Comparision of two DoEs and how to include controls

Question

Dear JMP-Experts,

I created two designs which you find in the attachment. I deleted the DoE dialog scripts cause of data security and provide here only the statistical plan for the experiment. Both are DoE plans with RSM modelling. The Design should be used for optimizing based on existing data.

Plan1: Here, factor settings for a continuuos and a categorical factor are set. However the categorical factor includes not only the type of a substance but also the concentration of the substance, and additionally one level has neither the substance nor the concentration. I marked it in the number 4 as a legend for the JMP experts here. Overall I end up with 17 runs, a control for the substance is already inlcuded, but I cant fit the concentration dependency of the substance in this plan, since it is a categorical factor.
Plan2: Here I didnt include the control, and separated the concentration of the substance and the substance type from each other. However I dont know any way to include control runs with conditions without the substance (and only the other continuuos factor is varied) in this model. Thats why I added by myself three extra runs with control and missing factor 2 and 3 (See legend).

Now my Questions:

1) What would be the better DoE approach for my purpose, Design 1 or Design 2? And why is one design better than the other? How can I judge this by myself? I want to identfy the optimum for Factor one, the optimal concentration for factor 2 and the best type and compare it in the design analysis platform with the control.
2) Is there an option to include the data from the control in the fitting procedure from Design 2, even 2 factors are missing. It would be great if there is an option to compare the control quantitatively and statistically with the result from the RSM experiment.
3) is there another, better design for my approach, I tried different things (even constraints) but it didnt really work for me.

Thanks a lot for your help in advance!

Design_2_JMP.jmp

Design_1_JMP.jmp

Victor_G · Answer

Hi @DualARIMACougar,

I understand that having a design with only 2 levels for a continuous factors (and the min level is 0) wouldn't be a good idea in your case since it ends up being a categorical factor with absence/presence.

However, you have assumed a RSM model (so quadratic effects are investigated, and you have 3 levels for X2) and you could perhaps force the generation of intermediate levels for this concentration continuous factor, by adding higher order effects (depending on the number of levels you want to investigate for the concentration factor) in the assumed model, or simply force the introduction of intermediate levels in the design by configuring factor setting type to Discrete Numeric ? This could force design generation to have intermediate levels as desired (to avoid absence/presence configuration but still have a min level set at 0), that you could reset for the analysis as continuous.

This conversation may help you : force levels in DoE

You could then use the Disallowed Combinations option to avoid non-feasible or "non-sensical" runs.

This option could be helpful to integrate control runs, as you would study the concentration range in a non-discontinued way, from 0 to max levels with intermediate levels.

Please find attached a design proposal for this scenario based on my understanding of your problem, with an RSM model assumed and 2 "control runs" in the design thanks to the Disallowed Combination used :

Substance type == "Control" & X2 >= 0.001;

To force the design generation of X1 values that match the control runs, maybe setting X1 as Discrete Numeric with the 3 levels 5,5 - 6,45 - 7,4 would do a better job and would enable to have your 3 control runs in the design.

Let me know if this option makes sense,

Design_3_JMP.jmp

DualARIMACougar · Answer

Hi Victor,

fiirst of all I want to thank you so much for your professional help each time, when I post a question in the JMP community. Your expertise is highly appreciated.
The goal here is to optimize type and concentrations of a formulation. Factor interactions are expected and not known. The substance type and concentration will have most likely a factor interaction due to its nonlinear concentration dependent chemical state change. I have to include a control here to account for the case when this substance class (where two types are tested) is not abundant and since I want to test a concentration range of each type and the effect is only appearing above a certain concentration, I cant simply set the lowest factor setting for the concentration to zero (cause I will end up with only two physical concentrations in the RSM (0, concentration 1, concentration 2). Yes the control is a assessment, if the presence of the substance type is 1.needed (and yes screening design first would be an option but not choosen) 2. I want to test for the effect of factor 1 in the abscence of the substance and still want to run everything together.

I now came up with a solution, where I include a dummy category called substancepresence into the screen and I model for this additionally account for the difference between the presence and abscence of the substance class.
I have no idea how to use split plot design and nested effects together to include my control.
Further Ideas or input would be highly appreciated!
Thanks again

Victor_G · Answer

Hi @DualARIMACougar,

It's hard to answer your questions, as it's more a question of domain expertise, objectives, and prior knowledge of the system :

* What is your goal with this experimental setup ? Understand relations between factors and responses or choosing a winner setup ?
* Do you suspect an interaction between substance type and concentration that could justify separating these factors and using them independantly in the design ?
* What is your use of the "control" ? Is it used to do relative comparison/assessment with the other experiments ? Or does it reflect actual conditions used for the system ? Why would you like to enforce these conditions ?

Based on your objectives, I would think that design 2 may be more suitable, as you independantly study the substance and its concentration, which could help increase the inference space and detect potential interaction between these factors.

You coul still add runs from your control experiments in the datatable to compare the relative performances of your experimental runs to your control runs. However, I wouldn't use these control runs in the modeling, as the conditions may be outside of your design space (concentration starts at 0,04 and your control runs are at 0 ? And is the substance type used in the control runs also used in the experimental runs ?).

You could also perhaps Restrict Factor Level Combinations to have the control runs inside your design space (for example specifying that if factor susbstante type = control type, then concentration is approximately 0), or use a nested design and modeling approach, through the use of Designs with Randomization Restrictions like Split-Plot designs and the use of Nested Effects. Some discussions about this type of designs and analysis :
Disallowed Combinations not working 
Using disallowed combinations to remove a factor from the DoE 
How can you add control runs to a split-plot design? 
Custom Designer and Random Effects / Desingn Evaluation and Random Effects

Hope this answer may help you,