A Loss Function Approach for Multi-characteristic Parameter Design

Abstract

Developed in this article is a loss function approach for multi-characteristic parameter design problems. The existing loss functions for multiple performance characteristics are shown to be irrational in that a point which is farther from the target component-wise might incur the same loss as does a point which is closer to the target component-wise. In this article, a more rational loss function is proposed and the expected loss is derived. For the case where nominal-the-best performance characteristics are involved, it is shown that the expected loss after adjustment is independent of the target values if the functional limits of a nominal-the-best characteristic are adjusted according to the magnitude of its target value. The expected loss after adjustment can be used as a criterion for compromising the conflicts among the levels of a design parameter selected optimally for the corresponding performance characteristics. The proposed approach is illustrated with an example.