Modeling and Multivariate Methods - SAS

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606 Visualizing, Optimizing, and Simulating Response Surfaces Chapter 24 The Simulator Now, the defect rate is down to about 0.004, much improved. Further reduction in the defect rate can occur by continued investigation of the parametric profiles, making changes to the distributions, and rerunning the simulations. As the defect rate is decreased further, the mean defect rates across the factors become relatively less reliable. The accuracy could be improved by reducing the ranges of the factors in the Profiler a little so that it integrates the distributions better. This level of fine-tuning is probably not practical, because the experiment that estimated the response surface is probably not at this high level of accuracy. Once the ranges have been refined, you may need to conduct another experiment focusing on the area that you know is closer to the optimum. Stochastic Optimization Example This example is adapted from Box and Draper (1987) and uses Stochastic Optimization.jmp. A chemical reaction converts chemical “A” into chemical “B”. The resulting amount of chemical “B” is a function of reaction time and reaction temperature. A longer time and hotter temperature result in a greater amount of “B”. But, a longer time and hotter temperature also result in some of chemical “B” getting converted to a third chemical “C”. What reaction time and reaction temperature will maximize the resulting amount of “B” and minimize the amount of “A” and “C”? Should the reaction be fast and hot, or slow and cool? Figure 24.57 Chemical Reaction The goal is to maximize the resulting amount of chemical “B”. One approach is to conduct an experiment and fit a response surface model for reaction yield (amount of chemical “B”) as a function of time and temperature. But, due to well known chemical reaction models, based on the Arrhenius laws, the reaction yield can be directly computed. The column Yield contains the formula for yield. The formula is a function of Time (hours) and reaction rates k1 and k2. The reaction rates are a function of reaction Temperature (degrees Kelvin) and known physical constants θ 1 , θ 2 , θ 3 , θ 4 . Therefore, Yield is a function of Time and Temperature. Figure 24.58 Formula for Yield You can use the Profiler to find the maximum Yield. Open Stochastic Optimization.jmp and run the attached script called Profiler. Profiles of the response are generated as follows.
Chapter 24 Visualizing, Optimizing, and Simulating Response Surfaces 607 The Simulator Figure 24.59 Profile of Yield To maximize Yield use a desirability function. See “Desirability Profiling and Optimization” on page 567. One possible desirability function was incorporated in the script. To view the function choose Desirability Functions from the Prediction Profiler pop-up menu. Figure 24.60 Prediction Profiler To maximize Yield, select Maximize Desirability from the Prediction Profiler pop-up menu. The Profiler then maximizes Yield and sets the graphs to the optimum value of Time and Temperature.
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Version 10 Modeling and Multivariat
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6 Emphasis Options for Standard Lea
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8 Models with Crossed, Interaction,
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10 8 Analyzing Screening Designs Us
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16 19 Analyzing Principal Component
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18 Interpreting the Profiles . . .
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20 Discriminant Analysis . . . . .
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Contents Book Conventions. . . . .
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24 Learn about JMP Chapter 1 Book C
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Contents Overview of the Screening
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232 Analyzing Screening Designs Cha
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Contents Introduction to the Nonlin
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244 Performing Nonlinear Regression
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Contents Overview of Neural Network
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280 Creating Neural Networks Chapte
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Contents Launching the Platform. .
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296 Modeling Relationships With Gau
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306 Fitting Dispersion Effects with
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318 Recursively Partitioning Data C
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Contents Launch the Platform . . .
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354 Performing Time Series Analysis
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Contents Principal Components. . .
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Modeling and Multivariate Methods - SAS

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