How can I calculate desirablity space?

Question

I've run a DOE on a system with two process factors (time & temperature) and 1 material factor (reagent A level). My goal is to determine how the reagent A level affects the range of time and temperature that can be used to create an acceptable result. So far, I have used the desirability functions for each response to create a desirability formula that can be profiled, as shown below for a particular reagent A level:

Essentially I want to be able to compute a "desirability volume" under that green shape but above some threshold desirability (e.g. 0.5) that will represent a viable application space. An alternative calculation would be the average desirability above the target value.

What would be the best way to go about doing this?

Byron_JMP · Accepted Answer

Ok, so I'm not entirely sure I get what you're looking for here; however, I think you can get there doing a Monty Carlo simulation with your model.

In the profiler, turn on the simulator, add a spec limit to your response(s), add an appropriate distribution model for your x(s), and then click the simulate button.

You'll get the proportion below the spec limit given your assumptions in the simulator.