Response Surface Design with continous factors and one categorical factor

[#1]

Hello Fellow JMPers'

I am trying to find the optimum manufacturing parameters using the RSM approach. My design has 5 responses and 5 factors ( 4 continuous and 1 categorical).  I tried using the DOE- Classical- Response Surface Design; but when I get to inputting the factors, it seems the factors can only be continuous? I was using the CCD design. I am not sure how I can navigate this. When I go ahead with putting my categorical factor as a continuous factor then I get some meaningless variations in the design table since this category is supposed to have just two levels.

What I have tried to do now is creating a Custom Design and choosing the RSM under Model (and I get the message that the categorical factor cannot appear in the polynomial model terms), and I go on to select minimum number of runs, and in this case 22 (with 2 center points), or should I select the default number of runs which is 26?

My issue is I am not sure if this is the correct approach? and if it is how do I evaluate the accuracy of the design? I also read somewhere here in the forum that one cannot use CCD when the design is a custom design? So I am not sure how I can then use the RSM. My goal is to optimise my process.

There was a similar question some time ago but its not clear what the user ended up doing hence my question here. Also I cant seem to find the post anymore.

Thank you i advance for your contributions.

[#2]

Hi,

First of all, given what you describe, the Custom Design approach is the right approach. This is what Custom Design was built for.

22 runs is the minimum number of runs because you have specified 20 parameters to estimate (1 intercept, 5 main effects, 10 2-factor interactions, 4 quadratic effects) plus 2 additional centre points. I assume the categorical effect has 2 levels - more levels would require more runs.

By the way, centre points are not mandatory.

JMP suggests some additional runs as the default to give a better estimate of the experimental noise and more power.

Evaluating the accuracy of the design is a big topic. Too much to cover here. I suggest that you read Optimal Design of Experiment: A Case Study Approach by Goos and Jones if you want to learn more.

Be assured that the Custom Design from JMP will be the optimal 26 run design (with 2 centre points) for the RSM optimisation model for your factors.

Alternatively you could use a sequential approach of screening then augmentation for optimisation. This is a standard approach in situations where you suspect that not all of your factors will have an important effect on the responses. A Definitive Screening Design could be a good choice for your screening experiment.

I hope this helps,

Phil

[#3]

Add to what Phil has shared, I would ask if a preliminary screening design was completed before executing a Response Surface Design? Not sure what the cost of each treatment combination is, but it is beneficial to examine many factors that may be varying in a process and understand the sensitivity of a wider number of factors before a RSD. 

[#4]

Thank you @louv for your response. 

Yes I had previously done some screening runs before, and these factors influenced the target parameters.

[#5]

Thank you so much @Phil_Kay for your response.

Yes, the categorical factor has 2 levels. I ended up doing the Custom design with the default number of runs; in this case 26. Upon analysing the design, I realised that I have 4 runs which are exactly the same? Is this a mistake or its a way for the design to test reproducibility? I have attached the file if that would help.

[#6]

Hi @Incr_ch22 ,

Looks good. 

The 4 repeated runs are the centre points. You specified 2 centre points, which is the minimum number that the design will contain. Custom Design has determined that it is better to have 4 centre points.

I have attached an alternative. To be clear, I am not saying that this is the "correct" design.

The difference is that I set centre points to zero.

And I made Powder Mixture into a discrete numeric factor. That is, a factor that is numeric and continuous but can only take certain values (50 and 100 in this case) in the design. That might not be the right factor type but I just wanted to make you aware of the possibility.

The alternative design has some slightly different properties. The correlation between quadratic effects is a bit lower (check the table script for Evaluate Design >  Color Map on Correlations). So you should be able to estimate the curvlinear relationships with slightly better precision.

But really, there are no huge differences.

I hope this helps.

Phil

[#7]

Hie @Phil_Kay 

Thanks for the explanation, it makes a lot of sense to me. I knew about the discrete numeric factor but it had never crossed my mind that it could actually be applicable here. Your contribution (s) have been very helpful.

[#8]

Hello Phil,

I have the same scenario w/ Incr_ch22. But I want to add block it in to two. When I do it, the power of the intercept is very low. Is it okay?

[#9]

Hello @Incr_ch22,

Just to add some info to the excellent advices and explanations by @Phil_Kay.

Evaluating a design and its "accuracy" can be done in the design creation, just after clicking "Make Design", by looking at the informations provided in the "Design Evaluation" part. To understand the different parts in the design evaluation, you can look at the JMP help provided in the section "Design Evaluation" : Design (jmp.com)
This may help you evaluate you current design, and you can also compare different designs with this platform : create your tables for each design, then click on DoE -> Design Diagnostics -> Compare Designs, and then select the different models you would like to compare.

My personal feeling is that given the low number of factors, there is a high "risk" (or chance) that most of them will be significant in the analysis, so a sequential approach (main effects, interactions, and then quadratic effects or Definitive Screening and augmentation), or the direct use of custom design for a custom RSM model will best suit your settings.

Hope this help you a little more

[#10]

Thank you @Victor_G for the tip on the Design Accuracy. I am definitely interested in learning more and I will read up on that!