Modeling and Multivariate Methods - SAS

616 Visualizing, Optimizing, and Simulating Response Surfaces Chapter 24
Noise Factors (Robust Engineering)
Example
To analyze a model with noise factors,
• Fit the appropriate model (using, for example, the Fit Model platform).
• Save the model to the data table with the Save > Prediction Formula command.
• Launch the Profiler (from the Graph menu).
• Assign the prediction formula to the Y, Prediction Formula role and the noise factors to the Noise
Factor role.
• Click OK.
The resulting profiler shows response functions and their appropriate derivatives with respect to the noise
factors, with the derivatives set to have maximum desirability at zero.
• Select Maximize Desirability from the Profiler menu.
This finds the best settings of the factors, balanced with respect to minimizing transmitted variation from
the noise factors.
As an example, use the Tiretread.jmp sample data set. This data set shows the results of a tire manufacturer’s
experiment whose objective is to match a target value of HARDNESS= 70 based on three factors: SILICA,
SILANE, and SULFUR content. Suppose the SILANE and SULFUR content are easily (and precisely)
controllable, but SILICA expresses variability that is worth considering.
For comparison, first optimize the factors for hardness without considering variation from the noise factor.
• Select Graph > Profiler to launch the Profiler.
• Assign Pred Formula HARDNESS to the Y, Prediction Formula role. Click OK.
• Select Desirability Functions in the Prediction Profiler menu.
• Double-click in the Desirability plot to open the Response Goal window. Change the pull-down menu
to Match Target.
• Select Maximize Desirability to find the optimum factor settings for our target value of HARDNESS.
We get the following Profiler display. Notice that the SILICA factor’s optimum value is on a sloped part of a
profile curve. This means that variations in SILICA are transmitted to become variations in the response,
HARDNESS.
Note: You may get different results from these because different combinations of factor values can all hit
the target.