2007 Fiscal Year Final Research Report Summary
Study on construction and analysis of balanced fractional3^m factorial designs-main effects being estimable
| Project/Area Number |
17500181
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Hiroshima University |
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Principal Investigator |
KUWADA Masahide Hiroshima University, Graduate School of Engineering, Professor (10144891)
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| Co-Investigator(Kenkyū-buntansha) |
KAGEYAMA Sanpei HIROSHIMA UNIVERSITY, Graduate School of Education, Professor (70033892)
HYODO Yoshifumi Okayama University of Science, Graduare School of Informatics, Professor (90189811)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Balanced designs / Resolution / Simple arrays / Matrix equations / Information matrices / Relationship algebras / Index set / Factorial effects |
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| Research Abstract |
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
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