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Modeling and Multivariate Methods - SAS

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572 Visualizing, Optimizing, <strong>and</strong> Simulating Response Surfaces Chapter 24<br />

Special Profiler Topics<br />

Figure 24.19 Propagation of Errors Bars in the Prediction Profiler<br />

propagation of error bar<br />

The POE is represented in the graph by a green bracket. The bracket indicates the prediction plus or minus<br />

three times the square root of the POE variance, which is calculated as<br />

N<br />

2 ∂f<br />

σ xi<br />

------<br />

<br />

× <br />

∂x <br />

2 2<br />

+ σ<br />

y i<br />

i = 1<br />

where f is the prediction function, x i is the i th factor, <strong>and</strong> N is the number of factors.<br />

Currently, these partial derivatives are calculated by numerical derivatives:<br />

centered, with δ=xrange/10000<br />

POE limits increase dramatically in response surface models when you are over a more sloped part of the<br />

response surface. One of the goals of robust processes is to operate in flat areas of the response surface so that<br />

variations in the factors do not amplify in their effect on the response.

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