The Taguchi robust design method traditionally deals with single-characteristic problems. Various methods have been developed for extending the Taguchi single-characteristic robust design method to the case of multi-characteristic robust design problems. However, most of those methods have shortcomings in that they do not properly consider the variance-covariance structures among performance characteristics and/or do not preserve the original properties of the Taguchi signal-to-noise ratio for single-characteristic robust design problems. To overcome these shortcomings, this paper develops a multivariate loss function approach to multi-characteristic robust design problems with an appropriately defined signal-to-noise ratio. Its performance is evaluated using simulated examples, and the results indicate that it generally outperforms existing representative methods for correlated as well as uncorrelated experimental data. Copyright (C) 2016 John Wiley & Sons, Ltd.