In parameter design, Taguchi's stated objective is to find the setting of product or process design parameters that minimize average quadratic loss-that is, the average squared deviation of the response from its target value. Yet in practice to choose the settings of design parameters he maximizeds a set of measures called signal-to-noise(SN) ratios. In general, Taguchi gave no justification for the use the SN ratios and no explanation of why the two-step procedure that he recommened will minimize average loss. The purpose of this study is comparing and analyzing of performance statistics by Leon et al(PerMIA), Box(Transformation theory), Vining & Myers(Dual Response Systems) and Taguchi(Signal-to-Noise ratios).