Abstract: Due to the multicollinearity, it is difficult to accurately calculate the Mahalanobis distance, which is puzzling in multidimensional system analysis. Gram-Schmidt method and adjoint matrix method of MTS, put forward by Genichi Taguchi, are used to solve multicollinearity problems by improving Mahalanobis distance function. However, both of them have some insuperable defects. The function of degree of disagreement (FDOD) measurement, a method based on entropy, is adopted to measure the degree of abnormality of multidimensional observations instead of Mahalanobis distance function. Also, FDOD measurement and Taguchi method are integrated for multidimensional system optimization and dimension reduction, which thoroughly solve multicollinearity problems. Cases of Spanish banks in financial crisis are analyzed to illustrate the effectiveness of the proposed method.

Key words: multidimensional system, multicollinearity, FDOD measurement, Taguchi method