Response Surface Design - Central Composite Design

[#1]

Hi there,

I am trying to build a Response surface Designs for 5 factors. I was thinking to use CCD-Faced but I have a doubt on the design to choose from the options. I introduce the number of factors and when I have to choose the design, there are two option for "Central Composite Design" with different number of Runs:

1) Number of Runs: 28, Block size: -, Center Points: 2.

2) Number of Runs: 44, Block size: -, Center Points: 2.

(see attached image)

Does anyone know the difference between this two options for Central Composite Design?

Thank you in advance

Regards,

[#2 · Accepted solution]

The difference between the two designs that you have found in the Table of Designs is that the first 28 run design is actually a Resolution V, 16 run fractional factorial along with the 2X5 = 10, axial points and 2 center points for a total of 28 runs. The 44 run design would be the full factorial 32 run design plus the 2X5 = 10 axial points and 2 center points for a total of 44 runs.

A fraction of the design space plot is shown below to illustrate the variance of the 28 run CCD (RED) vs. 44 run CCD (GREEN) vs. a RSM design generated using the Custom Designer for 44 runs (BLUE).

[#3]

Is there a reason that anyone would want to NOT use the custom design feature in JMP? I  can't see the benefit of using these older "classical" designs, and am wondering if I'm missing something.

Until the definitive screening design (DSD) was invented a couple of years ago, I virtually always used the custom design feature (which sometimes would default to a classical design) for my work. Now I uae DSD for a lot of exploratory work, and the custom design to build out d- and i-optimal designs for honing in the details. While JMP offers us all of those older designs, I haven't been able to understand why using the custom design and the DSD hasn't obsoleted  the classical designs in essentially all cases.

I'd be very interested in hearing other thoughts on this point.

[#4]

We attempt to make all capabilities available. I agree that the custom designer provides the experimenter with the most flexibility to deal with any type of design challenge including constraints, multiple level categorical factors, mixture factors, discrete numeric and continuous factors. We feel the desirable approach is fitting the right design to a given problem rather than a fitting a problem into a prescribed design. Having stated that there are times folks have invested heavily in training in the classical DOE approach and the newer design methods are not in their comfort zone. In addition the so called "fear of complex aliasing" also weighs into their hesitation. Another comment would be "we have been doing our designs this way for years" and they have been performing fine for us so "if it isn't broken don't fix it". These are just a few of the barriers to adoption in my opinion. The reason why my response included the design afforded using the custom designer although that was not part of the question was to suggest that if I had finite resources and wanted to choose an experiment with as many runs I would investigate all my options prior to experimentation since the cost involved is heavily weighted on the experimentation side and not the setup phase of the DOE.

[#5]

Hi Louv,

I am going to do a central composite design optimization with three factors: two continuous and one categorical (with 2 levels). I wonder if there is a published research study having a similar design. Minitab is giving me 26 runs. The response optimization equation is given in two sub-equations each one related to the 2 levels of the categorical variable. Like this:

Categ. Var.
High               PDI = ……………………..

Low                PDI = …………………….

I am not sure how to report the data or if I am on the right way. A similar article can really help me or your and other friends’ ideas on how to report the data are appreciated.

[#6]

If I interpret your explanation, you have a CCD with 26 runs for two continuous factors and one categorical factor with two levels. I am unaware of this design.

You intend to model the response separately for each level of the categorical factor. Why not use a single model with interaction effects?

You should not use the CCD in this case. It is intended, like all of the classical RSM designs, for only continuous factors. Additionally, it is a large design that is not as efficient as the I-optimal custom design of the same size. The size of the CCD is dictated by the design method (composition), the the number of parameters in the full quadratic model, and the selected properties (orthogonal, rotatable). Custom design any combination of factor types, any combination of model terms, and I-optimality. The number of runs is up to you as you deem necessary.

[#7]

Thanks a lot for the input. I understand that CCD may not be a perfect idea. But what about thinking of categorical variables as blocks. I will have 13 experiments with the 2 continuous variables and then these 13 experiments will be doubled due to the two levels of the categorical factor. I have no problem with 26 runs. During analysis, I will get two different equation representing each categorical variable.

I appreciate your ideas. 

[#8]

Can you interpret the graph in your repsonse to ajanda?  thanks.

[#9]

Fraction of Design Space Plot

The Fraction of Design Space Plot shows how much of the model prediction variance lies above (or below) a given value. See Fraction of Design Space Plot. This is most useful when there are multiple factors. It summarizes the prediction variance, showing the fractional design space for all the factors taken together.

Fraction of Design Space Plot

[#10]

Thanks a lot LouV for the response, it was very helpful.