How to build up a Face centered central composite design with JMP

[#1]

Hey JMP users,

I need to build up a Face centered CDD with 3 factors, each at 3 levels, 2 blocks and 4 center points. 

This is how I proceeded: 

1) select Classical > Response Surface Design 

2) add 3 factors > Continue

3) Here I don't know if I should select "Central Composite Design" or "CDD-orthogonal Blocks" as I need to add one blocking factors with 2 levels however the CDD does not allow me to add blocks and the CDD-orthogonal Blocks gives me one block with 3 levels.

Q1 : How should I proceed ?

Q2 : If I do the same with Custom design as it allows me to add blocks, that means it is no more a classical CDD design right ? 

Thanks in advance ! 

[#2]

When adding a blocking variable, the block will always be an orthogonal block. This is a good thing! For your situation there is no orthogonal design for two blocks. You need to use 3 blocks. With three blocks your axial points from your face-centered design will all be in the last block. The only blocking possible in the design creation process is a fixed block.

A custom design gives you more flexibility, but it will likely not match the CCD. There are multiple designs that could allow you to estimate the response surface model. However, this is where the nature of your blocking variable is important. What is the blocking variable? Blocking variables are also often called "nuisance" variables meaning it is not a factor you wish to study, but due to practical concerns it must change. Therefore, the Custom Designer is set up in such a way that you specify the number of runs per block rather than the number of blocks. Further, the custom designer allows you specify a fixed blocking variable (specific levels of the blocking variable or all possible levels) or a random block (the levels are a random selection from a larger set of possible levels).

There is much more that could be discussed with respect to blocking and the design types, but that would be better left for a design of experiments class.

[#3]

Thanks a lot for your answer.

The bloking factor is the membrane as I am considering the use of 2 different membranes for filtration. Does that mean that if I use 3 membranes instead of two, this problem will be resolved?

Another question : when building CCD there are different type to select at the first step, with different center points and blocking (see picture below). I don't understand what is the difference between the 4 CCD. 

I was trying to select Central Composite Design with 2 center points and then change "2" per "4" and jmp crushs. So the number of center points is fixed and could not be changed ?

Thank you in advance.

I

[#4 · Accepted solution]

If you really want to consider membrane as a block rather than a factor, then using a third membrane would resolve the issue. However, realize that you are treating your membranes as a fixed block, meaning that your conclusions are only good over those three membranes. It sounds to me like the membranes would be better treated as a random block. That would mean using custom design and calling them random and you estimate the variance due to the different membranes. You can change the membranes from fixed to random in the analysis phase of the project, if you want.

As for the differences in the CCDs, there are some slight differences. First, the biggest difference is the number of center points. 

The first design is a CCD with 2 center points.

The second design is a CCD with 4 center points which is the number required to achieve a mathematical property called Uniform Precision. However, that Uniform Precision is only achieved if you use the Rotatable axial distance. Since yours will be face-centered, you can ignore the Uniform Precision label.

The third design has a blocking variable, so it is a blocked design. That means that the blocks will be orthogonal. Since there will be 3 blocks, the number of center points should be a multiple of 3 so that they can be evenly distributed through the blocks.

The fourth design has 9 center points. This design would have Uniform Precision AND be orthogonal if you use the default Rotatable axial distance. Since you are not using that, it truly is just 9 center points.

Finally, after choosing your desired CCD (suppose the 2 center point design), you have the option to change the number of center points. You should be able to choose any number you want as long as there is at least one. If JMP crashes when you do this, what version of JMP are you using? If it is 15.2.1 (the latest), you should report it to Tech Support (support@jmp.com). If you are not using the latest version, you should probably upgrade to the latest version.

[#5]

Thanks a lot for your feedback. Actually I am using the 15.1.0.

[#6]

Dan has given some good "statistical" advice.  My thoughts would include...why are you doing an optimization design when you still don't understand the noise (membrane for filtration being one of the noise variables)?  It doesn't do much good to map the surface if the surface is continually changing with noise.

[#7]

Could you please develop ? for membranes I am using two new membranes for the 18 experiments. but I was wondering if it makes sense to add it as a blocking factor due to variability of the process conditions during DoE, but runs are randomized..

[#8]

Not sure exactly what you are asking, but the first questions are, since you are choosing 2 membranes:

1. How representative of ALL membranes are the 2 you choose?

2. Are you concerned with the effects of the factors changing based on the effectiveness of the membranes at filtering? You might think of this as membrane by factor interactions.

3. How much is the input material changing?

4. What other noise is changing between blocks, which will be confounded with membranes? (e.g., incoming material, environmental conditions, set-ups, etc.)

Here are some additional questions regarding membranes:

1. What are the membranes intended to do?  I will assume they are meant to filter particles of a certain size.

2. How is membrane "performance" measured/evaluated?  Is the measurement system capable? (what measurement system are you using?)

3. How much within membrane variability is there?  How uniform are the pore sizes within membrane?  Is this variability stable?

4. How much between membrane variability is there?  Is this variability stable?

5. How much variability in particle size is there in the incoming "material"?  Is this variability consistent?

Questions 2-5 can be answered with directed sampling or you can "nest" layers of these components into your experiment (within treatment).  My advice is typically, noise should be understood (e.g., identified, quantified, and tested for stability) before using ANY optimization type of design (mixtures, response surface, CC, BB, FCC, etc.).

Blocking is intended to:

1. Partition the noise (a chunk of factors not specifically manipulated during the experiment) form the design factors (the factors you are manipulating) thereby increasing precision of detecting design factor effects,

2. Increase inference space (by allowing noise to change during the experiment), and sometimes

3. Allow for estimation of noise-by-factor interactions (essentially the robustness of your model).

If you can identify the noise a priori (and assign it to the block), then treating the block as a fixed effect has some advantages.  If you cannot identify it then you are stuck with randomization.

A great Box quote (BH^2, p.102+):

"Block what you can randomize what you cannot"