Multivariate exponential families and the Taguchi loss function

Taguchi uses a loss function concept to quantify quality as loss due to functional variation. When there is one variable under study a quadratic loss function is used. When the system under consideration is defined by p-variables which may or may not be correlated a more general loss function should be defined. We use information theory to define a multivariate loss function based on a divergence measure between two probability distributions that belong to the multivariate exponential family. The two distributions are the ideal or factory distribution that our data should follow and the other is the real distribution of the multivariate data. This divergence measure uses the concept of the Kullback-Leibler information number. (C) 1999 Published by Elsevier Science Inc. All rights reserved.