Central Composite Design (CCD)

Hello !

I would like to obtain response surface for a problem driven by 4 variables. Hence I defined 5 levels for each variables (-alpha;-1;0;+1;+alpha), and used a CCD approach.

However, the extremum of one variables(+alpha and -alpha) seem to degrade the results.



I am fairly new to designs of experiment, and I would like to know the implications of only having 3 levels for 1 variable while having 5 levels for the others. Is the model still valid if I stay within the defined boundaries? Is there maybe a value or a set of values I can track to validate the model?

Any help is more than welcome =)

 

Sure ! I uploaded and xlsx file, hopefully anyone can read it. It is a copy paste from Minitab18 CCD sheet if it can help.

The "*" means this simulation was not done, because the parameters were not realistics. Since the results come from a numerical simulation, all center points (0,0,0,0) have the same value.
"A" is the parameter I have a problem with, so I woud like to remove simulation n° 21 and 22.

I can send you the minitab file if you want !

Thank you so much for spending time on my question !

 

I just logged from another computer and saw the size of the image I inserted inside my first message..... I'm really sorry this is so large ! A modarator can delete it, it is not required anymore since I uploaded the data set

 

Alright, I'll follow your advice, thank you so much !

I have a second question: what parameter(s?) should I check at the end to assess whether or not the model is valid ? So far I am using the histograms I showed you in the first post, but it feels like a very "light" validation. Is there something else I should check ?

Again, thank you very much for you time

 

They did not show up for me either until I switched for a much bigger screen. Anyway, thank you very much for your help, I'm going to launch these simulations tonight, I should get the results in a couple of weeks ! =)

 

Hello, me again !!

I managed to get my hands on a similar study done a few years ago, and I did exactly what you advice and used a Face Centered design (data attached). I have a few questions if you have a little more time to share:

I have two outputs for the simulations. The first one is a width (see data). This is basically what I would like to predict. Minitab gives me a R-sq(adj) of 94,2% and a R-sq(pred) of 76,66%. This numbers a quite high, but I am concerned about the difference between the two. I tried and fitted with a small enough error other points (not from the original set) to the model. However, I am wondering whether I just was lucky, or if given the R-sq(pred), this is normal. Any thoughts ?

As you may notice from the Pareto chart, when taking the width as an output, one of the parameters ("size") clearly dominates the model. To further study the influence of the 4 parameters, I normalised the output using the dominant variable (output called "width ratio"). The Pareto chart that is obtained seems to properly reflect the physic behind the simulation, however, R-sq(adj) is now equal to 83,21%, and the R-sq(pred) equals 34,46%. I realise the prediction is rather uncertain, however, I do not want to predict anything, I just would like to see the main trends. Would that model be reliable enough ?

Whether or not you reply, I would like to thank you again, you have already been of great help !