Learn JMP Events
Events designed to further your knowledge and exploration of JMP.Making the Best Choice for Defect Count Models - Mastering JMP
gail_massari
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Video was recorded in February 2025 using JMP 18.
Least Squares Regression is often the go-to method for building statistical models. But should it be? Quality measures, like defect counts that are used as response variables, often violate assumptions that must be met for standard least squares regression models to be successful. What should we use instead?
In this session, we use the following steps to develop a useful statistical model to minimize defect counts in a chemical mechanical planarization (CMP) process that is used for material removal and planarization of wafers in semiconductor manufacturing.
- Explore trade-offs of using standard least squares regression methodology that assumes a continuous response on defect count data.
- Develop and compare appropriate models of CMP defect count data in JMP and JMP Pro.
- Use the best model to find an optimal tool recipe that minimizes defect counts.
Suggested Prerequisites:
- Some experience evaluating process data.
- Basic familiarity with least squares regression models.
- Attending a related Jan. 24 session or viewing its video after the session: Designing Process Optimization Experiments Using Models Based on Production Data.
For additional detailed information about topics covered in the video, consider:
Questions answered by Jason Wigins @Jason_Wiggins and Clovis Weisbart @cweisbart at the live webinar demo:
Q: What assumptions are violated in this Least Square regression example for getting negative response?
A: As Jason mentioned, the normality assumption of the defect count is leading to those impossible negative values. The Residual by Predicted Plot Jason showed also looks for constant variance of the residuals and no non-random patterns should be expected for that assumption.
Q: Where are the options to fit the generalized models?
A: Generalized Regression is a JMP pro feature. The options for distribution and penalized estimation technique will be at the top of the report, and there are various distribution options for Generalized Regression
Q: How would you explore the data to find if there is one X factor setting resulting the high defect count wafers?
A: There are several ways withing the Fit Model Report. You can also use Predictor Screening, which deploys a tree-based based approach to see if there is one variable that pops out, but screening won't explain the interactions. JMP Pro Bootstrap Forest in JMP Pro is another approach to use and you will get a Profiler from that. It is always good to explore in Graph Builder. One caution, though, is that when you're just plotting a 2-dimensional graph, you may be missing something big, because two of your variables may be heavily interacting. Graphs Builder will not tell you anything, everything. That's why we build models.
Q: Would it make sense to transform the count with an offset log formula log? Is that a way to normalize the distribution and use standard least squares effectively?
A: Trying that that may work some of the time, but it does not always give you a good model. That is one reason JMP included Generalized Regression, which handles the issue better ad directly. One of the challenges of a transformation is you do a mathematical transformation to fit a model to that transformed response. And then you must untransform the model to get it back into the space that's familiar to you. So, it's extra steps.
