I had three numeric variables Temperature (48 - 60), Enzyme load (1 -4%) and alcohol to fatty acid molar ratio (1 - 4) . I've used the design expert software to optimize the conditions. I've chosen a quadratic central composite design with the following characteristics:
1. Type: Full
2. Not center points: 14
3. Center points: 1
4. Blocks: 1
5. No. of Runs: 15
the three dimensional graphs were plotted at fixed value of the different parameters (center points).
The experimental and predicted maximum conversions (93%) were obtained at temperature of 60, molar ratio of 4 and enzyme load of 4.
Recently I've received a reviewer comments on my paper, he said that he tried the empirical equation by MATLAB and he found that at temperature of 57.5C, enzyme load of 3.3 and molar ratio of 3.9, the conversion was 94.4% which is higher than the experimental as well as the predicted results I found.
First, does this mean lack in the experimental design?.
Second, How can I respond on this question to the reviewer?.
You have to check the assumption and methodology followed by design expert and compare it to the one he used to know where does discrepancy come from. I think you may try using other ways other than the quadratic one and check whether you will get better results or not. Best of tluck!
Try using Minitab software -Box & Benkhen statistical design when there are 3 variables and 15 runs. Hope this will help you.
Refer to :
https://www.wpi.edu/Pubs/ETD/Available/etd-082714-135653/unrestricted/How_to_Use_Minitab_4_Design_of_Experiments.pdf
Check your input data and expected out put.
This will helps you to correlate your experimental and predicted results. In Central composite design, I think it might be difficult to use 3 factors and 15 runs.
As suggested Dr.Shanthi try with Minitab.
Box-Behnken Design
Factors: 3 Replicates: 1
Base runs: 15 Total runs: 15
Base blocks: 1 Total blocks: 1
Center points: 3
In CCRD, 3 variable will normally give 8 full factorial points, 6 axial points and a centre point replicated 6 times; giving a total of 20 experimental runs.Please remember that in accomplishing optimization task with design expert, no unique solution is tenable. You may have up to 100 solutions or more depending on your choice.Therefore, it is possible that some of the solutions may return a response greater or less than 93% at different conditions. Selection of the optimal depends on the necessary trade-off you made. The MATLAB results shown above seems to be more viable and economical. Hence, you may wish to try the CCRD template given above and check the solutions
Regarding your first question, I don't think it has to do with the experimental design, this is an issue on the optimization of the empirical model (function) you fitted.I believe Matlab performed an optimization on the empirical model (compute first and second order derivatives, etc) and gave the settings that maximize it. I don't know how you obtained such settings, but note that your recommended conditions are one of the experimental points in the Central Composite Design (CCD) while the settings recommended by the reviewer are inside the experimental region. This is sometimes the case when the quadratic effects have a strong effect on your response. The CCD allows you to find the best experimental settings inside your experimental region given that your empirical model is valid. Therefore, it is good to investigate the whole region and provide the maximum or minimum using either graphical methods or a solver.
Regarding the second question, I recommend you to do the following. First, see if the settings suggested maximize the response. Also verify that is the global and unique maximum. Then you have three possibilities. One is that you work with the settings suggested by the reviewer. Perform some confirmatory runs on such experimental conditions. The second possibility is to argue that, for some reasons, it is easier to work on the experimental conditions you are suggesting. For instance, that is cheaper, less time consuming, etc.So you show that, although you did not reach the maximum, your settings are close enough and are easy to work with. One third possibility is to compute the confidence intervals for the predicted response on the two settings recommended and show that they overlap. So they are now statistically different.
If your result is a "% complete", you should use the logit transformation on your data.
If MatLab comes up with a different optimal solution, based upon your regression equation, that can be due to the fact DX uses float point calculations and your regression equation has 4-6 digits in each coefficient. The truncation in the coefficients can cause some issues.
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