Response Surface Methodology

Response surface methodology fits a second-order polynomial of coded factors to experimental data and uses canonical analysis to locate the stationary point and classify it as a maximum, minimum or saddle.

반응표면법은 부호화한 요인의 2차 다항식을 실험 자료에 적합하고 정준분석으로 정상점의 위치와 그것이 최대·최소·안장점 중 무엇인지를 찾는 방법입니다.

Given my central composite design on temperature and time, what settings maximize the yield?

온도와 시간으로 중심합성설계 실험을 했는데, 수율을 가장 높이는 조건이 어디인가요?

Fit a full quadratic model with linear, squared and cross-product terms in coded units, then solve for the stationary point where all partial derivatives are zero. The signs of the eigenvalues of the quadratic coefficient matrix tell you whether that point is a maximum, a minimum or a saddle.

When to use Response Surface Methodology

• Two to four continuous factors were run in a central composite, Box-Behnken or similar design
• You want the factor settings that optimize a response
• Curvature is expected near the optimum

When to use something else

• You are still screening many factors; use a two level factorial design first
• The response is binary or a count; use a generalized linear model with quadratic terms

Assumptions and requirements

• A second-order polynomial approximates the true surface within the region
• Residuals are independent, approximately normal and homoscedastic
• The stationary point lies within or near the experimental region

What the analysis reports

• Coefficients of the second-order model with tests
• Model, linear, quadratic and interaction F tests and lack-of-fit test
• Stationary point in coded and natural units with predicted response
• Eigenvalues and eigenvectors of the canonical analysis

How to report it

The second-order model explained R² = [value] of the variance, F([df1], [df2]) = [value], p = [value]; lack of fit was not significant, F([df1], [df2]) = [value], p = [value]; canonical analysis indicated a [maximum] at [factor] = [value] and [factor] = [value] with predicted response [value].

Related methods

• Two Level Factorial Design Analysis
• Polynomial Regression
• Multiple Linear Regression

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