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Table S14-7 Central Composite Design for Example S14-4 Observation Number 1 2 3 4 5 6 7 8 9 10 11 12 13 Time (minutes) 50 60 50 60 48 62 55 55 55 55 55 55 55 Temperature ( F) 160 160 170 170 165 165 158 172 165 165 165 165 165 Coded Variables x1 x2 1 1 1 1 1.414 1.414 0 0 0 0 0 0 0 1 1 1 1 0 0 1.414 1.414 0 0 0 0 0 Conversion (percent) Response 1 65.3 68.2 66 69.8 64.5 69 64 68.5 68.9 69.7 68.5 69.4 69 Viscosity (mPa-sec) Response 2 35 39 36 43 30 44 31 45 37 34 35 36 37

14-17

Qi-2 Qi-3 Qi-4

x2 +2 (0, 1.414) ( 1, 1) (1, 1)

( 1.414, 0) 2 (0, 0)

( 1, 1)

Qi- 1

(1, 1) (0, 1.414) 2

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From its closed position, the vari-angle LCD monitor is positioned for shooting by ipping it out to the left, away from the camera body, rotating the top edge of the LCD 180 degrees away from you, and then ipping it back to the right, lling the indentation on the back of the camera for a streamlined t. You can position the LCD to allow full view of the lens coverage area from a convenient shooting angle, such as when holding the camera above your head in event or concert situations, or low to the ground when photographing children, wildlife, owers, or pets. Another cool feature of the vari-angle LCD monitor is the mirror-image display the LCD switches to when the monitor is positioned facing the front of the camera as when composing a shot with you in it. This way you can see exactly what the picture will look like when holding the camera away from you. You can compose the shot with you and your family or friends and see what the background looks like before you make the exposure. To change the display when the LCD monitor is positioned towards the front of the camera, follow these steps: 1. Press the Menu button. 2. Press the up area of the 4-Way Controller to select Reverse Display. You can turn this feature on or off.

Figure S14-10 Central composite design for Example S14-4.

Qi-2

Table S14-9 summarizes the analysis of variance for this model. The response surface is shown graphically in Fig. S14-12. Notice that viscosity increases as both time and temperature increase. As in most response surface problems, the experimenter in this example had con icting objectives regarding the two responses. The objective was to maximize yield, but the acceptable range for viscosity was 38 y2 42. When there are only a few independent variables, an easy way to solve this problem is to overlay the response surfaces to nd the optimum. Figure S14-13 shows the overlay plot of both responses, with the contours y1 69% conversion, y2 38, and y2 42 highlighted. The shaded areas on this plot identify unfeasible combinations of time and temperature. This graph shows that several combinations of time and temperature will be satisfactory. Example S14-4 illustrates the use of a central composite design (CCD) for tting a second-order response surface model. These designs are widely used in practice because they are relatively ef cient with respect to the number of runs required. In general, a CCD in k

Table S14-8 Analysis of Variance for the Quadratic Model, Yield Response Source of Variation Model Residual Total Independent Variable Intercept x1 x2 x2 1 x2 2 x1x2 Sum of Squares 45.89 4.30 50.19 Coef cient Estimate 69.100 1.633 1.083 0.969 1.219 0.225 Degrees of Freedom 5 7 12 Standard Error 0.351 0.277 0.277 0.297 0.297 0.392 Mean Square 9.178 0.615 f0 14.93 P-Value 0.0013

14-18

Qi-3

Table S14-9 Analysis of Variance for the First-Order Model, Viscosity Response Source of Variation Model Residual Total Independent Variable Intercept x1 x2 Sum of Squares 195.4 61.5 256.9 Coef cient Estimate 37.08 3.85 3.10 Degrees of Freedom 2 10 12 Degrees of Freedom 1 1 1 Mean Square 97.72 6.15 Standard Error 0.69 0.88 0.88 f0 15.89 P-Value 0.0008

1 172.0

Qi = (Qi-4

64.00 65.00

x2 (temperature)

+ F(Qi-I, Qi-2,

167.3 70.00 0 165.0 68.00 162.7 67.00 66.00 65.00 64.00 63.00 50.33 52.67 55.00 0 x1 (time) Contour plot (a) 57.33 59.67 62.00 +1 69.00

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