RSM - CCD for 29 iterations of an experiment

[#1]

Good day! Me and my group mates are currently doing our thesis and we have been instructed by our adviser to make use of JMP for RSM and CCD. We don't really understand how to go by it. We have 4 variables and we would like to test their effect on three other variables. If we just do CCD with 4 continuous factors then we would only have 26 runs and we're confused because it will only fit 26 of the results when we need 29. We're sorry for the ignorance, this is our first time making use of JMP. We're using JMP Student Edition and attached is the sets of data we would like to treat with columns 1 - 4 being the factors and 5 - 7 being the affected variables. Again, we apologize for any wrong terms, it really is our first time making use of this software and treating data like this. Thank you for all the responses! 

[#2 · Accepted solution]

Hi Furiosoreo,

Where has the need for 29 runs come from?

The way that a CCD will work is it will take the number of factors (4 in your case, so k=4) and then produce a number of runs based on the addition of a factorial portion (the 'corners'), the axial values (the extreme values) and the number of centrepoints:

Factorial portion = 2^k = 16

Axial portion = 2 x k = 8

Centrepoints = 2

Sum number of runs = 26

In your case, you can add more centrepoints to make it up to the 29 value.  You will also want to consider what type of axial values you are using, in the case above I've mentioned axial values as 'extreme' (usually sticking outside of the cube made by the DoE), but they can on the face, orthogonal or 'rotatable'.  

Rotatable is a popular choice because the final model has equal prediction variance, whereas a 'face' choice may be better when you can't go to the extreme values that the design demands.

Here's an old but gold resource from NIST that I used to learn about CCD's back in the day, I'd recommend you give it a read.

Thanks,

Ben

[#3]

I'm not really sure as to why there is a need for 29 runs because there are 5 centrepoints in the data set that we are going to treat that and we gave values of -1 to the lowest values under LA, FA, SF, SP 0 for the middle values and 1 for the highest values. According to our adviser we need to replicate the surfaces given in our reference paper and from there we'll do fuzzy optimization of the data sets that were given. Attached here is the reference paper we will use. Thank you for the response, the material is proving to be useful. For reference, our thesis is called Fuzzy Optimization of Lateritic Concrete Mixes and we will be using the data set from Table 6 in the reference study. 

[#4]

Looking at your results, you are trying to recreate a face centred CCD design

Having a look at the data, I changed the columns into a 'Pattern' (this makes them easier to read), as you can see, the number of replicates seems to be randomly arranged in pattern.

I've tried to reproduce this in JMP with a face centered CCD

And a Box-Benkhen design

And I can't get them to match what you've put in your original table, as you can see these designs will simply add more centrepoints, if you add replicates, it will add them for each pattern.

Thanks,

Ben

[#5]

Hi @furiosoreo,

Welcome in the Community !

@Ben_BarrIngh gave a lot of information on the design part. I can also recommend using Design Evaluation platform, to better assess the performances of your design in this experimental space, and generate several designs and use the platform Compare Designs to choose the most relevant design for your use case.

I would like to mention some data and analysis potential problems :

• In your datatable, there seems to be a typo in column 1, row 25, where the value is "74375" instead of "743,75". I also have some doubts on response value for column 7 "296" (might be "2,96" instead ?).
• When fitting Response Surface regression model to your response columns, a strange pattern appears in tthe predicted vs. actual and residuals :
  

  It seems you have a strong difference between response values depending on the factor 1 that leads to the creation of 3 groups of points. Did you realise the experiments in the order of the table or did you arrange the order of the experiments by the value of factor 1 ?
  I wonder if this groups situation is linked to a possible re-ordering of the experiments, or if the ranges difference between factors may explain why experiments can be grouped by factor 1 values. I would recommend trying to validate your model for factor 1 levels between min and middle levels, and/or between middle and max levels, to be sure the trend is consistent over your experimental space. 

Hope this complementary answer may help you,