I used categorical factors in a screening DOE such as 60min_at_70C or 30min_at_90C. In the next DOE I'd like to explore each factor (time, temp.) as continuous factors. Since time and temperature are linked to rate of reaction, I would like to constrain the times at each temperature. For example: 30-60min at 70C and 10-30min at 90C. Is there a simple way to do this in JMP and maintain continuous factors?
Thank you for your thoughtful responses. The "Response Surface" approach shown by Prof. Goos is well suited to my needs. Thanks to Prof. Goos the for excellent explanation and thanks to Ian for bringing it to my attention.
There are multiple options available, but they depend on what questions you are trying to answer. Before I offer my thoughts, I some questions about the dependent variables. You indicate rate of reaction is important, but reactions may not start throughout the "batch" simultaneously? What is the product of the reaction? Do you care about the "quality" of the reaction (e.g., % concentration)? How much of a change in the dependent variables is of interest? Are there other variables (particularly noise) that may affect the rate or quality of the reaction (e.g., purity of chemicals, ambient conditions)? Are you concerned with batch-to-batch variation of the reaction rate and quality?
It appears you ran an experiment with 1 factor a combination of 2 different time and temperatures. Of course, with this approach, you have confounded time and temperature. Now it appears you want to separate these confounded factors.
If you are trying to understand causal relationships between the two independent variables time and temperature and the dependent variables, then experimentation is a great tool (this approach may be different if you are trying to "pick a winner" (what is the best combination to get the "best" dependent variable results...in the current study!). For experimentation, you should start your study by choosing levels for the factors that are bold, but reasonable. Remember, you are not necessarily interested if all the combinations work. You are trying to create variation and study what factors contribute to that variation. Start bold and focus you study through iterations (possibly adding higher order terms as you go).
If you want to constrain levels for one factor dependent on another, this can be handled through nesting. You could nest the time (2 different levels) in temperature. Of course, if you do this you lose the ability to quantify the interaction effect, but this interaction is likely already known.
Another approach is to stipulate which combinations of factors you want to include. In the Custom Design platform, you can Define Factor Constraints (linear, disallowed). JMP can easily do this for you. I want to be careful here as there are many differing opinions, but IMHO, this defeats the purpose of experimentation. This approach is more the "pick a winner" mentality. Do you want to know what creates better reactions and what creates worse reactions. You don't just want all the "good" results. You want to create variation, the more you create, the easier to detect the factor effects. It is OK to have failed reactions while studying how to make better reactions! Rant over.
In reality, what option you choose is very situation dependent and we don't have enough information to provide advice as to what is your best option.
If I apply time constraints, they need to be unique for each temperature of reaction. I'm not sure that constraints for all trials is the right way to go.
You could also take a look at the second video by Professor Peter Goos ("Yield Maximization Experiment: A Response Surface Design in an Irregularly Shaped Factor Region") on this page.
did you try to put your lower and upper contrains into the linear equations?
