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R&D researchers and manufacturers desire to know the factor ranges in their products and processes that will deliver in specification product.


A prerequisite to calculating acceptable ranges is to have a predictive model with an error estimate. You can then simulate thousands of predicted data over the design space and identify which factor combinations produce in spec product. 

JMP 17 makes this exercise easy with its Design Space Profiler. The Design Space Profiler allows you to explore the factor ranges with the predicted output being the proportion of In Spec Product. 

Cy Wegman is a Senior Analyst at Predictum. Before joining Predictum, he worked for 38 years at Procter & Gamble, where he led, designed and executed all design of experiment (DOE) and process definition courses for P&G.
Cy is a member of the P&G Prism Society, which represents the top 1% of P&G engineers, for profitably applying his technical mastery. His contributions have resulted in hundreds of millions of dollars in annual savings.

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. 

A semiconductor engineer in a full-body suit interacts with machinery in a brightly lit work space.
A screenshot of the interactive prediction profiler in JMP 17. This screenshot displays system behavior for a manufacturer that is looking to optimize wafer thickness.
A screenshot of the design space profiler in JMP 17.

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. 

Screenshot of the Design Space Profiler in JMP 17. The screenshot continues with the wafer example discussed in the blog post. It shows that temperature as a factor must be tightly controlled while other factors may vary to a greater degree.

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. 

A screenshot of a prediction profiler in JMP 17 which is displayin predicted wafer thicknesses for a semiconductor manufacturer.

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. 

Concluding Thoughts

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.

How can you improve your analyses?

Contact us for private data analysis and statistics instruction, covering topics such as JMP Fundamentals, Design of Experiments, and Mixture Experiments. Our courses are available live or via e-Learning and are available as soon as you need, so you don’t waste your time waiting for results.

Contact us for data analysis consulting. Our team of data analysis consultants boast 30+ years of industry expertise each, helping our clients find solutions to engineering and science problems.

Meet our experts. Schedule a no-obligation call.

For over 25 years, Predictum has enabled companies to achieve higher levels of productivity, operational improvement and innovation, and realize significant savings in cost, materials, and time. Our team of engineers, data scientists, statisticians, and programmers leverages deep expertise across various industries to provide our clients with unique solutions and services that transform data into insightful discoveries in engineering, science, and research. To get in touch with our team, visit www.predictum.com/contact.

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