Modeling and Multivariate Methods - SAS

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600 Visualizing, Optimizing, and Simulating Response Surfaces Chapter 24 The Simulator Figure 24.50 Results If unit price can’t be raised anymore, you should now investigate lowering your cost, or increasing sales, if you want to further decrease the probability of being unprofitable. The Defect Profiler The defect profiler shows the probability of an out-of-spec output defect as a function of each factor, while the other factors vary randomly. This is used to help visualize which factor’s distributional changes the process is most sensitive to, in the quest to improve quality and decrease cost. Specification limits define what is a defect, and random factors provide the variation to produce defects in the simulation. Both need to be present for a Defect Profile to be meaningful. At least one of the Factors must be declared Random for a defect simulation to be meaningful, otherwise the simulation outputs would be constant. These are specified though the simulator Factor specifications. Important: If you need to estimate very small defect rates, use Normal weighted instead of just Normal. This allows defect rates of just a few parts per million to be estimated well with only a few thousand simulation runs. About Tolerance Design Tolerance Design is the investigation of how defect rates on the outputs can be controlled by controlling variability in the input factors. The input factors have variation. Specification limits are used to tell the supplier of the input what range of values are acceptable. These input factors then go into a process producing outputs, and the customer of the outputs then judges if these outputs are within an acceptable range. Sometimes, a Tolerance Design study shows that spec limits on input are unnecessarily tight, and loosening these limits results in cheaper product without a meaningful sacrifice in quality. In these cases, Tolerance Design can save money. In other cases, a Tolerance Design study may find that either tighter limits or different targets result in higher quality. In all cases, it is valuable to learn which inputs the defect rate in the outputs are most sensitive to. This graph shows the defect rate as a function of each factor as if it were a constant, but all the other factors varied according to their random specification. If there are multiple outputs with Spec Limits, then there is a defect rate curve color-coded for each output. A black curve shows the overall defect rate—this curve is above all the colored curves.
Chapter 24 Visualizing, Optimizing, and Simulating Response Surfaces 601 The Simulator Figure 24.51 Defect Profiler Overall defect profile. Defect profile for ABRASION. Current center (mean) for factor. Standard deviation of overall defect curve with respect to factor distribution, which shows sensitivity. Expected mean of overall defect curve, with respect to factor distribution. Roughly equal across factors. Graph Scale Defect rates are shown on a cubic root scale, so that small defect rates are shown in some detail even though large defect rates may be visible. A log scale is not used because zero rates are not uncommon and need to be shown. Expected Defects Reported below each defect profile plot is the mean and standard deviation (SD). The mean is the overall defect rate, calculated by integrating the defect profile curve with the specified factor distribution. In this case, the defect rate that is reported below all the factors is estimating the same quantity, the rate estimated for the overall simulation below the histograms (i.e. if you clicked the Simulate button). Since each estimate of the rate is obtained in a different way, they may be a little different. If they are very different, you may need to use more simulation runs. In addition, check that the range of the factor scale is wide enough so the integration covers the distribution well. The standard deviation is a good measure of the sensitivity of the defect rates to the factor. It is quite small if either the factor profile were flat, or the factor distribution has a very small variance. Comparing SD's across factors is a good way to know which factor should get more attention to reducing variation. The mean and SD are updated when you change the factor distribution. This is one way to explore how to reduce defects as a function of one particular factor at a time. You can click and drag a handle point on the factor distribution, and watch the mean and SD change as you drag. However, changes are not updated across all factors until you click the Rerun button to do another set of simulation runs.
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Version 10 Modeling and Multivariat
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INDIRECT OR CONSEQUENTIAL DAMAGES O
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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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12 Examining the Residuals . . . .
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14 Response Frequencies . . . . . .
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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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180 Fitting Generalized Linear Mode
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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 Introduction to Clustering
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472 Clustering Data Chapter 18 K-Me
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474 Clustering Data Chapter 18 Norm
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476 Clustering Data Chapter 18 Norm
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478 Clustering Data Chapter 18 Self
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480 Clustering Data Chapter 18 Self
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Contents Principal Components. . .
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484 Analyzing Principal Components
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494 Performing Discriminant Analysi
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650 References Umetrics (1995), Mul
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654 Statistical Details Appendix A
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Modeling and Multivariate Methods - SAS

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