Parameter design is a method, popularized by Japanese quality expert G. Taguchi, for designing products and manufacturing processes that are robust to uncontrollable variations. In parameter design, Taguchi's stated objective is to find the settings of product or process design parameters that minimize average quadratic loss—that is, the average squared deviation of the response from its target value. Yet, in practice, to choose the settings of design parameters he maximizes a set of measures called signal-to-noise ratios. In general, he gives no connection between these two optimization problems. In this article, we show that for certain underlying models for the product or process response maximization of the signal-to-noise ratio leads to minimization of average quadratic loss. The signal-to-noise ratios take advantage of the existence of special design parameters called adjustment parameters. When these parameters exist, use of the signal-to-noise ratio allows the parameter design optimization procedure to be conveniently decomposed into two smaller optimization steps, the first being maximization of the signal-to-noise ratio. We show, however, that under different models (or loss functions) other performance measures give convenient two-step procedures, but the signal-to-noise ratios do not.