See how to:
- Analyze experimental design data in a way that can help achieve an ideal stress-strain behavior
- Understand the case study where the goal is to new, harder plastic for a product
- Experimental Factors are 1) additive amounts of glass beads, calcium carbonate and 2) pressure and temperature process variables
- Data available from the testing lab are Stress (Force/Area) and Strain (change in Length/Length)
- Summary data normally used for analysis are modulus (slope of elastic region), yield stress (point where stress vs. stain is non-linear), tensile stress (maximum stress) and failure point (stress at breaking point)Analyze information from a designed experiment to help achieve ideal stress-strain behavior for a case study.
- Use JMP Pro Functional Data Explorer to understand and model stress vs. strain across the entire curve rather than summarize to a few key points on the curve
- Design a plastic formulation experiment, collect tensile data on the test specimens, model the stress and strain data
- Use Predition Profiler to help identify ideal stress-strain behavior
Stress vs. StrainStress vs. Strain
Questions answered by Jason @Jason_Wiggins and Peter @Peter_Hersh after the demo.
Q: How many levels were associated with each factor?
A: Three levels, so it was a Definitive Screening Design.
Definitive Screening Design Used in the ExampleDefinitive Screening Design Used in the Example
Q: Is there an auto fit option to use, instead of trial and error?
A: Functional Date Explorer gives you a Direct Functional PCA that is basically an auto fit option. However, in certain cases you're going to get a better fit with different fit types. It really depends on how complex your your data is and how many peaks and valleys it has.
Q: Can the analysis be done if you don't have a target function?
A: Absolutely. The target function really helps us in the optimization problem, but it's not strictly necessary. It just saves us a lot of time rather than using the prediction profiler trying to dial the shape that we're wanting.
Q: For the desirability analysis would you have had to have set desirability first?
A: No, there is no need to set desirability first, because you already defined the ideal curve using the target function, and JMP tries to minimize the integrated air from that target function and that's that bottom.
Q: For the desirability analysis would you have had to have set desirability first?
A: No, there is no need to set desirability first, because you already defined the ideal curve shape using the target function, and JMP tries to minimize the integrated error from that target function. If you turned on the Desirability Function graphs, you would just see. If you have a different goal, you could set also set Desirability. See how and how controlling that might impact your result.
Q: For the desirability analysis would you have had to have set desirability first?
A: No, there is no need to set desirability first, because you already defined the ideal curve shape using the target function, and JMP tries to minimize the integrated error from that target function. If you turned on the Desirability Function graphs, you would just see. If you have a different goal, you could also set Desirability. See how and how controlling that might impact your result.
Q: Where is the actual model?
A: It is a Generalized Regression Model based on the number or shape parameters you have. In this case we have three. JMP looks at those, does a variable selection for you to create what JMP calls Best Subset. In this example you saw that a couple of factors weren't included in the model. Because they were not impacting that shape, they were not included.
Generalized Regression Models for Each ShapeGeneralized Regression Models for Each Shape
Q: What are the purposes of the ID and Z choices in the dialogue?
A: ID is batch. We're looking at stress vs strain curves for each of these batches and they must be separated because it's not one
curve. Z parameters are the DOE factors that we're looking at. They are consistent throughout that entire stress strain curve and we're using those to do that functional do the analysis, so, if you look at the data, they're not changing but are set at a level for that curve analysis.
ID and Z Value OptionsID and Z Value Options
Q: How did you pick P-spline for modeling or was it just trial and error?
A: It is a little bit of trial and error and the best clue you have when you run those models for the basis functions, is to look at the look at the fit. If the fit describes the shape of your curves for each one of your batches, then you've done it you've done a good job. B-splines gave a result that's a little weird. Some of those curves flattened out and moved away from the actual data collected that's why the B-splines didn't work. So, we did iterate. P-splines was our next choice and they ended up matching the signal data a lot better.
Q: In your data to create the DOE curves, did you upload your test data or just the 4 summary points that you referred to?
A: We used all the stress strain curve data. Typically, you go to the lab, run each of my tests and then I get a stress strain signal just kind of like I showed with the graphs in Graph Builder. Then we must match this up with our DOE table. So, I only have one batch 287 but if I look at my stress strain curve data, see that I have collected 8 data points along that stress strain curve for that trial in the DOE. So, we must merge the test data with the DOE table.
Q: Is there a function that describes how much of the variance is accounted for by any of the Z variables?
A: We can definitely export that and run the model separately in the summaries. We can also assess variable importance from the interaction profiler. In this case, form the Variable Importance summary Report, we see that strain and is going to be the top because it's varied on purpose, but we see pressure and glass are having a big impact overall, and there is hardly any influence from that calcium carbonate in temperature. It is a little different than it would normally look because the strain is going to be the top contributor always. We can at least get an idea of where the other factors fall relative to each other and just ignore that top line because it's the response.
