Example_RSM

Example_RSM - Response Surface Methodology Example, n = 3...

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Comment: A Taguchi design array (3 parameters and 3 levels) is used below. The original operating condition, although not part of the Taguchi array, is also included in the regression analysis, since that data point is available. original parameters response coded variables a b c y operating point 20 6 -2 260.41 0 0 0 18 5.5 -3 274.85 -1 -1 -1 18 6 -2 274.39 -1 0 0 20 6.5 -1 258.33 0 1 1 20 5.5 -2 257.04 0 -1 0 22 6 -1 234.4 1 0 1 22 6.5 -3 247.37 1 1 -1 mimimum 18 5.5 -3 -1 -1 -1 maximum 22 6.5 -1 1 1 1 range 4 1 2 2 2 2 mid value 20 6 -2 0 0 0 SUMMARY OUTPUT Regression Statistics Multiple R 0.99 R Square 0.98 Adjusted R Square 0.97 Standard Error 2.56 Observations 7 ANOVA df SS MS F Significance F Regression 3 1210.54 403.51 61.7 0 Residual 3 19.62 6.54 Total 6 1230.16 Coefficients ndard Er t Stat P-value Lower 95%pper 95% wer 95.0 pper 95.0% Intercept 258.12 0.97 267.05 0 255.04 261.19 255.04 261.19 X Variable 1 -17.5 1.49 -11.72 0 -22.25 -12.74 -22.25 -12.74 X Variable 2 3.15 1.49 2.11 0.13 -1.6 7.9 -1.6 7.9 X Variable 3 -3.8 1.34 -2.85 0.07 -8.05 0.45 -8.05 0.45 Vector of steepest ascent in coded variables = ( -17.5 3.15 -3.8 ) magnitude of this vector = 18.18 Unit vector of steepest ascent in coded variables = ( -0.96 0.17 -0.21 ) Verify: magnitude of this vector = 1 -2 -1 Response Surface Methodology Example, n = 3 parameters Note: Coded (i.e. normalized) variables x 1 , x 2 , and x 3 are used for the regression analysis instead of a , b , and c . x 1 x 2 x 3 Perform a regression analysis with x 1 through x 3 as the independent variables, and y as the dependent variable: (Excel 2003: Tools -Data Analysis -Regression ) (Excel 2007: Data tab, in the Analysis area-Data Analysis -Regression ) Comment: Since coded variable x 1 has the largest magnitude, we choose the increment of its dimensional (uncoded) value, which is parameter a . The increments of the other two parameters will be calculated, based on the direction of steepest ascent. Choose increment in parameter
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This note was uploaded on 07/23/2008 for the course ME 345 taught by Professor Staff during the Spring '08 term at Penn State.

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Example_RSM - Response Surface Methodology Example, n = 3...

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