Project/Area Number  03680028 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
Informatics

Research Institution  Gifu University 
Principal Investigator 
JIMBO Masakazu Gifu University, Department of Electronics and Computer Engineereng, Associate Professor, 工学部, 助教授 (50103049)

CoInvestigator(Kenkyūbuntansha) 
KURIKI Shinji Osaka Women's University, Department of Applied Mathematics,Associate Professor, 学芸学部, 助教授 (00167389)
WATANABE Toshihiro Gifu University, Department of Applied Mathematics, Associate Professor, 工学部, 助教授 (70021623)

Project Fiscal Year 
1991 – 1992

Project Status 
Completed(Fiscal Year 1992)

Budget Amount *help 
¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1992 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1991 : ¥1,500,000 (Direct Cost : ¥1,500,000)

Keywords  Design of experiments / Orthogonal array / Correlated error / Universally optimum / Optimality / Covariance structure / Hamming scheme / Hamming distance / 実験計画 / 直交配列 / 直交表 / 共分散構造 / 最適性 / ハミング距離 / ハミング・スキーム / 直交実験 / 相関のある誤差(correlated error) 
Research Abstract 
In factorial experiments, it is wellknown that an orthogonal array of strength 2 is universally optimum for the estimation of main effects among the all factorial designs with given size and constraints. In this project, we consider the case when the observations of experiments are correlated. We assume that the covariance between two observation depends only on the Hamming distance of the corresponding assemblies. Under this covariance structure, we showed that if the minimum distance of each row vectors of an orthogonal array of strength 2 exceed a given distance d, then it is universally optimum for OLSE among every orthogonal arrays under the covariance structure such that correlation may occur only when the Hamming distance of two assembly is less than d. Furthermore, it was shown that if the orthogonal array is linear, then the covariance matrices of OLSE and GLSE are diagonal and they coincide. Using this result we showed that a linear orthogonal array with large minimum distance is optimum among all linear orthogonal array for some covariance structures, The construction of an expert system is now still preceeding, since in the period of this project we mainly devote ourselves to the theoretical aspects of factorial designs.
