Parameter Design under General Loss Functions

일반적 손실함수 하에서의 파라미터 설계방법

In a recent article, Leon et al. lucidly explained the ideas of the Taguchi two-stage procedure for parameter design optimization, and proposed alternative performance measures called PerMIA to the signal-to-noise ratios. On the other hand, Box proposed an empirical approach to the problem based upon monotone transformations of the performance characteristic(y). This paper develops procedures for parameter design optimization under the assumptions that the expected loss(not necessarily a mean squared error loss) is increasing with respect to the variance of the error in y, and that the mean of y satisfies certain conditions of adjustability. It turns out that the variance of the error in y can play the role of PerMIA, and it is further shown that the derived PerMIA can be adapted to the Box empirical procedure for the minimization of the expected loss in the original metric.