In this research, we investigated the mathematical aspects of Taguchi method. Especially, we studied on the following four topics : i) statistical inference of SN ratio, ii) analysis of orthogonal array, iii) online quality control, iv) theoretical analysis of MT system. As a result, we obtained some new results : an improved version of T method, a new method for diagnosis of process by change-point detection, an application of MT system for outlier detection, a new method for supersaturated designs, and so on.