Modeling and Multivariate Methods - SAS

Chapter 24 Visualizing, Optimizing, and Simulating Response Surfaces 603
The Simulator
Figure 24.53 Defect Profiler
The black curve on each factor shows the defect rate if you could fix that factor at the x-axis value, but leave
the other features random.
Look at the curve for SILICA. As its values vary, its defect rate goes from the lowest 0.001 at SILICA=0.95,
quickly up to a defect rate of 1 at SILICA=0.4 or 1.8. However, SILICA is itself random. If you imagine
integrating the density curve of SILICA with its defect profile curve, you could estimate the average defect
rate 0.033, also shown as the Mean for SILICA. This is estimating the overall defect rate shown under the
simulation histograms, but by numerically integrating, rather than by the overall simulation. The Means for
the other factors are similar. The numbers are not exactly the same. However, we now also get an estimate of
the standard deviation of the defect rate with respect to the variation in SILICA. This value (labeled SD) is
0.055. The standard deviation is intimately related to the sensitivity of the defect rate with respect to the
distribution of that factor.
Looking at the SDs across the three factors, we see that the SD for SULFUR is higher than the SD for
SILICA, which is in turn much higher than the SD for SILANE. This means that to improve the defect rate,
improving the distribution in SULFUR should have the greatest effect. A distribution can be improved in
three ways: changing its mean, changing its standard deviation, or by chopping off the distribution by
rejecting parts that don’t meet certain specification limits.
In order to visualize all these changes, there is another command in the Simulator pop-up menu, Defect
Parametric Profile, which shows how single changes in the factor distribution parameters affect the defect
rate.