DoE design for a chemical reaction with time point data

[#1]

I would like to generate a DoE design to optimize a chemical reaction. In this example, let's say there are three factors to be varied, but I would also like to include time as additional factor. To reduce the number of reactions required to be performed, I would like to take samples at three time points and measure all the responses.

I think it would be wrong to include time directly as a factor in the DoE design and treat it the same as the other three factors, because this would be making the incorrect assumption that the time is being varied independently. 

My question is which is the best way to incorporate the time factor if I want to avoid having to run a separate reaction for each time point? I've been reading that split-plot designs could be used to handle this by creating a separate "whole plot" for each reaction and then each "run" within the "whole plot" would be an individual time point. I think this can be done by setting the first three factors as "hard" to change and time as "easy" to change. Is this correct?

Is this the best way to deal with time when setting up a DoE such as the one I've described above or is there a better alternative way? Is there anything else I need to be careful about or to consider when dealing with the time factor?

[#2]

Hi @djw238,

It seems that in your case, time is indeed not directly a factor, but more part of the response (time-dependant response), so I wouldn't include time in the design directly, but more use it in the recording/collecting of the responses.

The most appropriate way would be to use the Functional Data Explorer in JMP Pro, using time as X variable and your time-dependant response as Y variable, and specify your DoE factors as supplementary variables, so they can be used in the Functional DoE analysis platform, to vary your factors and see how the shape of your responses curves behave with these factors' variations.

If you don't have JMP Pro, two other options :
- Creating several columns for each response for the several time periods, and try with the "Group Profiler" to optimize all the several time-responses.
- You can also fit the several curves in the "Fit Y by X" platform (with time as X and response as Y), extract the coefficients of the best curves model for each experiment, and use the coefficients of the curves as a response in the DoE in order to optimize them in order to match a "golden curve"/ideal functional response.

I hope this first answer will help you,

[#3]

Hi Victor,

Thank you for reply. Since I will only be able to take a few measurements during the reaction (e.g. 3 time points), would this really be enough data to fit a response curve over time using the functional data explorer?

In any case, I unfortunately do not have JMP Pro, so perhaps your first alternate suggestion would still work.

Thanks.

[#4]

Hi,

Yes 3 points may not be optimal regarding the use of a functional model.
Another option in addition to my previous suggestions is to record "raw" responses measurements, but to use "transformed" responses that may be more useful in the modeling such as : maximum yield, maximum/minimum impurity, time to reach 25-50-75% yield, etc...
These transformed responses could provide better insights compared to "raw" responses and may highlight some antagonisms, like you can't optimize both maximum yield, minimum impurity and time to reach xx% yield, so it might provide indications about which compromise you have to choose.

I hope this additional answer will help you,

[#5]

There are several options as Victor points out.  It all depends on what you want as an outcome.  Is a mixture design needed for the correct combination of chemicals? Do you want to see if the response changes over time?  How will that help you?  Do you want to perhaps try and reduce the time required to achieve certain results?  Are you interested in  causal structure or to "pick a winner"?  What is your hypothesis regarding what is happening over time (what x's are changing over time)? How confident are you in your measurement systems?  Have they been studied or do you want to nest those into your experiment? Sorry, without more information, I am  unable to provide specific advice.  In any case, design multiple experiments (easy in JMP), consider what knowledge you would might possibly gain from each experiment  and evaluate that against the resources required.  Consider you might need to iterate.

[#6]

Thanks for the reply and the other points to consider when designing the DoE study.

In this case the goal would be to build an accurate model and hopefully predict the optimal conditions to balance the reaction yield with any impurity formation. The responses (yield and impurities) are expected to change over time during the course of the reaction.

I will think about your other points some more. Thank you.

[#7]

To build on @Victor_G's suggestion, another possibility is to calculate a time-independent response. In my previous experience running DOE on chemical systems, I would often take multiple time point measurements (as you are suggesting) and then calculate a time-independent response, like reaction rate constant (k) or a reaction half life (t1/2). In addition, you can calculate the rate constant at each time point. In a well-behaved system, the rate constants should be similar at each time point; so this is also a check to see if your reaction is well-behaved or if there are factor settings that lead to a stalled or accelerating reaction rate.

Good luck with the DOE!