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To demonstrate a possible workflow with the Defect Profiler, we use Tiretread.jmp. The experimental data in the Tiretread.jmp sample data table comes from an experiment to study the effects of SILICA, SILANE, and SULFUR on four measures of tire tread performance.
1.
Select Help > Sample Data Library and open Tiretread.jmp.
2.
Select Graph > Profiler.
3.
Select Pred Formula ABRASION, Pred Formula MODULUS, Pred Formula ELONG, and Pred Formula HARDNESS and click Y, Prediction Formula.
4.
8.
Click Save to save the Spec Limits to the data table.
Figure 8.9 Profiler Random Specifications
Figure 8.10 Defect Profiler
Consider the overall curve for SILICA. As silica varies, the defect rate goes from the lowest rate of 0.001 when silica is about 1 and increases quickly up to a defect rate of nearly 1 as silica increases or decreases from 1. However, SILICA is itself random. If you integrate the density curve of SILICA, you would estimate the average defect rate to be about 0.03, which is shown as the Mean for SILICA. This estimate of the overall defect rate estimated by the simulation is shown in the defect table under the simulation histograms. The Mean value for the overall defect rate for all factors are similar.
The Defect Profiler also includes an estimate of the standard deviation of the defect rate with respect to the variation in each factor. This value (labeled SD) is 0.057 for SILICA. The standard deviation is related to the sensitivity of the defect rate with respect to the distribution of that factor. Comparing the SD values across the three factors, the SD for SULFUR is higher than the SD values for SILICA and SILANE. This indicates that to improve the defect rate, shifting the distribution in SULFUR should have the greatest effect. A distribution can be shifted by changing its mean, changing its standard deviation, or by truncating the distribution by rejecting inputs that do not meet certain specification limits.
2.
Figure 8.11 Defect Parametric Profile
Consider SULFUR and note that the current defect rate (0.03) is represented in four ways corresponding to each of the four curves in the Parametric Profiler.
For the red curve, Mean Shift, the current rate is where the red curve intersects the vertical red dotted line. The Mean Shift curve represents the change in overall defect rate as the mean of SULFUR changes. One opportunity to reduce the defect rate is to shift the mean slightly to the left. If you use the crosshair tool on this plot, you see that a shift down in the mean reduces the defect rate to about 0.02.
The orange curve, USL Chop, suggests a way to improve the defect rate. Reading the curve from the right, the curve starts out at the current defect rate (0.03). Then as you start rejecting more parts by decreasing the USL for SULFUR, the defect rate improves. However, moving a spec limit to the center of the distribution is equivalent to throwing away half the parts, which might not be a practical solution.
Looking at all the opportunities over all factors, it now looks like there are two good options for further investigation. You could shift the mean of SILICA to about 1 or reduce the variation in SULFUR. Because it is generally easier in practice to change a process mean than a process variation, the best first adjustment might be to shift the mean of SILICA to 1.
Figure 8.12 Adjusted Defect Rates

Help created on 3/19/2020