Hello everybody
I used a RCCD to optimize phenolic compounds extraction parameters of a plant. Before this, I performed a factorial design to choose an adequate zone. As a result, central point was used for optimization. Levels for the factors in RCCD were adjusted near to central point values. Finally, response surface was generated (image attached). The aim was to obtain the highest phenolic content but it was opposite. Lack of fit was significant which indicates that experimental values don't adjust well to the model.
It is known that central points show repeatibility of treatments in an experimental design, but what happen if a RCCD is generated from a factorial design in which central points (0/0) showed an optimum zone to work besides of other treatments (+1/+1, +1/-1 or -1/-1)? I mean, I worked in an optimum zone through RCCD but response surface is opposite when it must reflect a maximum optimum. How do you explain this?
Thank you in advance.
Hi Andres, the central point is important to explain the combined effect of two or more different variables. According to your figure, I believe that you are long away from a maximum region. On the other hand, an increase in the solvent quantity always increases the compounds extraction.
Dear Dr. Mario
I edited the question. Please, share your advice. Thank you.
Regards
I suggest that you actually do an experiment at the central point in your experimental design and observe the magnitude of difference of this mean of experimentally obtained values with the predicted mean response of your regression model obtained based on the RCCD. You are saying that the model shows a significant lack of fit, it could be that the curvature of the actual response surface in the region of experimental space you are considering is far more severe and more complex than that can can be modeled by the Quadratic Model associated with RCCD. I suggest in this regard you can use a more sophisticated regression model, containing higher order terms that is also compatible with the RCCD, or use a more complex type of Experimental design that suits this new type Regression model, and do the parameter estimates accordingly.
You used a factorial design with center points. With this DOE, you can estimate main effects and eventually interaction effects, depending of the resolution of your design. If the center points are out of the confidence interval for the prediction at the center of the experimental domain, it means that at least one factor has a quadratic effect, but you cannot know which ones. To answer this question, you must add experiments. This can be easy with a central composite design, because you keep all the runs from the factorial design.
If you have a center point effect (curvature effect), you cannot interpolate your model with main effects and interaction effects (eventually) because you don't know what factors are responsible of the curvature.
When you analyse the results of your DOE, did you remove non significant effects? Examining the contour plot with the experimental results does not show evidence effect of the factors, but it can be an "optical" effect.
With the data, it would be more simple.
Hope this can help you.
Pierre Chagnon
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