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Community Trekker

## How can you fill out (augment, space-fill) a 20 factor, all continuous, DSD with levels >3?

I need to design a DSD with 20 continuous factors, which if I add two dummy variables, would call for 45 runs. The problem is that the levels can vary from 0 to 1 and the responses can cluster around the extreme factor levels. I would like to add more points between the mid-point and the extremes. How can I augment a DSD, ideally with something like the space-filling design? I guess that I would love to have a DSD that has five levels (or more) that is close to the RSM design but as efficient as the DSD. Can such a design be constructed, even if a hybrid (DSD plus space-filling?) pending the next big development in DOE by Brad Jones and Chris Nachtscheim?

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Accepted Solutions
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Super User

## Re: How can you fill out (augment, space-fill) a 20 factor, all continuous, DSD with levels >3?

Hmmm, I guess I would just augment the design with more center points then. I’m not sure what 5 levels is going to buy you unless you want to fit cubics or quartics. The only exception to that is adding axial values to reduce correlation with quadratic terms, but those will extend outside your [0, 1] factor space.

If you want an honest opinion, I think you’re overthinking this. I’ve been designing experiments for quite a while, and the ones that prove to be least effective are the ones where we tried to get too cute. Keep it simple. If you got 20 factors, just screen with a factorial design, and maybe add some center points to detect curvature. Follow up with an RSM on your significant factors.

I like DSDs, but I would be hesitant to try one with that many factors.
-- Cameron Willden
Community Trekker

## Re: How can you fill out (augment, space-fill) a 20 factor, all continuous, DSD with levels >3?

Yes, I am beginning to think that a 20 factor DSD may be used for a screening objective, after which an RSM design may be necessary. I suspect that there are a few second-order active effects in the final model.

6 REPLIES 6
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Super User

## Re: How can you fill out (augment, space-fill) a 20 factor, all continuous, DSD with levels >3?

What do you mean the response can cluster around the extreme factor levels?

-- Cameron Willden
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Community Trekker

## Re: How can you fill out (augment, space-fill) a 20 factor, all continuous, DSD with levels >3?

Responses looks lie a U-curve with maxima around zero and 1 with very few in the middle point.

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Super User

## Re: How can you fill out (augment, space-fill) a 20 factor, all continuous, DSD with levels >3?

So you're saying you don't have many centerpoints for your factors?

-- Cameron Willden
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Community Trekker

## Re: How can you fill out (augment, space-fill) a 20 factor, all continuous, DSD with levels >3?

Yes, and ideally would like more around the center points.

Highlighted
Super User

## Re: How can you fill out (augment, space-fill) a 20 factor, all continuous, DSD with levels >3?

Hmmm, I guess I would just augment the design with more center points then. I’m not sure what 5 levels is going to buy you unless you want to fit cubics or quartics. The only exception to that is adding axial values to reduce correlation with quadratic terms, but those will extend outside your [0, 1] factor space.

If you want an honest opinion, I think you’re overthinking this. I’ve been designing experiments for quite a while, and the ones that prove to be least effective are the ones where we tried to get too cute. Keep it simple. If you got 20 factors, just screen with a factorial design, and maybe add some center points to detect curvature. Follow up with an RSM on your significant factors.

I like DSDs, but I would be hesitant to try one with that many factors.
-- Cameron Willden
Community Trekker

## Re: How can you fill out (augment, space-fill) a 20 factor, all continuous, DSD with levels >3?

Yes, I am beginning to think that a 20 factor DSD may be used for a screening objective, after which an RSM design may be necessary. I suspect that there are a few second-order active effects in the final model.