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## Designing Full Factorial Experiments

Statistical Thinking for Industrial Problem Solving

In this video, we show how to design full factorial experiments using the Full Factorial platform in JMP.

To do this, we select DOE, then Classical, and then Full Factorial Design.

In the Responses panel, we can change the response name and the response goal, and we can add responses if we want to study multiple response variables in the same experiment.

For this example, we change the response name to Yield. The goal of this experiment is to maximize the yield, but you can change this if needed.

For this example, we enter a lower limit of 90 for the response. But you can leave this field blank if needed.

Now we’ll add the factors. We can add a combination of continuous and categorical factors.

To start, we add three continuous two-level factors.

We double-click the names to change them. We change X1 to Temp, X2 to Time, and X3 to Catalyst. Next, we change the values. The low level of Temp is 50, and the high level is 120. For Time, the values are 4 and 24, and for Catalyst, the values are 1 and 5.

Now we click Continue.

You can see that this is a 2x2x2 design with eight runs, or a 23 full factorial design.

By default, the design is run in random order. Randomization is important, because it averages out the effects of uncontrolled variables.

If you enter a value in the Number of Center Points field, design points are added halfway between the low and high values for each of the continuous factors. For example, if we add two center points, the design will include two runs in which Temp is 85, Time is 14, and Catalyst is 3. These runs can be used to test for the adequacy of your model.

We won’t add center points for this example.

The Number of Replicates field tells JMP how many times to replicate the design. When this value is zero, a design with each possible treatment is generated. If you change this value to 1, the entire design is replicated one time.

To see this, we enter 1 in the field and click Make Table.

You can see that this is a 2x2x2 design, with 16 runs.

The Pattern column is shorthand notation for the factor levels to use for each run. For example, the first trial will be run with all three factors set at the low level.

This is a fully replicated design, so each of the treatments is run twice, in random order. For example, rows 1 and 14 are replicates. These runs use the same factor levels.

Three scripts are saved to the data table.

After conducting the experiment, you can use the Model script to run the analysis. This is also useful, before collecting data, for seeing the model that you will be able to estimate.

You can run the Evaluate Design script to evaluate the statistical properties of the design.

And you can use the DOE Dialog script to return to the full factorial design window to make changes.

Let’s add another factor to this design. We’ll add a four-level categorical factor. To do this, we select Categorical, 4 level. This results in a 2x2x2x4 design with 32 runs.

We don’t want to replicate this design, so we change Number of Replicates to zero, and click Make Table.

The resulting design is a randomized 32-run full factorial with four factors.

If you will conduct this experiment, this design table is your guide. It tells you which treatments to run and provides a column to record the response values. You’ll want to save this table with a new name to make sure that you don’t lose your work.

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