extend Definitive Screening Designs to Face Centered central composite designs (FCCCD)

[#1]

Hallo,

can JMP extend Definitive Screening Designs to  Face Centered central composite designs (FCCCD) and evaluate them?

It seems that FCCCD are the only designs which contain a considerable number of runs in common with definitive screening designs.

Sincerely

Thommy7571

[#2]

Hi @Thommy7571,

You can augment a Definitive Screening Design to a (Face Centered) Central Composite Design manually or automatically: 

• Manually, you can add the missing points from DSD in the centre of the faces, corners and middles of the sides.
• If you want to do it automatically through the platform Augment Designs, the repartition of points will depend on the augmentation option (and assumed model). Specifying an augmentation with "Add Axial", you can obtain a CCD, and you can specify the distance you want for the axial points of the CCD, so you can obtain circumscribed, face-centered or inscribed CCD. Knowing the appropriate distance to obtain the design type you want may require to look at the documentation for CCD and how the axial points are determined and calculated : Choose a Design
  You can also generate a CCD with the Classical Response Surface Designs platform, generate the type of CCD you want for the appropriate number of factors you have, and use the axial values from this design for your augmented design.

If you augment your design using the "Augment" option and specifying main effects, 2-factors interactions and quadratic terms for the important effects in the model, you won't obtain a face CCD, as points in the centre of the faces will be missing (and possibly some of the other points depending on the number of points allowed for "completeness" of the design). The augmentation will use the points already created, and augment the design optimally to take into account assumed model. 

Depending on your needs, obtain a CCD or any optimal response surface model design, the augmentation platform will help you. 

Evaluating the augmented design can be done throught the platform Evaluate Designs or if you have generated several possible design options, you can compare them with the Compare Designs platform.

More infos about the several CCD (circumscribed, face-centered, inscribed) : 

5.3.3.6.1. Central Composite Designs (CCD) (nist.gov)

5.3.3.6.3. Comparisons of response surface designs (nist.gov)

Hope this answer will help you,

[#3]

I deepend my knowledge concerning the points used for the different designs, especially  CCD and DSD. Thereby I found out that the points used in those two differ very much. In principle I don't see how to use all runs of a DSD - if ever necessary - and add further runs to get a CCD. However I had the impression that the points used in a FCCCD are more similar to those used by DSDs.  Perhaps I misunderstood something, namely that in FCCCD the axial points have another distance to the center than the facial centered points. 

Thus - based on the following

1. Factorial Points: - DSDs do not fully employ factorial points as in CCDs. 

2. Axial Points: - Similar to CCD, DSDs include axial points.

3. Center Points: - DSDs include center points to estimate experimental error, similar to CCD and FCCCD. 

I conclude that CCD include the center point and the axial points.

Thus if I use a DSD I can use the latter and extend it to a CCD using einter further points of the same type or add a factorial point with two or more levels. Am I correct. This was not clear since I got a negative answer somewhere concerning the possibility to extend a DSD to a CCD. And yes I would like it automatically although this is of secondary importance. Of course I know that after the DSD the important factors should be reduced. 

Sincerely

Thommy7571

[#4]

Hi @Thommy7571,

To answer on your remarks :

1.Factorial Points: - DSDs do not fully employ factorial points as in CCDs. 

2.Axial Points: - Similar to CCD, DSDs include axial points.

3.Center Points: - DSDs include center points to estimate experimental error, similar to CCD and FCCCD. 

I conclude that CCD include the center point and the axial points.

Factorial points and center points are similar between DSDs and CCDs. The axial points are NOT included in DSD by default. DSD are 3-levels screening designs, so it contains middle levels for each factor. See the repartition of points between DSD and augmented CCD (factorial points and centre points are already present in the DSD, so the augmentation in CCD doesn't add factorial points but may add centre points) :

And between DSD and Face-Centered CCD : 

In principle I don't see how to use all runs of a DSD - if ever necessary - and add further runs to get a CCD.

Thus if I use a DSD I can use the latter and extend it to a CCD using einter further points of the same type or add a factorial point with two or more levels. Am I correct. 

As stated before, use the Augment Designs platform with the Add Axial Points to a Design option to add axial points and augment a DSD to a CCD.

Perhaps I misunderstood something, namely that in FCCCD the axial points have another distance to the center than the facial centered points.

See the documentation I have added in my previous answer to better understand the differences between circumscribed, face-centered or inscribed CCD designs, and how to setup this distance value depending on your needs and the type of design you want :

More infos about the several CCD (circumscribed, face-centered, inscribed) : 

5.3.3.6.1. Central Composite Designs (CCD) (nist.gov)

5.3.3.6.3. Comparisons of response surface designs (nist.gov)

Face Centered = FCCCD -> distance =1

Hope this clarify my answer,

[#5]

Very interesting indeed. I didn't know inscribed CCDs.  also thanks for the link to the NIST page, However, there are two points which are unclear.  In your design red points are on the corners of the cube and marked as points for the DSD. This is not possible according to the article of Bayiley. These are simple factorail points - at least in case of two levels. e.g. +1, +1, +1   so such points -cannot be in a DSD. 

