An improved multivariate loss function approach to optimization

Abstract

The basic purpose of a quality loss function is to evaluate a loss to customers in a quantitative manner. Although there are several multivariate loss functions that have been proposed and studied in the literature, it has room for improvement. A good multivariate loss function should represent an appropriate compromise in terms of both process economics and the correlation structure among various responses. More important, it should be easily understood and implemented in practice. According to this criterion, we first introduce a pragmatic dimensionless multivariate loss function proposed by Artiles-Leon, then we improve the multivariate loss function in two respects: one is making it suitable for all three types of quality characteristics; the other is considering correlation structure among the various responses, which makes the improved multivariate loss function more adequate in the real world. On the bases of these, an example from industrial practice is provided to compare our improved method with other methods, and last, some reviews are presented in conclusion.

Keywords

Multivariate loss function / correlation / optimization / principal component analysis

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