关列向量只有1，而对于3层SA，则为1或2.设计的构造：（1）平衡二阶（3^m-BSO）设计：在二阶模型下，如果主效应的线性分量可估计，则称设计具有分辨率R（{10}<$S| Ω）。一个SA的索引，其足够的至少有一个零被称为“限制SA（RSA）”。分辨率R（{10}）≤ S的3^-BSO设计|Ω）由RSA构造，其中N<v（m），除了只有一个设计，其中 ...更多信息 其中N是实验单元的总数，v（m）是不可忽略的因子效应的数量。(2)分辨率为IV的3^m-BFF设计：使用类似于（1）的方法，我们可以从一个SA得到分辨率为IV的3^m-BFF设计，其中N<v（m）。在BFF设计类中，一般有十四种分辨率IV设计.最优性准则：遗传算法最优性准则是在前面的研究中引入的。两因子交互作用之间的混杂（或混叠）关系（某些情况下包括一般均值）表示为复数公式。因此，我们引入新的最优性准则，这是所谓的“GA^*-最优性准则”。它是遗传算法最优性准则的改进.最优设计：（1）3”-BSO设计：从SA导出的最优3^m-BSO设计，其中N<v（m）w.r.t.得到了4 μ m × 6遗传算法最优性准则。(2)3^m-BFF设计：在这种情况下，从SA导出的最优设计，其中SA具有N<v（m）w.r.t. GA*-最优性准则尚未得到。少

项目成果

Balanced fractional 3^m factorial designs of resolutions R({00,10,01}∪S_2|Ω)

分辨率 R({00,10,01}∪S_2|Ω) 的平衡分数 3^m 因子设计

• 发表时间: 2007
• 作者: S.;Yagi;M.Sawa;景山 三平;E. Taniguchi
• 通讯作者: E. Taniguchi

GA-optimal partially balanced fractional 2^<m1+m2> factorial designs of resolutions R ({00.10,01,20,02}|Ω) and R ({00.10,01,20,11)|Ω) with 2〓m_1, m_2〓4

分辨率为 R ({00.10,01,20,02}|Ω) 和 R ({00.10,01,20,11)|Ω) 且 2〓m_1 的 GA 最优部分平衡分数 2^<m1+m2> 因子设计, m_2〓4

• 发表时间: 2006
• 期刊: J. Japan Staist. Soc 36
• 作者: M.;Kuwada
• 通讯作者: Kuwada

A-optimal diallel crosses for test versus control comparisons

• DOI: 10.1080/02664760600679726
• 发表时间: 2006-07-01
• 期刊: JOURNAL OF APPLIED STATISTICS
• 影响因子: 1.5
• 作者: Das, Ashish;Gupta, Sudhir;Kageyama, Sanpei
• 通讯作者: Kageyama, Sanpei

Constructions of nested pairwise efficiency and variance balanced design

嵌套成对效率和方差平衡设计的构建

• 发表时间: 2005
• 期刊: Commun. Statist.-Theory Meth. 34
• 作者: Tokosumi;A.;Matsumoto;N.;Noda;K.;Moriyasu;D.;Constantinescu;A.;Murai;H.;K.Sinha;S. Kageyama;K.Matsubara;S. Rudra
• 通讯作者: S. Rudra

A-efficient balanced treatment incomplete block designs

A-高效平衡处理不完全区组设计

• 发表时间: 2005
• 期刊: Austral. J. Combin. 32
• 作者: Tokuda;T.;Tokunaga;T.;Tokosumi;A.;Ashish Das;景山 三平;A. Das
• 通讯作者: A. Das