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## Creating 2k-r Fractional Factorial Designs

Statistical Thinking for Industrial Problem Solving

In this video, you learn how to create 2k-r fractional factorial designs in JMP. We’ll create a fractional design to study five 2-level continuous factors.

To create a fractional factorial design, we select DOE, then Classical, and then Screening Design.

We’ll use Y as the response name, with Maximize as the response goal.

You can add continuous, discrete numeric, or categorical factors. We’ll add five continuous 2-level factors. To do this, we enter 5 in the Add N Factors field and click Continuous.

Factors X1 through X5 have been added, with coded values -1 and 1. We’ll use these default values for this video.

To see the available design types, we click the Continue button.

You can choose from a list of fractional factorial designs, or you can construct a main effects screening design.

The main effects screening option is useful when you want to create a design to screen for important main effects, with a small number of experimental runs.

We’ll select a design from the list of available fractional factorial designs.

When we click Continue, we see the list of available designs for five 2-level factors.

The designs with a block are used to create designs in which the experiment is run in blocks. We’ll focus on the designs without blocks for this video.

If you want to run all possible treatments, you’d select the 32-run 25 full factorial experiment. The resolution column tells you the effects that you can estimate with this design. With full factorial designs, you can estimate all main effects and all possible interactions.

If you want to run a ½ fraction of this design, you’d select the 16-run fractional factorial design. This is a 25-1 resolution 5 design. With this design, you can estimate all main effects and 2-way interactions.

If you want to run a ¼ fraction of this design, you’d select the 8-run fractional factorial design. This is a 25-2 resolution 3 design. With a resolution 3 design, you can estimate only main effects. Main effects are aliased with 2-way interactions, and 2-way interactions are aliased with other 2-way interactions.

One additional design, which requires 12 runs, is a Plackett-Burman design. This is also a resolution 3 design, but it has four more runs than the 25-2 design.

We’ll generate the 8-run 25-2 design. To do this, we select the design and click Continue.

When you open the Aliasing of Effects outline, you can see which effects are aliased with other effects up to 2-way interactions. When you analyze your experimental results, you can estimate only the terms in the effects column.

By default, the design is generated in random order.

You can add center points to this design, or you can replicate the entire design one or more times.

We’ll use the default settings and click Make Table.

This produces the design table, with several saved scripts.

We haven’t run the experiment, but let’s take a look at the model that we can fit. To do this, we run the Model script.

With this 25-2 fractional factorial design, we can estimate five main effects and two of the 2-way interactions. If you need to estimate all of the 2-way interactions, you’d need to generate a larger screening design.

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