Consideration and a Proposal Concerning the S/N Ratios of Dynamic Characteristics

Abstract

Among the S/N ratios that indicate the robustness of a system undergoing functional evaluation, here the S/N ratios of dynamic characteristics are considered with particular attention to those cases in which the ideal function is a zeropoint ratio. The S/N ratios under consideration are the widely used zero-point proportional S/N ratio, the energy-ratio type of S/N ratio described by Odamura or by Tetsumi et al., and the S/N ratio based on the mean square log loss and asymmetric exponential loss function described by Kawamura et al. Features derived from the formulas for each of these are shown, and a new formula for calculating the S/N ratio is proposed. The proposed S/N ratio takes the form of the ratio of the output of the function to its variance, making it compatible with the formula for the S/N ratio of a nominal-is-best characteristic. The variance in the denominator of the proposed S/N ratio indicates what is due to noise factors and to other factors, simplifying the determination of the appropriateness of a functional evaluation given by, for example, the variance ratio of the two. It is also flexible in that the S/N ratio can be calculated from any input values.