Multivariate quality loss functions are commonly used in product and process design parameter optimization, which involves simultaneous consideration of multiple responses in determination of the levels of design parameters that provide high quality performance. These functions are also used in statistical tolerancing and quality improvement decision making. This study investigates the bivariate loss function in terms of its ability to represent different values or preferences a decision maker may attribute to different settings of responses. Then, an interactive and evolutionary method for estimating parameters of the multivariate quality loss function is proposed. This method can be used for such functions regardless of the number of quality characteristics under consideration. It is shown that the method converges to the true underlying loss function after a few iterations even when the information provided by the decision maker contains certain degrees of errors.