(I'm assuming that you have already collected your data).
You could view the second video (by Robert Anderson, 'Using historical production data to identify manufacturing process improvements') at this link (SAS profile required). It uses observational data, but the mechanics of how to use JMP are the same.
At a high level, there are any number of possible ways to arrive at a solution which I like to call 'on aim, with minimum variability'. Using DOE you could take a purist Taguchi style approach and use his signal to noise ratios (lots of reasons to avoid this method...but I don't want to turn this thread into a Taguchi vs. Classical methods discussion). Another approach is to model the mean and variance of the response as two separate and distinct responses...then using JMP's co-optimization capability to help balance deviation from target with minimum variance. A third approach is through simulation.
Myers et. al. give a good overview of simultaneously modeling mean and variance in this reference:
Essentially it's no different than modeling two responses...of course you'll need replication within your design to estimate the variance for each treatment combination. All the usual co-optimization, simulation tools in the Fit Model platform, for the specific modeling personality you choose, will come into play.
On the simulation side of things one path is within the JMP Prediction Profiler (which I assume you'd use, since you can fit a model of your experimental results) you can use the Simulator from the Profiler framework to assign target values for each predictor variable, distributional forms for each variable, and estimates of mean and variance for predictors. Add other sources of noise as you see fit. You can even run a simulated experiment with the assumed mean and variance for each factor setting within the Profiler...so lots of different ways to go at this from a simulation point of view.
You can always used the log-linear variance model through the Fit Model dialog for this purpose. Change the fitting personality to Loglinear Variance. Then you define the linear predictor for the Main Effects (mean) and another for the Variance Effects as you normally would for a multivariate linear model. This way you also have a profiler for each. You can save the fitted models as column formulas and then use them in other platforms outside of the fitting.
You do not need replicates for this model, but they help. You do need a large number of degrees of freedom for the error.
Read more about it in Help > Books > Fitting Linear Models. Chapter 10 is devoted to this platform.