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full factorial design and blocking factors

Hi,

 

A prospect try to reproduce an example suggested by Jacques Goupy in his book related to Yates beens.

 

In this example, Mr Goupy has 5 factors and  introduce 2 blocking factors. In this case, he doesn't do a full factorial design but a 2^(7-2)fractional design.he chooses to assign an alias between factor 6 (first blocking factor) to 124 interaction and factor 7 to 135 interaction.

 

He has a lot of question around that.
How can we define this in JMP (I suggest him Custom Design, but he really want to reproduce the same table than Jacques Goupy)? How can we specify the correct alias? How can we check if blocking factors have impacts?

 

Jacques Goupy give the data table in this forum: http://jacques.goupy.pagesperso-orange.fr/Questions.htm (answer to Guillaume Machinet question)?

Does anybody try to reproduce this example and be able to create the datatable and analysis provided by Jacques Goupy?

 

Thank for your help,

Florence

Re: full factorial design and blocking factors

Two two-level blocking factors can be represented as a four level blocking factor

Re: full factorial design and blocking factors

In order to regenerate Mr. Goupy's table I just set up a 5 factor Full Factorial with a model to degree 3. Then sorted left to right to generate the table shown on p229 Introduction to Design of Experiments-Third Edition.

Then using the formula column as indicated above by Phil Kay, one obtains the blocks indicated in the book. The JMP table and Model script to agree with the book are attached.

Re: full factorial design and blocking factors

This can be done using DOE > Classical > Screening Designs.

1. Add 5 continuous factors
2. Add 2 2-Level categorical factors. These will be your blocking factors. They need to be added last to get this to work correctly.
3. Use the default, select from a list of designs, and pick the 32 run design without blocking.
4. After clicking Continue, go to the Change Generating Rules outline. In the first row, check the boxes for factors 1, 2, and 4. In the second column select factors 1, 3, and 5. The last two check boxes should either both be selected or both unselected. Click Apply.
5. The table should match the design in 10_Yates.JMP. The trick is to figure out which combination of levels for each block correspond to the values found in the column Bloc.

You also have to modify the script in Model. You'll need to remove any interaction containing a blocking factor and add those interactions that were aliased with them. This will give you all 2 factor interactions for the five continuous factors. Also, you'll want to make the two blocking factors random effects.

 

I'm attaching an example. I set the last two check boxes in the generating rules to off.

Re: full factorial design and blocking factorsHi,

I'm on the road, so can't see the data. But if I have understood correctly and they really want to do this (and why would they?!), it should be possible, I think.

Start with the fractional factorial in the coded form (-1, +1). Then add formula columns for the interactions that you want to alias with. For example X1 * X3 * X5. That should give you the blocking factor.

Phil
Re: full factorial design and blocking factorsJust an observation, the table that's provided appears to only have 1 blocking variable, not 2.Re: full factorial design and blocking factors

You could put the example in a JMP data table and use DOE > Evaluate Desigh to get the alias matrix. This information could guide you to selecting a fractional factorial design and changing the generating rules.

I should add that including two blocking factors is not easy with the factorial designs. All of this design work would be much easier if you use custom design to solve the problem. Why is it so important to re-create a design from a book?