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Statistical Thinking for Industrial Problem Solving
In this video, we show how to analyze an experiment with multiple responses, and how to optimize multiple responses, using the file Anodize.jmp.
In this example, a 12-run custom design with five factors was conducted. The experimental objective is to find settings of the factors to optimize the four responses: Thickness, L*, a* and b*.
To do this, we run the model script that was saved to the data table. With these data, we can estimate five main effects and four 2-way interactions.
Different effects might be important for the different responses, so we want to analyze the four responses separately. To do this, we select the Fit Separately box and click Run.
This produces four separate analyses that are grouped in one window.
Now, we use the Effect Summary table to reduce the model for each response. We'll remove the effects with p-values greater than 0.10.
For each response, a Prediction Profiler is provided. But we want to optimize all of the responses at the same time.
To do this, we select Profiler from the red triangle for Fit Group.
This opens a new Prediction Profiler, with all five factors across the bottom and all four responses on the side.
For each response, you see the predicted value and the margin of error at starting values for each of the factors. Here, the starting values are the middle values for each factor.
When the experiment was designed, the response limits and the response goal were saved as column properties in the data table. For all four responses, we want to match a target.
This information is used in the Prediction Profiler for optimization.
To see the response limits and goal for Thickness, we double-click in the desirability panel. The goal is to match the target, and the most desirable value of Thickness is 0.9. The low and high values provide an acceptable range for Thickness, but you can see that these values aren't as desirable as matching the target.
This is reflected in the desirability curve. The desirability is 1 for the target and zero beyond the response limits.
For each response, you can specify the importance of the response relative to the other responses. For example, if optimizing Thickness is three times more important than optimizing the other responses, we'd enter 3 in the Importance field.
For this scenario, all four of the responses are equally important.
Let's see how to find optimal settings for the five factors.
To do this, we select Optimize Desirability from the red triangle for the Prediction Profiler and then Maximize Desirability.
The optimal settings are provided, along with the predicted values for the responses at these settings.
Looking at the desirability curves, you can see that at these settings we can get close to matching the target for all four of the responses.
Note that there are many possible ways of optimizing the responses, and if you run Maximize Desirability again, JMP will find a new solution.
Here's a common scenario. You might want to lock in a factor at a specific value and re-optimize.
