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Optimal experimental design for correlated errors and its expert system

相关误差优化实验设计及其专家系统

基本信息

批准号：
03680028
负责人：
JIMBO Masakazu
金额：
$ 1.28万
依托单位：
Gifu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1992
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03680028/
关键词：
Design of experiments Orthogonal array Correlated error Universally optimum Optimality Covariance structure Hamming scheme Hamming distance 相関のある誤差(correlated error)

项目摘要

In factorial experiments, it is well-known 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.

在析因试验中，已知强度为2的正交表在给定尺寸和约束条件的所有析因设计中对主效应的估计是普遍最优的。在这个项目中，我们考虑的情况下，实验的观察是相关的。我们假设两个观测值之间的协方差仅取决于相应集合的汉明距离。在此协方差结构下，我们证明了如果强度为2的正交表的每个行向量的最小距离超过一个给定的距离d，则在此协方差结构下，每个正交表的OLSE是普遍最优的，使得只有当两个集合的Hamming距离小于d时，相关才可能发生.此外，还证明了如果正交表是线性的，则OLSE和GLSE的协方差矩阵是对角的，并且它们是重合的。利用这一结果，我们证明了对于某些协方差结构，具有大的最小距离的线性正交表是所有线性正交表中最优的。由于在本项目期间，我们主要致力于析因设计的理论方面，因此专家系统的建立仍在进行中。