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Level III

## DoE: Box-Benhken or Face Centered Central Composite design ?

Hey JMP users,

Here we want to compare the use of Box-Behnken or Face Centered Central Composite design (both with 3 levels for each factor).

- For 3 factors, the Box-Behnken design (BBD) offers the advantage in requiring a fewer number of runs. For 4 or more factors, this advantage disappears.

- the BBD contains regions of poor prediction quality. Its "missing corners" may be useful when the experimenter should avoid combined factor extremes. This property prevents a potential loss of data in those cases.

- The Face Centered Central Composite Design give poor precision for estimating pure quadratic coefficients. Does that mean that BBD gives better pure quadratic coefficients ?

Any other consideration ?

Many thanks,

2 ACCEPTED SOLUTIONS

Accepted Solutions
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Staff

## Re: DoE: Box-Benhken or Face Centered Central Composite design ?

JMP Community members are happy to help but be warned that DOE is a broad and deep subject. It is difficult to convey knowledge about it in a few replies.

Custom Design is unique to JMP but other software implements 'optimal design' methods including the 'coordinate exchange' algorithm. The older methods were based on the technology at hand: paper and pencil and mathematics. It was based on combinatorics and group theory. It was largely from a 'design-centric' view. A new view developed in the 1970s that was more of a 'model centric' view. It is based on an optimality criterion and numerical solution. There are many criteria that can be used. You mention D-optimal and I-optimal designs. D-optimal designs minimize the confidence region of the estimates of the model parameters. This result is best when you are most interested in inference about the estimates. (That is, are they significantly different from zero?) I-optimal designs minimize the integrated variance of estimates of the response. (That is, the model predictions have the smallest confidence intervals.)

So you get to choose the way in which the design is optimal. You also get to specify any linear model, if any terms must be estimated or not, aliasing to be avoided, fixed or random blocking, restricted randomization, and the number of runs. You cannot do any of that with either of the two classical designs that you mentioned.

Learn it once, use it forever!
Highlighted
Staff

## Re: DoE: Box-Benhken or Face Centered Central Composite design ?

I am sorry that I misunderstood what you were looking for. I thought other considerations would include a different design approach.

As for comparing CCD to BBD, you pretty much nailed the comparisons. For completeness I am including a JMP journal that compared the two designs using JMP's Compare Designs platform. CCD does better at detecting the main effects and interactions. The BBD does slightly better at detecting the quadratic terms. The CCD has slightly lower prediction variance in the center of the design space, but the BBD does slightly better at the edges (see the prediction profiler).

I think the design to choose will depend on your situation. Do you expect the optimum area to be near the center? Maybe go CCD. If you think it may be closer to an edge? Maybe BBD. Do you really need to worry about power for main effects and interactions with a response surface design? You probably already know the significant factors. Will running the corner points be problematic? If so, avoid BBD.

Notice that these questions are all about your process and your situation. Both designs are good designs. And, as Mark stated so well earlier, you should not rule out optimal designs. The real world limitations plus making better use of your knowledge of the process make the optimal designs very attractive and they can outperform the classic designs.

Dan Obermiller
7 REPLIES 7
Highlighted
Staff

## Re: DoE: Box-Benhken or Face Centered Central Composite design ?

Consider an I-optimal custom design.

Learn it once, use it forever!
Highlighted
Staff

## Re: DoE: Box-Benhken or Face Centered Central Composite design ?

I agree with Mark. There are limitations with both B-B and face-centered CCD. Those limitations do typically disappear with an I-optimal Custom Design.

Dan Obermiller
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Level III

## Re: DoE: Box-Benhken or Face Centered Central Composite design ?

Thank you for your feedback.
My knowledge in Custom Designs are very limited. Are they available only in JMP but not in other software? Can you tell me why those designs are better than the classical ones ?
I have tried to have more details about those designs and saw that there are two types : I-optimal and D-optimal Custom designs. Could you tell me what it the difference between the two designs?

Thanks a lot!

I
Highlighted
Staff

## Re: DoE: Box-Benhken or Face Centered Central Composite design ?

JMP Community members are happy to help but be warned that DOE is a broad and deep subject. It is difficult to convey knowledge about it in a few replies.

Custom Design is unique to JMP but other software implements 'optimal design' methods including the 'coordinate exchange' algorithm. The older methods were based on the technology at hand: paper and pencil and mathematics. It was based on combinatorics and group theory. It was largely from a 'design-centric' view. A new view developed in the 1970s that was more of a 'model centric' view. It is based on an optimality criterion and numerical solution. There are many criteria that can be used. You mention D-optimal and I-optimal designs. D-optimal designs minimize the confidence region of the estimates of the model parameters. This result is best when you are most interested in inference about the estimates. (That is, are they significantly different from zero?) I-optimal designs minimize the integrated variance of estimates of the response. (That is, the model predictions have the smallest confidence intervals.)

So you get to choose the way in which the design is optimal. You also get to specify any linear model, if any terms must be estimated or not, aliasing to be avoided, fixed or random blocking, restricted randomization, and the number of runs. You cannot do any of that with either of the two classical designs that you mentioned.

Learn it once, use it forever!
Highlighted
Staff

## Re: DoE: Box-Benhken or Face Centered Central Composite design ?

I am sorry that I misunderstood what you were looking for. I thought other considerations would include a different design approach.

As for comparing CCD to BBD, you pretty much nailed the comparisons. For completeness I am including a JMP journal that compared the two designs using JMP's Compare Designs platform. CCD does better at detecting the main effects and interactions. The BBD does slightly better at detecting the quadratic terms. The CCD has slightly lower prediction variance in the center of the design space, but the BBD does slightly better at the edges (see the prediction profiler).

I think the design to choose will depend on your situation. Do you expect the optimum area to be near the center? Maybe go CCD. If you think it may be closer to an edge? Maybe BBD. Do you really need to worry about power for main effects and interactions with a response surface design? You probably already know the significant factors. Will running the corner points be problematic? If so, avoid BBD.

Notice that these questions are all about your process and your situation. Both designs are good designs. And, as Mark stated so well earlier, you should not rule out optimal designs. The real world limitations plus making better use of your knowledge of the process make the optimal designs very attractive and they can outperform the classic designs.

Dan Obermiller
Highlighted
Level VII

## Re: DoE: Box-Benhken or Face Centered Central Composite design ?

I'm confused?  Do you want alternatives or do you want to understand the pros and cons of the two mentioned designs?

Highlighted
Level III

## Re: DoE: Box-Benhken or Face Centered Central Composite design ?

-The pros and cons of each

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