Looking for help building a CCD RSM DOE with both blocks and custom axial levels.

[#1]

Hello,

I'm currently trying to build a response surface model using a central composite design, but I want to add both blocks and custom axial points. My study has 3 continuous factors and will need to be split into 2 blocks of experimenting, and I prefer to set my axial levels to 2.0 instead of 1.0 to explore more of the design space and help correct for non-linearity a little better. I can build my experiment in DOE > Classical > Response Surface Design with the CCD model to get my target axial level of 2, but I can't find a way to add blocks. Alternatively, I can build it in DOE > Custom Design by adding a blocking factor to my factor list and using the RSM model, but I can't find a way to set my custom axial levels. Can someone help me figure out how to add both customizations into a single study design?

Thank you!

[#2]

Custom design will give you an RSM design/model with blocking, but it will not be a CCD, and therefore, no choice on axial distances.

Classical designs will allow you to have blocking, but blocking will always be orthogonal which establishes the axial distance. If you change that axial distance, the design will no longer be orthogonal. But you could change the distance in the data table once the design is created.

So a question for you: why do you think you need the axial points? If you want to explore the design space further, adjust your low and high factor settings to the range you wish to explore and use Custom Design. Custom Design will not go beyond your low and high settings. Further, adding more levels to a factor does not really improve the estimation of the quadratic model terms. Assuming the quadratic model is correct, only 3 levels are needed, so anything more than that actually decreases the estimation precision. If you want additional levels because you are concerned that you may actually have a cubic or higher-order polynomial, use Custom Design and put in the higher-order terms and set their estimation to be "If Possible" to get a design that is robust to those possibilities.

Ultimately I believe the Custom Design is going to be the way for you to go to get a design that meets your criteria because it is the most flexible approach. I hope this helps.

[#3]

Hi Dan,

Thanks so much for your answer! I generally prefer to set extended axial points because my process tends to have unexpected cliffs and some fairly extreme nonlinearity. For example, while I only want to characterize the design space of ± 0.4 pH units, I need to know if my process stops functioning at ± 0.8 pH units to establish process robustness, and it is convenient to build those checks into an initial design space DOE as axial levels to save time later on. Admittedly, I was assuming that the more extreme levels also supported the math behind the DOE, so thank you for the explanation that the design prefers face-value axials rather than extended axials!

Honestly, I usually use a CCD RSM out of habit more than anything else, would you recommend any other DOE designs for characterizing a process with some fairly extreme nonlinearity and known significant factor interactions?

Thank you!

[#4]

I agree with everything my former (I'm retired from the JMP division of SAS) colleague @Dan_Obermiller wrote. On your second response...some of what I'm going to recommend depends where in your problem solving process you are and your apriori knowledge. If you are still in screening mode and are willing to assume negligible effects above second order, then maybe a Definitive Screening Design would work well? If more in optimization prediction land then perhaps an I-optimal approach? That way you can define the desired effects as part of design specification. And this 'nonlinearity' you speak of...is the nature such that a quadratic effect really wouldn't fit very well? My experience with 'cliff' type responses is quadratic effects don't predict very well over the factor space. If that's the case some nonlinear modeling approaches may be called for? Starting with the Fit Curve platform...try those first?

[#5]

Hi @MorganM,

Welcome in the Community !

You have received excellent responses by @Dan_Obermiller and @P_Bartell. I might have a different (and hopefully complementary) view on your topic.

The first question that comes to my mind is either you would like to understand the factors influencing your response variation, or if you are more concerned about the predictive accuracy of the response model. Since you mentioned "unexpected cliffs and some fairly extreme nonlinearity" and that your design consists in 3 continuous factors, I would perhaps consider Space-Filling Designs as an alternative option. Space-Filling designs are versatile designs that are extremely useful when the number of continuous factors is relatively low and the expected response highly non-linear.  Since you have two "scopes" in your experimental space and mentioned 2 blocks, you could proceed with a Space-Filling design iteratively :

1. Create a first small batch of experiments with extended ranges (-2 to +2 in coded levels like you mentioned for your axial points),
2. Augment the design in Space-Filling way and reducing the ranges to focus in the area of interest (-1 to +1 in coded levels for example).

This Space-Filling design option comes with (many) pros and cons, but here are the two main points :

• Pro : Points are homogeneously and randomly distributed in your design space, and enable various model fitting methods, from regression models to Machine Learning models (SVM, Gaussian Process, etc...). Good for model's predictivity.
• Con : This design is not particularly helpful for model explainability. If you want to understand the response variation in terms of main effects and interactions/quadratic/higher-order effects, depending on the model type used, you might not be able to get a simple understanding and decomposition of the relative importance of these terms (you could still calculate/estimate a posteriori features/factors importance on most Machine Learning models, but it can become complex). Points may also not be located at the borders of your design space.

You could also think about a sequential approach with a screening design first (to enable the creation of points at the borders of your experimental space), and then augment the design with Space-Filling design points. You can mix and match different design options sequentially with the platform Augment Designs.

To expand and complement the response from @Dan_Obermiller on the different use and benefits/drawbacks of the axial point distance, you can read a comparative study I have done on a similar topic : Solved: Re: why are no star points in custom design RSM - JMP User Community  

Hope this complementary answer might be helpful for you,

[#6]

Hi Everyone,

Thank you so much for all your input! I've done some digging in JMP and read over your responses and I think I'm going to switch this design back to normal axial levels to maintain the blocking factor for practicality in the lab. Unfortunately, I'm at a point in the process development life cycle of the unit operation I'm working on that I only have the resources to do up to 20 runs (I'm trying to limit myself to 16-18 in case I need to rerun any conditions) and I only have the time to do one study before I need to choose "optimal" conditions to send into an early proof-of-concept study. I'll have time to do a more thorough evaluation of the design space later in the project and I'll absolutely reference the advice you've provided here! But I think given my time and resource restrictions, a relatively simple RSM with 2 center points (16 runs total) in a moderately understood design space will be the most informative option for my purposes. If I can get the study run without needing too many reruns, I'll absolutely take your advice @Victor_G to augment with a few space filling points to flesh out the interior of the model!

Speaking to the long term goals of this project, I am primarily interested in evaluating how the levels and variability of my factors will impact my product quality attributes. While I'm in the early phases now, my end goal is to take this process from the research scale up to a manufacturable scale, so I'll need to not only find the ideal center points for my process parameters, but how the process performs at the edges of my spec limits. 

Again, thank you @Dan_Obermiller @P_Bartell , and @Victor_G ! You've been so much help!

[#7]

Maybe you are prepared for this already...but your last response raises a whole other issue. Scalability. Do you have some sense of the scalability pathway? When I worked in industry...well we had a wide variety of what I'll call scalable paths. Some translated very nicely from lab to production. Others? Not even close. For this latter case you may end up running repeated designed experiments to discover optimum process/product settings as you move along the scalability pathway. Good luck.