I performed 17 experiments according to BBD design and RSM methodology. I had 3 numerical factors on 3 levels. However, one factor was in range from 1 to 4, and according to BBD coded values are (-1, 0, 1) which results with real values (1, 2.5, 4): However, due to the process limitations i used in experimental plan process values (1, 3, 4) or integer numbers of the proposed with BBD. Obtained model were statisticaly strong and significant. Experiments were time and money expensive so I dont want to repeat experiment, but I am interesed can I be sure that my models are good due to the fact that these models will be part of my PhD thesis. Thank You.
No, using 3 instead of 2.5 in this case is just wrong. The whole purpose of BBD and similar designs is that you should have three equidistant levels. 1, 3, 4 are far from being equidistant.
Besides, you introduce a strange artificial bias if you always round 2.5 to 3. It would be equally correct to round it off to 2. In order to avoid introducing a bias, perhaps you can round your 2.5 to EITHER 2 or 3, in a random fashion?
Thank you for your answer. Furthermore, Design Expert software allowed me to put 3 instead 2.5 and all experiments were performed for 3 as well as analyis. I also put data in historical design where i used 1,3 and 4 as categorical factor. Difference on predictive models for BBD and historical plan are negligible with strong R Squared. You really think this kind of pretrubation od wrong? Could i use than historical data design as relevant? Obtained model is also very similar to ANFIS model, but not completly same as expected. What do you think about both models obtained with BBD and ANFIS comparison?
Ideally, the experimental levels must be equi-distant. In your case, if regular coding formula is applied, the coded levels for original level (1, 3, 4) would be (-1, .33, 1) instead of (-1, 0, 1). This results in loss of design properties, for example, the G-efficiency (indicate the power of prediction) is reduced by 4%, etc. Regarding the estimation of the model coefficients, the sensitivity of the factor level change matters. If practically, the factor at 2.5 level performs as equally as at the level 3, the response values obtained would be more or less the same in either cases. In this case, only the statistical properties of the RSM will be affected. Many studies have compared performances of RSM based model and ANFIS model, and found that ANFIS model perform better than RSM model.
Honestly, if I were one of your PhD examiners I would not accept your thesis with this biased design, because the obtained statistical model would be certainly wrong.
Furthermore, I assume that you wish to publish this study after years of laborious work and in this case you will find difficult, if not impossible, to publish it.
So, I suggest that you would rather perform a new set of experiments using equi-distant values, as other researchers have advised you.
Good luck with your doctorate.
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