An Example from the Semiconductor Industry
A semiconductor manufacturer has three different wafer processes. For this organization, it is desirable to deliver thicknesses within a range of 3850 to 4150. The manufacturer’s staff executes a DOE and builds predictive models using SVEM (Self Validating Ensemble Model).
JMP’s interactive prediction profiler displays the system behavior, shown in the image below. The shaded area in this profiler displays the prediction intervals of individual data points. The Design Profiler is found under the red triangle menu in the Prediction Profiler.
Using simulated data, the platform allows you to move the limits of the factors and provides the proportion of product within specification limits. The blue and red traces show the effect on proportion of in spec product. The Move Inward command adjust the ranges incrementally to increase the InSpec Portion.
In this example I used the RASE (Root Average Squared Error) as the error standard deviation. The following ranges contained all product within specification and account for 0.54% of the entire factor space volume. You can see that the Temperature must be tightly controlled while the other two factors may vary to a greater degree. You also have the option to explore by tool if desired.
A Note on Manual Data Exploration
It is important to mention that the platform finds a feasible solution and not necessarily all possible ranges that may work. Hence you may want to manually explore for other feasible solutions.
In this example note in the profiler the prediction error varies by location. Therefore, we want to simulate our solution to take this into account. The platform allows you to send the factor midpoints and ranges to the profiler so that you can simulate and test your conclusions more thoroughly.
In the profiler simulator you must specify how you will allow the factors to vary in the simulation. In this example I allowed the factor values to vary normally within 2 sigma limits.
The simulated solution estimates a defect rate of 0.16%. The standard deviation is 49.16 which is higher than our RASE value of 38.5 due to the variation being higher at the selected ranges. If this is deemed close enough, the next step would be to validate the solution on the process.
JMP’s Design Profiler makes the process of finding feasible ranges that can produce within specification product much simpler and easier.
Across industries, companies need to optimize their products, utilizing information on factor ranges, for example. Clients seek out Predictum for our experience working with engineers in all industries and supporting their data analysis.
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