A 2⁶⁻² fractional factorial design (FFD) was performed; however, due to experimental conditions and economic constraints, it is not possible to carry out another experiment such as response surface methodology (RSM) for optimization. Moreover, the fitted models obtained show a very good fit, and no curvature was detected. Therefore, we aim to validate the idea of performing the optimization based solely on the FFD.
You may or may not perform the optimization based solely on the FFD. Explanation is here:
No, it's not possible to reliably carry out an optimization based solely on a fractional factorial design, even if the model shows a good fit. Although the 2⁶⁻² FFD is excellent for identifying significant factors, it's inherently a screening design with confounded effects. The absence of detected curvature is likely because the design lacks the specific points needed to estimate quadratic terms; you can't be certain there's no curvature. Relying on an FFD for optimization, without confirming the location of a maximum or minimum, risks selecting a non-optimal point. Therefore, even with a seemingly good fit, the design itself is fundamentally unsuitable for optimization, as it doesn't provide the full picture of the response surface.
or
Yes, it is possible to perform optimization (numerical or overlay) based solely on a 2⁶⁻² fractional factorial design (FFD), particularly if the fitted models demonstrate a good fit and no curvature is detected. In such cases, the FFD may adequately capture the linear behavior of the system, making it suitable for first-order optimization. While fractional designs inherently involve aliasing, careful interpretation of effects and confirmation that critical interactions are not confounded can support valid optimization. If model diagnostics confirm reliability and the region of interest is adequately explored, optimization within the studied factor space is justifiable. However, the results should be interpreted with caution, and any conclusions should be validated through practical confirmation or pilot-scale testing.
So, its your call to take up the experiments on your own.
I agree that you must be aware of the confounding pattern. One example of a 2^(6-2) FFD and an approach for resolving the present confounding pattern and validate optimization by a few additional experiments can be found here: Article Multivariate methods in tablet formulation suitable for earl...
I appreciate your feedback. I'll take a look at the paper you sent me.
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