DoE design for a chemical reaction with time point data

Question

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?

scott_allen · Answer

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!

Victor_G · Answer

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,

djw238 · Answer

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.