Which design to choose

[#1]

Dear All,

I am planning to build an RSM to optimize my method. I have 8 continuous factors and 2 responses. The levels of each factor were determined according to some internal methods and previous experiences of the team. I have no idea if there are interactions between factors or not. I can not identify the source of noise and I am planning to randomize

After a small research, I think they are two ways to do this, and I do not know which one is more suitable?
1) sequential experimentation using Central Composite Design (Box-Wilson) because I can run a classical screening design with some center point and continue if needed with axial points.

2) Use a Placket Burman design to screen the main effect and then a central composite design. And this way is the most used in my field

thank you

[#2]

You have more than two choices, but lets explore the options that you mentioned.

CCD - Your classical screening design would be the 16 run fractional factorial design + center points. This would be a resolution IV design, meaning your main effects would not be confounded with your two-factor interactions. This is desirable. Even if you do not see curvature, you MIGHT need to add some additional runs in order to fully understand the two-factor interactions, so you should plan on at least two stages of experimentation, and likely three.

Plackett-Burman design - The PB design is only 12 runs (+ center points), but it is resolution III, meaning your main effects will be confounded some two-factor interactions. Typically, this is not a great basis for a response surface design because two-factor interactions should be expected in an optimization study. So, you will likely need to have few of your 8 factors be "active" and will probably need to plan on three stages of experimentation.

But what about other options? For example, you could use Custom Design to create a design to estimate the main effects model. Then augment that to add interactions/squared terms. This approach could be similar to your classical approaches, but might be able to save you some trials. Further, you can decide which optimization criteria to use, so you could tune the different stages of the design for determining significant factors or for improving the prediction.

Another possibility is to use a Definitive Screening Design. This design is meant to be a screening design (which you are looking for) but can often estimate a response surface model as long as the number of active factors is near 50% or fewer of your 8 possible factors. This design can be accomplished in 21 runs, and that includes the 4 extra runs that JMP recommends. It also has the advantage of being completed in one set of trials rather than being built sequentially. 

For a situation that you have described, I would recommend considering the Definitive Screening Design.

I hope this helps. 

[#3]

Dear Dan Obermiller,

Thank you very much for your quick answer. I forget to mention that one of my factors is Discrete Numetic that I can take values 1, 2 and 3. The all propositions remain valid in this case?

best regards 

[#4 · Accepted solution]

A discrete numeric factor does complicate things a little bit, but not that much.

With a CCD, the middle level does not affect the fractional factorial portion of the design at all. If you need axial points, you will need to specify on-face axial scaling. No real changes.

With the P-B, again, the screening portion of the design does not utilize the middle level. When you go to adding axial points, you will need to specify on-face scaling. 

With the custom design, absolutely no changes.

With the Definitive Screening Design, discrete numeric is not technically available. However, you can create the design with that factor being a 3-level categorical variable. All of the advice stays the same.

[#5]

Dear @Dan_Obermiller,

I have one further question.

Before I start my real design I am performing some preliminary experiments and as a first step

I want to perform a fractional factorial design and I have 5 factors one of them is Hard to change. Using Custom design including a spilt plot design I got a table with 20 experiments with 5 whole plots. When I did the experiments I found a negative value in the Whole plots variation and I do not know what I should conclude from this? Attached please find a screenshot 

thank you in advance 

[#6]

One point of clarification: if you are using Custom Design, you are likely NOT getting a fractional factorial design for your situation. I just want to make sure you realize that Custom Design is using a different criteria to create the design. 

As for your negative whole plot variance, that means that your whole plot variance is quite small, and is most likely negligible. I have never been concerned with that negative estimate, and always focused on how I would use the information. Finally, one other point to keep in mind is that the design is created to estimate your model parameter estimates. The design is NOT optimized to estimate that whole plot variance. Therefore, there will be more uncertainty in the estimate, which is the typical reason for a negative estimate. The combination of a small value and the uncertainty can yield that negative result.

[#7]

Dear @Dan_Obermiller 

Attached please find my data, would you please have a look on it

best regards 

[#8]

There are many people in the community that would be happy to answer any question that you might have. Analyzing data borders on consulting services, which is further complicated by the fact that most community users will not likely know the objectives and background information to provide an appropriate analysis with conclusions. So is there a question that has not already been answered?

[#9]

Dear @Dan_Obermiller,

back to your proposition, in the software, I did not found how to include a 3-level categorical variable for Definitive screening design. Only 2 level - categorical variable can include 

many thanks 

[#10]

You are correct. I was going from memory, and forgot that a 3-level categorical variable is not permitted in a definitive screening design. However, if the factor is numeric, couldn't you consider treating your discrete numeric factor as continuous? DSDs will only use 3 levels, so it will not cause a problem with running the design.