Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Hybrid Constrained Extrapolation Experimental Design

하이브리드형 제약 외삽실험 계획법

  • Received : 20110800
  • Accepted : 20111000
  • Published : 2012.01.30
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Abstract

In setting an experimental design for the prediction outside the experimental region (extrapolation design), it is natural for the experimenter to be very careful about the validity of the model for the design because the experimenter is not certain whether the model can be extended beyond the design region or not. In this paper, a hybrid constrained type approach was adopted in dealing model uncertainty as well as the prediction error using the three basic principles available in literature, maxi-min, constrained, and compound design. Furthermore, the effect of the distance of the extrapolation design point from the design region is investigated. A search algorithm was used because the classical exchange algorithm was found to be complex due to the characteristic of the problem.

실험영역을 벗어난 점에서의 분산을 최소화 하는 외삽-최적의 문제는 모형의 불확실성을 내재하고 있다. 즉, 실험영역을 벗어나게 되면 모형의 불확실성이 높아지므로 모형의 타당성 여부를 진단하여야 한다. 본 연구에서는 외삽(extrapolation) 문제하에서 기본적인 3가지 실험, 즉 제약 실험과 최대최소 실험, 그리고 복합실험 등을 융합한 새로운 제약조건형의 실험 2가지를 제안하였다. 그리고 실험영역의 바깥에 위치한 점의 위치가 실험영역을 얼마나 벗어나느냐에 따른 실험결과에 대한 영향력도 고려하여 보았다. 문제의 특성상 유전 알고리즘을 이용하여 해를 구하였다.

Keywords

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