Answer:
Responses being correlated (unless totally!) does not create any issues. Press ahead and model each one individually and then put them together in the multiple response optimization with no worries.

However, you will do well by using Stat-Ease software's Custom Graph features to assess the relationships between responses before proceeding with further analysis. This will be very helpful for reaching your final conclusions.

For example, see the plot of R1 vs R2 below from the chemical conversion data provided in our program Help for the Response Surface tutorial.


         
In this case, the positive correlation (0.224) manifests as pink on the grid. Negative correlations are shown in shades of blue. The intensity of the colors relates to the degree of correlation, e.g., the dark reds for the squares connecting any variable with itself (such as Run vs Run at the upper left corner of the grid).

This particular matrix of variables—stemming from a central composite design (CCD)—displays white boxes for A versus B and C, and B versus C. This is ideal—no correlation between the factors.

By following the tutorial through the optimization phase (part 2), you will see that the correlation of responses does not hinder the final outcome—a maximization of conversion with activity (a product quality attribute) exactly on the specified target.

PS I highly recommend using Custom Graphs to view not only the relation of responses, but how each gets affected by individual factors. Try its features to size or shape the points in different ways. Perhaps this will provide more insightful visualizations. Also, try 3D views, which can be rotated. Continue on by exploring other features in Custom Graphs.

(Learn more about multiple-response process optimization by enrolling in the next Modern DOE for Process Optimization or, if you develop products, an upcoming Mixture Design for Optimal Formulations. See the current schedule of workshops below.)

Check out Rachel Poleke's 2023 Online DOE Summit Wrap-Up for free recordings of a great series of talks by DOE experts from Stat-Ease and around the world. I found it interesting that immediately after my presentation on a “Masterful experiment delivers delectable chocolate chip cookies” came a talk on “Application of DOE in the development of an alcoholic beverage”. This provides inspiration to develop optimal pairings of cookies with the ever expanding selection of craft seltzers and ready to drink cocktails. ; )

I will present two webinars in February for professional societies:

New features released for Design-Expert^® and Stat-Ease^® 360!
Our developer team released the following new features in mid-October (*asterisked ones exclusive to Stat-Ease 360):

• Gaussian process models (GPM) for noisy responses*—previously GPM only worked on deterministic responses, for example from computer simulations
• Lifetime analysis with Weibull*—this tool for reliability DOE comes via a Python script
• Transpose tables—simply right-click on the top-left header cell to re-format
• Analysis summary now includes lack of fit and curvature p-values—very helpful for comparing models
• Excel import/export—previously available only in SE360, this handy tool is now provided in Design-Expert

Contact our Sales team now to purchase a license or lay out the path for an upgrade to these leading-edge statistical tools developed by the world-class team of Stat-Ease programmers, statisticians, and engineers. Stay tuned for further upgrades per our “release early, release often” approach, which keeps our users at the leading edge of DOE tools.

PS We encourage all licensees, e.g., v13, to, at the very least, update their current version (but better yet to the newest release!).

• November 30—Keys to Analyzing a Response Surface Design by Shari Kraber
• December 6—DOE Crash Course for Experimenters by Shari Kraber 
• December 12—Curso Intensivo en Diseño de Experimentos (EN ESPAÑOL / SPANISH edition) by Steven Zagarola

Expanding on this succinct advice and other guidance by Box that he provided in presentations I attended (also in “Split Plot Experiments,” Quality Engineering, 8(3), 515–520,1996), I suggest that experimenters:

• randomize what they can,
• group via split plot and/or block out what they cannot;
• but, if necessary, rather than going back to one factor at a time, that is, abandoning DOE, they proceed in whatever run order they must.

If an experimenter does abandon randomization in their design, they should pay little attention to the statistics and, instead, focus on the magnitude of effects as a matter of practical importance.

Circulation: Over 2500 worldwide