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Thommy7571
Level I

axial points are not tken into account for designs?

Hello,

I wanted to add this question to my last post, but there is no button to edit it.

Id I create adesign, do I not need into account that in a further optimisation design axial points might be necessary? 

If I use the real maximum values for the points |-1| and +1 snd later I want to realise a rotable CCD with a  (coded) axial point at |3.36| how will JMP handle this? Why does it not take this into account in the frame of the creation of the design?

 

Sincerely

 

Thommy7571

 

 

 

4 REPLIES 4
Victor_G
Super User

Re: axial points are not tken into account for designs?

Hi @Thommy7571,

 

Did you check my responses to your previous post : extend Definitive Screening Designs to  Face Centered central composite designs (FCCCD) ?
Since we were discussing about factorial, axial and centre points, you might have already some answers there.

 

Concerning your questions :

Id I create adesign, do I not need into account that in a further optimisation design axial points might be necessary? 

If you want to create an optimization design (Response Surface Model design), you can use the platforms Custom Designs or Response Surface Designs.

Note that classical designs from Response Surface Design, like CCD, will use axial points with possible different distance values (depending if you want circumscribed (>1), face-centered (=1) or inscribed (<1) Central Composite design), whereas optimal RSM designs from Custom Design will only create axial points with distance = 1 (face-centered type).

If you already have a design you would like to augment to a RSM design, you can use the platform Augment Designs and see which points have been added to your existing design.

 

If I use the real maximum values for the points |-1| and +1 snd later I want to realise a rotable CCD with a  (coded) axial point at |3.36| how will JMP handle this? Why does it not take this into account in the frame of the creation of the design?

Concerning the value you would like to have for your rotable design, where does it come from ?

In a response from @Mark_Bailey to a previous post about CCD, you have the details behind the values of specific CCD designs, depending on the number of factors and/or runs : Re: Central Composite Design - Orthogonal Axial Values - JMP User Community

Does that mean your design has around 128 runs ? If less than that, I would recommend following the calculations provided by JMP in the platform, where the alpha distance value is calculated depending on your design specifications. Example here with a CCD for 4 factors :

Victor_G_0-1719228820549.png

If you still would like to change the axial value, you can edit your datatable after having created the design.
Note that on a practical side, I don't see the point of having axial points so far away from the centre of your experimental space (where the optimum is supposed to be, or at least close from it). The main objective of this optimization design is to be close from the optimum point to have a precise and useful model at the proximity of this optimum.

 

Hope this answer will help you,

Victor GUILLER
L'Oréal Data & Analytics

"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)
Thommy7571
Level I

Re: axial points are not tken into account for designs?

Yes I have finally 7 factors and the full factorial design would have 128 runs. But I won't realise all of them. I just wanted to have some buffer outside the range given by -1 and +1. The alpha value of 3.36 is calculatated for the rotary CCD by the formula given by Wikipedia  https://en.wikipedia.org/wiki/Central_composite_design, but it has been also used by RStudio. I think I know what you mean. The alpha value is not given before, so a circumscribed CC will not be possible. Instead an inscribed CCD would be suggested to extend the present design to a response surface design. Is that what you mean?

Victor_G
Super User

Re: axial points are not tken into account for designs?

Ok, so you're in the case described before, generating a 7-factors and 128 runs (starting at 144 runs in JMP in the Classical design platform for a CCD) would indeed generate an alpha value of 3.36 for a rotatable design :

Victor_G_0-1719233565497.png

If you're planning on augmenting an initial design to a CCD, then you may need to know "in advance" the total number of runs and centre points you will need to fix the axial value (if you're augmenting your design with the option "Add Axial") : 

Victor_G_1-1719233957696.png

So you could augment your design to a circumscribed or inscribed design type, but that will require to know in advance how many runs (and types of runs) you would like to add to your original design.

What I mean is that augmenting your design to a face-centered design is a lot easier in practice, as it doesn't require to plan number and type of runs, and you could generate several designs and compare them to see the advantages of bigger sample sizes. It is also a good balance between the two mentioned design types and ensure the factor values are physically/experimentally feasible.

Hope this answer will help you, 

Victor GUILLER
L'Oréal Data & Analytics

"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)
Thommy7571
Level I

Re: axial points are not tken into account for designs?

Hello, that is why I asked. If I want to extend a screening design later to a CCD it would be preferible to ask in advance for a value that is lower than the physically feasible maximum value. I know I could use a facial point but they are less adequate for models with nonlinear dependencies as the range is smaller. I wonder how the value of 1,97 is calculated for the orthogonal case, I found a value of 1,909 for 1 centre point with the formula given by Wikipedia.