I ran a experiment in design expert and obtained three identical runs which seems weird. Checked few papers and they have three identical runs too and are published. Whats the reason behind this?
The selection of a particular range of critical components in RSM (CCD/Box-Behnken) is a prerequisite. The identical runs you are asking about are the central points of the range you selected. It's better that you run a higher number of the central points which give very good results. You can even select more than 3 central points in that case.
You can check my profile for RSM related papers.
2 components are involved in the process model development. They are terms in (i) model equation and (ii) error. Generally, error may be due to lack of fit of model or experimenter's lack of knowledge. If the error is due to experimenter, then the significance of error term is notified from centre points (identical runs). More centre points reveal the signifiance of experimenter's performance.
Selvaraju Sivamani
Prashant Kishor Bhagwat
My concern is that when we input three factors for 15 runs before carrying out experiments, I have three identical runs placed separately.
I did check few papers , they have 3 identical runs as well.
What is the reason behind this ?
2 designs of RSM are central composite design (CCD) and Box-Behnken design (BBD). Number of experiments to be performed according to CCD is 2^k.2*k+c and according to BBD is 2*k*(k-1)+c where k is number of factors, c is number of centre points. The value of k is minimum 2 for CCD and minimum 3 for BBD. The purpose of identical runs (c in the above equations) is to identify the experimenter's ability in experimentation.
Dr. Selvaraju Sivamani ,
Thank you so much. This clarifies my query. Do you have some papers for reference of this quote. Anyways, such a help.
Thanks
Sushil
My publications on RSM-BBD:
Article Response surface optimization of acid pretreatment of cassav...
Article Process design and optimization of bioethanol production fro...
Article Optimization of bioethanol production from cassava peel usin...
If you are going to run a 2^3 design with all continuous variables the most efficient use of your time would be to run two center points for a total of 10 experiments. Assuming the usual precautions of randomization you should analyze the results. The two center points give you replication as well as a test for possible curvilinear effects. You can throw in more if you wish (for better estimates of error) but the whole point of DOE is minimum work for maximum effort. Three full replicates of an entire design is a poor allocation of time and effort. The two center points in addition to the usual terms from the basic 8 point design should give you a pretty good understanding of the behavior of the 3 variables of interest.
The value of the replicated center points is to give you the ability to compute pure error and thus, by subtraction, lack of fit and to give you a visual indication, via the residual plots, of the need for investigating curvilinear effects. Since the center points will not allow you to identify the variable(s) contributing to the curvilinear behavior you can put in the square of any one of the model terms and have it enter the final regression as significant. Under these circumstances inclusion of the squared term does nothing more than make your residual plots look nice and, as you noted, inflate your R2. Sushil Koirala
nothing weird, it's just a replicate of the center points (at the same operational conditions) which must increase gradually with the number of factors and is used to better estimate the pure error ( increase the probability of detecting significant)
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