Quartic Loss Function and Its Application to the Parameter Design Problem

Abstract

There are two functional forms that are commonly used to represent a quality loss function. One form is the conventional step function that is based on classifying the units as defective and non-defective, and the other form is the quadratic loss function that was proposed by Taguchi. Either of these functional forms has a specific functional profile, and as a result we do not have any degrees of freedom in choosing a desired functional profile in either context. This thesis propose a loss function that not only allows some degrees of flexibility in this regards, but it also can be applied in the case where a non-symmetric function is desirable. At one extreme the proposed loss function can be close to a quadratic loss function, and it can be close to a step function at the other extreme. We refer to this loss function as a quartic loss function. We also present the application of the quartic loss function to the parameter design problem in the case where the transfer function between a quality characteristic of interested and design parameters can be determined analytically.