Optimal experimental design for correlated errors and its expert system

点击翻译按钮获取中文摘要

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.