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## Fractional factorial with 3-level factors

I have a product mix with three components I am trying to minimize while maximizing my response. I have one response and four continuous factors. 3 of the factors are components of the product and the fourth factor is the starting temperature of the test that yields the response.

I would like to perform a fractional factorial rather than the full factorial method. I want all four factors to have three levels but reduce the number of trials from 81. A Screening design only allows 2-level factors. A Taguchi design allows 3-level factors but doesn't seem to be the right modeling method for my project.

Can a 3x3x3x3 fractional factorial be done using JMP6 or JMP7 to do this?
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Staff (Retired)

## Re: Fractional factorial with 3-level factors

If the three components as you mention are truly components in a formulation then I would simply use the Custom Design capability in JMP to set up a 4 factor design where the first three factors are mixture components and the 4th factor is a continuous factor = Temperature. Adding the interactions to the model and specifying some center points (N=3) the number of runs required would only be 15. By treating this as a two level design with center points you get your three levels as you desired.

## Re: Fractional factorial with 3-level factors

In JMP5, the answer is YES, you can get a fractional factorial of a 3**4 design (so I assume later versions of JMP can do this also).

The fractional factorial you are interested in is indeed the Taguchi 9-run design or the Taguchi 27-run design. These are identical to a standard fractional factorial. No difference. Go ahead, use it without qualms.

I also point out that a central composite design (response surface design) often has better statistical properties than the fractional factorial of a 3**4, and usually involves fewer runs as well.

Message was edited by: Paige
3 REPLIES 3
Highlighted
Staff (Retired)

## Re: Fractional factorial with 3-level factors

If the three components as you mention are truly components in a formulation then I would simply use the Custom Design capability in JMP to set up a 4 factor design where the first three factors are mixture components and the 4th factor is a continuous factor = Temperature. Adding the interactions to the model and specifying some center points (N=3) the number of runs required would only be 15. By treating this as a two level design with center points you get your three levels as you desired.

## Re: Fractional factorial with 3-level factors

In JMP5, the answer is YES, you can get a fractional factorial of a 3**4 design (so I assume later versions of JMP can do this also).

The fractional factorial you are interested in is indeed the Taguchi 9-run design or the Taguchi 27-run design. These are identical to a standard fractional factorial. No difference. Go ahead, use it without qualms.

I also point out that a central composite design (response surface design) often has better statistical properties than the fractional factorial of a 3**4, and usually involves fewer runs as well.

Message was edited by: Paige
Community Trekker

## Re: Fractional factorial with 3-level factors

Thank you Lou and Paige. I will try them out.