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Dual Response Surface Optimization

Dual Response Surface Optimization
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대학원 통계학과
이화여자대학교 대학원
Robust design에 대해 single response의 최적화 연구가 많이 선행되어져왔다. 실제로 제조업체에서는 수많은 quality characteristic들에 의한 특징이 다루어진다. Dual response surface optimization procedure는 반응변수의 mean 뿐 만 아니라 variance까지 고려하여 두 개의 surface를 동시에 최적화시키기 위한 분석법이다. 전형적인 Response Surface Method를 통한 분석은 분산이 안정화되어 있지 않은 경우에 잘못된 오류를 범할 수 있기 때문에 이러한 문제점을 해결하기 위해 dual response surface optimization procedure가 고려되었다. Vining and Myers는 mean response와 variance(또는 standard deviation) response를 full second order model에 적합 시키는 방법을 제안했다. 즉 secondary response surface(variance response)를 적절하게 제한한 상태에서 primary response surface(mean response)를 최적화시키는 것이다. 이보다 더 현실적이고 향상된 방법으로 Mean Square Error Appoach의 방법이 제안되었다. MSE Approach는 Vining and Myers Approach와는 달리 full second order model로 제한하지 않고 mean response에 대해 약간의 오차를 허용한다. Dual response surface optimization에 대해 Vining and Myers Appoach와 MSE Approach의 분석 방법을 비교해보려 한다.;Most of the published literature on robust design methodology is basically concerned with opimization of a single response or quality characteristic which is often most critical to consumers. Dual response surface optimization procedure refers to the mean response and the variance response of the process. Then it should simultaneously examine and optimize the mean response and the variance response. When the variance is not a constant, classical response surface methodology can be misleading. For the solving this problem, it refers to the dual response surface optimization procedure. Vining and Myers Approach is fit full second order model to both mean response and variance(or standard deviation) response surfaces. And then applied the dual response surface approach to opimize the primary response(mean response) subject to an appropriate constraint on the value of the secondary response(variance response). Mean Square Error Approach refers to the mean response and the variance response of the process. It can handle more realistic models and much more complicated models than polynomial. MSE Approach is not necessarily restricted to a full second order model. And it allows of a slight bias on the expected mean but a much smaller variance. This paper's goal is to compare the effectiveness of the Vining and Myers Approach and MSE Approach for dual response surface optimization
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