(A) study of the model that taguchi's 2-step optimization is possible

Abstract

In parameter design, Taguchi``s stated objective is to find the settings of product or process design parameters that minimize expected quadratic loss -that is, the expected 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 (SN) ratios. In general, he gives no connection between these two optimization problems, but using the concept of a performance measure independent of adjustment (PerMIA), Le$\acoute{o}$n et al. (1987) showed that for certain underlying models for the product or process response maximization of the signal-to-noise ratio led to minimization of expected quadratic loss. In this paper the possibility of Taguchi``s 2-step optimization is defined and it will be shown that the expected loss function is minimized if Taguchi``s 2-step optimization is possible. Furthermore, the necessary and sufficient condition for the possibility of Taguchi``s 2-step optimization will be introduced. From this result, the constants for the underlying models of Le$\acoute{o}$n et al. can be weaken.