A Geometric Interpretation of Taguchi's Signal to Noise Ratio

The notion of quadratic loss is used to arrive at a formal definition of Taguchi's 'signal to noise' ratio. It is shown that this ratio can be interpreted as a measure of the angular deviation of a product or process functional characteristic from the desired value of this characteristic. Also, a geometric interpretation of the decomposition of loss into systematic and random components are presented along with the two step optimization procedure based on it.