Studies on Features of Improved T-methods and the New Normalization Methods

Abstract

　Taguchi’s T-method is one method of the Mahalanobis -Taguchi (MT) system, which is used for prediction. In addition, two improved T-methods have been proposed to address the problem of selecting the unit space for the T-method. These refinements have been reported to show better prediction accuracies than the original T-method. Although the accuracies of these two methods differ depending on the conditions, reasons for this discrepancy have not yet been extensively studied.
　This paper first discusses the features of normalization in the Tb-method, which is one of the improved T-methods. We point out that the Tb-method may have the feature of a shrinkage estimator. Moreover, considering the feature of the Tb-method, we propose three normalization methods different from the improved T-methods. Subsequently, we verify whether the Tb-method has the feature of the shrinkage estimator by Monte Carlo simulations. As the results, the estimated output is smaller than the theoretical value, and the output variance is stable. Furthermore, we compare prediction accuracies of the proposed methods and the improved T-methods using Monte Carlo simulations under several models. Our findings indicate that the accuracies of the proposed methods are equal to or superior to those of the improved T-methods in many cases.