예제: 2차 반응 표면 분석

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예제: 2차 반응 표면 분석

boxwilson, polyfitc 및 polyfit 함수를 사용하여 실험을 설계하고 조사 대상인 공정의 모델을 생성합니다. 그런 다음 풀이 구간을 사용하여 모델에서 예측한 최대 산출값을 구합니다.

1. boxwilson 설계 행렬을 정의합니다.

2. 조사할 화학 공정의 자연 변수인 A(분 단위 반응 시간)와 B(화씨 온도)의 실제 값을 정의합니다.

3. doelabel 함수를 호출하여 설계 행렬의 코드화된 값을 자연 변수의 실제 값으로 변환합니다.

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4. 각 실행(Run)에 대해 화학 공정의 산출값을 기록합니다.

5. polyfitc를 호출하여 코드화된 값으로 2차 다항식 회귀를 수행합니다.

6. polyfitc의 출력에서 회귀 계수를 추출합니다.

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7. 화학 반응을 모델링하는 코드화된 값의 함수를 만듭니다. 이 함수를 사용하여 A=-1이고 B=1일 때의 결과를 예측합니다.

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              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
              <real>5</real>
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              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
              <real>2</real>
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            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
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8. polyfit을 호출하여 화학 반응을 모델링하는 실제 값의 함수를 만듭니다. 이 함수를 사용하여 t=80분이고 T=170F일 때의 결과를 예측합니다.

예상한 대로 계산된 결과가 7단계에서 얻은 결과와 같습니다.

9. 풀이 구간을 사용하여 최대 결과를 구합니다.

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10. 등고선도를 사용하여 t_max 및 T_max 주위에서 결과가 어떻게 변하는지 시각화합니다.

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참조

Montgomery, D.C., Design and Analysis of Experiments, 5th ed., John Wiley & Sons, New York, 2001년, 페이지 442.