Modeling and Multivariate Methods - SAS

602 Visualizing, Optimizing, and Simulating Response Surfaces Chapter 24
The Simulator
Simulation Method and Details
Assume we want a defect profile for factor X1, in the presence of random variation in X2 and X3. A series of
n=N Runs simulation runs is done at each of k points in a grid of equally spaced values of X1. (k is generally
set at 17). At each grid point, suppose that there are m defects due to the specification limits. At that grid
point, the defect rate is m/n. With normal weighted, these are done in a weighted fashion. These defect rates
are connected and plotted as a continuous function of X1.
Notes
Recalculation The profile curve is not recalculated automatically when distributions change, though the
expected value is. It is done this way because the simulations could take a while to run.
Limited goals Profiling does not address the general optimization problem, that of optimizing quality
against cost, given functions that represent all aspects of the problem. This more general problem would
benefit from a surrogate model and space filling design to explore this space and optimize to it.
Jagged Defect Profiles The defect profiles tend to get uneven when they are low. This is due to
exaggerating the differences for low values of the cubic scale. If the overall defect curve (black line) is
smooth, and the defect rates are somewhat consistent, then you are probably taking enough runs. If the
Black line is jagged and not very low, then increase the number of runs. 20,000 runs is often enough to
stabilize the curves.
Defect Profiler Example
To show a common workflow with the Defect profiler, we use Tiretread.jmp with the specification limits
from Table 24.3. We also give the following random specifications to the three factors.
Figure 24.52 Profiler
Select Defect Profiler to see the defect profiles. The curves, Means, and SDs will change from simulation to
simulation, but will be relatively consistent.