This paper extends Taguchi's quadratic quality loss function (QQLF) and signal-to-noise (S/N) ratios to a trivariate case by considering correlations between all pairs of quality characteristics. Single static quality characteristics (QCHs) are classified as: (1) smaller the better (STB), (2) larger the better (LTB), and (3) nominal the best (NTB). Initially, Taguchi studied single-response models. Later Chang (1993), Maghsoodloo and Chang (2001), and Maghsoodloo and Huang (2001) obtained relationships for the bivariate response cases. Chang (1993) and Maghsoodloo and Chang (2001) developed relationships for cost coefficients of the bivariate QQLF and S/N ratios for the cases of (NTB, NTB), (STB, STB), and (LTB, LTB). Later Maghsoodloo and Huang (2001) developed relationships for the remaining cases, which are (STB, LTB), (STB, NTB), and (LTB, NTB).