Any measurement system needs to define an origin or a reference point and an unit measure,What would be a reasonable origin and unit measure for functional space or multidimensional space.
Quality engineering defines that an ideal function between signal and output should be the origin and the distance should be the inverse of Signal-to-Noise Ratio in a functional space. Quality engineering also define that Mahalanobis distance obtains from a certain unit space is an unit measure and mean vector of the multivariate space is the zero point or the origin. Those two generalized measurement systems are discussed in this article.