# Response surface model which is generally used for

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response surface model which is generally used for prediction, the I-criterion is an appropriate choice for a computer generated design. JMP Output Custom Design Factors Add N Factors 1 X1 Continuous X2 Continuous X3 Continuous X4 Categorical ModelIntercept Intercept X1 X2 X3 X4 X1*X2 X1*X3 X1*X4 X2*X3 X2*X4 X3*X4 X1*X1 X2*X2 X3*X3 Design Run X1 X2 X3 X4 1 0 0 0 L2 2 -1 -1 -1 L2 3 1 -1 1 L1 4 1 1 1 L2 5 0 -1 -1 L1 6 0 1 1 L1 7 -1 0 1 L1 8 0 1 -1 L2 9 -1 -1 0 L1 10 0 -1 1 L2 11 -1 1 -1 L1 12 1 -1 -1 L2 13 1 0 -1 L1 14 0 0 0 L2 15 1 1 0 L1
Solutions from Montgomery, D. C. (2008) Design and Analysis of Experiments, Wiley, NY 11-46 16 -1 1 1 L2 Prediction Variance Profile Variance1.7500.599174X1-110X2-110X3-110X4L1L211.29. Suppose that you want to fit a second-order model in k= 5 factors. You cannot afford more than 25 runs. Construct both a D-optimal and an I-optimal design for this situation. Compare the prediction variance properties of the designs. Which design would you prefer?The following JMP outputs identify both D-optimal and I-optimal designs. The prediction variance profile shown in each JMP output is appreciably less for the I-optimal design as well as flatter in the middle of the design. JMP Output D-optimal Design Factors Add N Factors 1 X1 Continuous X2 Continuous X3 Continuous X4 Continuous X5 Continuous Design Run X1 X2 X3 X4 X5 1 -1 -1 1 1 0 2 -1 1 1 -1 -1 3 -1 1 -1 -1 1 4 1 -1 -1 -1 1 5 -1 -1 -1 1 1 6 0 1 1 -1 0 7 0 -1 0 1 -1 8 -1 -1 -1 -1 -1 9 1 -1 -1 1 -1 10 1 -1 1 1 1 11 -1 -1 1 -1 1 12 1 -1 1 -1 -1 13 -1 1 -1 1 -1 14 1 1 1 1 -1 15 0 -1 -1 0 0 16 -1 0 0 -1 0 17 1 1 1 -1 1 18 1 1 0 0 -1 19 -1 -1 1 0 -1 20 -1 1 1 1 1 21 1 1 -1 1 1 22 1 1 -1 -1 -1
Solutions from Montgomery, D. C. (2008) Design and Analysis of Experiments, Wiley, NY 11-47 23 0 0 1 0 1 24 0 0 1 1 -1 25 1 0 -1 0 0 Prediction Variance Profile Variance1.6800.682507X1-110X2-110X3-110X4-110X5-110Prediction Variance Surface
Solutions from Montgomery, D. C. (2008) Design and Analysis of Experiments, Wiley, NY 11-48 JMP Output I-Optimal Design Factors Add N Factors 1 X1 Continuous X2 Continuous X3 Continuous X4 Continuous X5 Continuous Design Run X1 X2 X3 X4 X5 1 -1 0 -1 1 0 2 1 1 1 -1 -1 3 1 1 -1 1 -1 4 0 -1 0 -1 0 5 -1 1 0 0 0 6 0 0 0 1 1 7 -1 0 1 -1 1 8 1 -1 -1 1 1 9 1 0 0 0 -1 10 1 0 -1 -1 0 11 -1 -1 -1 -1 1 12 -1 -1 1 -1 -1 13 1 -1 1 0 1 14 1 1 0 -1 1 15 0 1 1 1 -1 16 -1 0 0 0 -1 17 1 1 1 1 0 18 0 1 -1 0 1 19 1 -1 1 1 -1 20 0 0 0 0 0 21 -1 1 1 1 1 22 -1 1 -1 -1 -1 23 -1 -1 1 1 0 24 0 -1 -1 0 -1 25 0 0 1 0 0 Prediction Variance Profile Variance1.6800.327287X1-110X2-110X3-110X4-110X5-110
Solutions from Montgomery, D. C. (2008) Design and Analysis of Experiments, Wiley, NY 11-49 Prediction Variance Surface 11.30.Myers and Montgomery (2002) describe a gasoline blending experiment involving three mixture components. There are no constraints on the mixture proportions, and the following 10 run design is used. Design Point x1x2x3y(mpg) 1 1 0 0 24.5, 25.1 2 0 1 0 24.8, 23.9 3 0 0 1 22.7, 23.6 4 ½ ½ 0 25.1 5 ½ 0 ½ 24.3 6 0 ½ ½ 23.5 7 1/3 1/3 1/3 24.8, 24.1 8 2/3 1/6 1/6 24.2 9 1/6 2/3 1/6 23.9 10 1/6 1/6 2/3 23.7 (a)What type of design did the experimenters use?