In general it is recommended to take for +1 and -1 the extreme values of a parameter. Starpoints would be out of the range, no? If so, how can I take points outside the limits if this is physically impossible? What are recommended experimental values to be used for +1 and -1  compared to the limiting values (concentration e.g. 0 % and 100 % - less or more is not possible!)  Am I right or is there nothing on DSDs on Nist.gov?  Is it finally perhaps not a good idea - using 6 or 7 factors - to start with a DSD if runs cannot be reasonably used for the following design? Why did nobody decvelop a design similar to CCD which bases on the DSD, since the latter is so useful for the gain of information?

[#6]

Hi @Thommy7571,

Sorry for the delay, your responses were in the spam folder, I just marked them as "safe".

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@Thommy7571 wrote:

In your design red points are on the corners of the cube and marked as points for the DSD. This is not possible according to the article of Bayiley. These are simple factorail points - at least in case of two levels. e.g. +1, +1, +1   so such points -cannot be in a DSD. 

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You can have "simple factorial" points in your design if you have a very low number of factors : less factors than 5 will still create designs with 13 runs, so you might end up with factorial points. This 13-runs design is in fact a DSD with 5 factors and the minimum number of runs, projected in a 3 factors dimensional space. Take into account projection property of factorial-based designs (DSD, CCD and others) : if one of the k factors is not important/active, you can still project the experiments in a k-1 dimension experimental space, which could give you the impression that you have factorial points.

More info here : https://www.linkedin.com/posts/victorguiller_designofexperiments-statistics-dataanalytics-activity-7...

Hope that clarifies this point.

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@Thommy7571 wrote:

In general it is recommended to take for +1 and -1 the extreme values of a parameter. Starpoints would be out of the range, no? If so, how can I take points outside the limits if this is physically impossible? What are recommended experimental values to be used for +1 and -1  compared to the limiting values (concentration e.g. 0 % and 100 % - less or more is not possible!)  

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It depends what is the value for your axial point, as you could have a circumscribed (>1), face-centered (=1) or inscribed (<1) Central Composite design.

The choice of the value for the star point is a compromise between physical feasability of the runs (can you extend the factors range below the -1 or above +1 coded values) and the objective(s) behind your CCD. On a similar topic, I showed that the farthest the star points are from the centre of the experimental space :

• The higher the power for main effects and quadratic effects, but the lower the power for the intercept,
• The higher the variance in the centre of the experimental space, but the lower the variances at the border of the experimental space.

You can read more here: https://community.jmp.com/t5/Discussions/why-are-no-star-points-in-custom-design-RSM/m-p/603144/high...

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@Thommy7571 wrote:

Am I right or is there nothing on DSDs on Nist.gov?  Is it finally perhaps not a good idea - using 6 or 7 factors - to start with a DSD if runs cannot be reasonably used for the following design? Why did nobody decvelop a design similar to CCD which bases on the DSD, since the latter is so useful for the gain of information?

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I haven't seen updates about Definitive Screening Designs on Nist.gov. You can check here the recent updates : : https://www.itl.nist.gov/div898/handbook/index.htm

Definitive Screening Design are very helpful at screening main effects and detecting possible strong higher order effects such as 2-factors interactions and quadratic effects. They are very powerful when dealing with 5+ factors, as they can significantly reduce the required number of runs compared to classical design approaches.

You can always use runs from any design using the platform Augment Designs. If you have run a DSD, you can augment your design into a Response Surface model design, very similarly to what you could get with a classical sequential approach with CCD.

The main benefit of the DSD is to start investigate non-linear quadratic effects from the screening phase : it avoids "binary" responses and discard a statstically non-significant factor that could have a quadratic effect. 

Hope this clarifies your doubts, and that the elements provided will help you find a solution,

[#7]

Hello,

I regret to need to indicate you that there is something wrong. If you have a look at the article on definitive screening designs of Bradley Jones and Nachtsheim (2011), there are no factorial points in the dsd. In your picture there is a point - the one n the corner at the bottom on the front part of the cube - which is situated -1,-1,-1.thus a factorial point. 

Thus factorial points are not indsd normall. I wonder how is it possible that there are no axial points by default since except for the center point there are no other possible points, especially no factorial points. I also wonder why nobody ever developped a design for further evaluation based on a definitive screening design. Finally the question arises what values should be used for the level -1 and +1 in case of given limits for the experimental values (e.g. 0 % and 100 % concentration. The experimental values for the axial points would need to be these ühysical limits. Are there recommendations how to select the values for the levels -1 and +1?  

[#8]

Even factorial points may sometimes represent factors combination that are impossible, dangerous or not feasible to run.
This was one of the reason behind the success of Box-Behnken designs, and also of Optimal designs, in which you can specify any constraints on your factors to generate a feasible design (and avoid impossible combinations).

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@Thommy7571 wrote:

 Are there recommendations how to select the values for the levels -1 and +1?  

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This is a vast question, and very domain-dependent.

Some advices or recommandations could be to use your domain expertise (or gather some domain experts) and/or use historical data (if available) to better assess the levels of interest in your design. You can also use Screening designs or the more economical Scoping designs to assess the practical feasibility of your experiments, as well as checking if your response measurement is discriminant enough.

Hope this will finally help you,