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Statistical Thinking for Industrial Problem Solving
In this video, we show you how to analyze full factorial experiments in JMP using the file 2x2x2 Unreplicated.jmp.
As the name implies, this is an unreplicated 23 full factorial experiment. The factors are Temperature, Time, and Catalyst, and the response is Yield.
Because this experiment was designed in JMP, we can run the Model script to launch the analysis. Instead, for illustration, we select Analyze and then Fit Model.
You can see that the Model Specification dialog has been populated with the response, Yield, and several model effects. By default, the model includes only main effects and two-way interactions.
We’ll select these effects and click Remove to start over and populate the model effects panel from scratch.
We’ll add the main effects and two-way interactions.
To do this, we select the three factors in the Select Columns panel, and then we click the Macros button and select Factorial to Degree. You can see that, by default, Degree is 2. So the model effects panel is populated with main effects and two-way interactions.
We’ll click Run to run this analysis.
By default, you see the Effect Summary table and the Prediction Profiler.
The terms in the Effect Summary table are sorted in ascending order based on PValue. The most significant term is Temperature, followed by the Temperature*Time interaction.
You can see that the other two-way interactions are not significant.
We’ll reduce the model by removing nonsignificant effects, one at a time. To do this, we select the Temperature*Catalyst interaction in the Effect Summary table, and click Remove. We also remove the Time*Catalyst interaction.
The coefficients for the effects in the model are listed in the Parameter Estimates table.
The Prediction Profiler enables you to visualize your model. Temperature, which is the most significant term, has the steepest profile line. When we click and drag this line to the low value of Temperature, and then the high value, you can see how the predicted yield changes.
You can also see the interaction between Temperature and Time. Notice what happens to the slope of the line for Time as you change Temperature from the low level to the high level. The slope of the line for Time changes.
To better see this interaction, we click the top red triangle and select Factor Profiling and then Interaction Plots.
You can see that the profile lines are nonparallel. This tells you that the effect of one factor on the response depends on the setting of the other factor.
Let’s take another look at the Prediction Profiler.
The goal of this experiment is to maximize Yield. So, you see some desirability panels. The last box in the top row is the desirability function, which shows the response goal. When we double-click this box, we see the goal and the desirability. Higher values of Yield are more desirable. When we tell JMP to find settings of the factors that will maximize the response, we optimize this desirability function.
Let’s do this now. We select Optimize and Desirability from the red triangle for the Prediction Profiler and then Maximize Desirability.
The settings of our factors that result in the highest predicted yield are Temperature at the high level (120), Time at the low level (4), and Catalyst at the high level (5). At these settings, the predicted yield is 89.32. The bracketed values form a confidence interval for the mean for this predicted yield. At these factor settings, you can be 95% confident that the mean yield will be between 88.2 and 90.5 (assuming, of course, that the process hasn’t changed).
There are many additional options under the top red triangle for exploring and analyzing your results, which we won’t discuss in this short video.
We encourage you to explore these options on your own.
