2006 Fiscal Year Final Research Report Summary
Optimality and construction of search designs in factorial experiments
| Project/Area Number |
16540104
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kobe University |
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Principal Investigator |
SHIRAKURA Teruhiro Kobe University, Faculty of Human Development, Professor, 発達科学部, 教授 (30033913)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASHI Tadashi Kobe University, Faculty of Human Development, Professor, 発達科学部, 教授 (30179494)
MIYATA Takahisa Kobe University, Faculty of Human Development, Associate Professor, 発達科学部, 助教授 (30280390)
INABA Taichi Kobe University, Faculty of Human Development, Lecturer, 発達科学部, 講師 (80176403)
KAKIUCHI Itsuro Kobe University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (90091248)
KURIKI Shinji Osaka Prefecture University, Graduate School of Engineering, Professor, 工学研究科, 教授 (00167389)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Design of experiments / Factorial designs / Search designs / Search linear model / Main effects / Two-factor interactions / Treatment combinations / Optimality |
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| Research Abstract |
Consider factorial experiments with m factors each at two levels. It is assumed that the general mean and main effects are completely unknown. However the effects of interactions are partially unknown in the sense. At most k interactions are nonzero and the remaining are zero, where k is a quite small integer. Then it is not known which are the nonzero effects. Such a model is called a search linear model. The problem is to search the k nonzero interactions and to estimate them along the general mean and main effects using observations. A experimental design which makes possible to solve the problem is called a search design of order k.□ Consider for two cases; (i) the k effects searched are among the two-factor interactions, and (ii) they are among the two-factor and three-factor interactions. In this researches, search designs of order k = 1, 2 were constructed for the cases (i) and (ii), and search designs of order k = 3 were constructed for the case (ii). Also we define a searching power how large the precision is that a search design could search the k nonzero effects. Using searching powers, search designs were compared.
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