• 한국산학기술학회논문지
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• 제16권1호
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• pp.97-105
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• 2015

다중반응표면 최적화는 다수의 반응변수(품질특성치)를 최적화하는 입력변수의 조건을 찾는 것을 목적으로 한다. 다중반응표면 최적화를 위해 제안된 가중평균제곱오차(Weighted Mean Squared Error, WMSE) 최소화법은 평균제곱오차의 구성요소인 제곱편차와 분산에 서로 다른 가중치를 부여하는 방법이다. 지금까지 WMSE 최소화법과 관련하여, 개별 반응변수의 WMSE를 구성한 후 이들의 가중합을 최소화하는 가중합 기반 WMSE 최소화법이 제안되었다. 그러나 가중합 기반법은 목적함수 공간에서 볼록하지 않은 구간이 있고 이 구간에서 가장 선호되는 해가 존재할 경우 이 해를 찾아내지 못한다는 한계를 지니고 있다. 본 논문에서는 기존의 가중합 기반법의 한계점을 극복하기 위하여 Tchebycheff Metric 기반 WMSE 최소화법을 제안하고자 한다.

• 지식경영연구
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• 제21권1호
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• pp.27-40
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• 2020

Response surface methodology (RSM) empirically studies the relationship between a response variable and input variables in the product or process development phase. The ultimate goal of RSM is to find an optimal condition of the input variables that optimizes (maximizes or minimizes) the response variable. RSM can be seen as a knowledge management tool in terms of creating and utilizing data, information, and knowledge about a product production and service operations. In the field of product or process development, most real-world problems often involve a simultaneous consideration of multiple response variables. This is called a multiple response surface (MRS) problem. Various approaches have been proposed for MRS optimization, which can be classified into loss function approach, priority-based approach, desirability function approach, process capability approach, and probability-based approach. In particular, the loss function approach is divided into univariate and multivariate approaches at large. This paper focuses on the univariate approach. The univariate approach first obtains the mean square error (MSE) for individual response variables. Then, it aggregates the MSE's into a single objective function. It is common to employ the weighted sum or the Tchebycheff metric for aggregation. Finally, it finds an optimal condition of the input variables that minimizes the objective function. When aggregating, the relative weights on the MSE's should be taken into account. However, there are few studies on how to determine the weights systematically. In this study, we propose an interactive procedure to determine the weights through considering a decision maker's preference. The proposed method is illustrated by the 'colloidal gas aphrons' problem, which is a typical MRS problem. We also discuss the extension of the proposed method to the weighted MSE (WMSE).