Analysis of CCD results

[#1]

Hi everyone,

I did screening desing and steepest ascent which showed me a saddle point. Then, I conducted experiment (ordinary central composite design) on this area to capture the curvature. But I don't know how to analyse the results, my model isn't significant with quadratic terms and the lack of fit is significant (the model only become significant when I raise my model to the power of 4).

Could someone please help me to understand more?

[#2]

Hi, Aaron

看起来温度是一个重要因子。

从3D plot上看，任意2个维度组成的曲线看起来不像一个抛物线。因此二次拟合效果会不好，高次拟合会造成过度拟合。

同理，如果把温度当作Z轴，剩余的两个参数当作X和Y轴，也看不出一个抛物曲面（想象一座山）。因此响应曲面应该不会很好。

高次拟合会取得更好的R平方，但是很有可能是过度拟合。

希望可以帮助到你。

[#3]

非常感谢您的回复

[#4 · Accepted solution]

I'm not seeing much as being significant here either. In fact, I do NOT see a significant lack of fit as the p-value for that test with the full response surface model is 0.2195. The main issue seems to be that there is not a large change in the response over the ranges you have selected.

Even removing the axial points from the design and fitting a full factorial model does not show any significant effects (and does not show a lack of fit either). I think that the variability on your center points (standard deviation = 5.22) is large relative to the standard deviation in the rest of the data. I will say that the ranges for your variables are not very wide. Typically, you want ranges to be wide enough to be able to detect an effect. A seven degree swing from the low axial point to the high and only a four degree difference between the -1 and +1 levels is not very large. 

[#5 · Accepted solution]

I agree with @Dan_Obermiller . The factors do not seem to have much effect on the response over the ranges that you have used. As a chemist, the temperature range does seem very narrow - intuitively I would not expect to see a big change in the response if I change the temperature from 175 to 182 degrees.

This might be a good thing, if this is a robustness study. The results here tell you that you could vary the factors over these ranges and get a consistent response. 

But it sounds more like this was an optimisation study. In which case you will have to experiment more boldly to obtain a useful model. You could use Augment Design in the DOE menu to add runs from an expanded factor range. 

An option is that you could include the data from your screening design. The combined data set will probably not be balanced but I expect it will include data from a wider factor space and might enable you to build a more useful model.

I have attached you data as a JMP data table.

I hope this all helps.

Phil

[#6]

Thank you very much @Phil_Kay  and @Dan_Obermiller  for your insightful comments.  Given that I did steepest ascent with 9 steps and saddle point was shown between step 3 and 4 which correspond to my range (176-180°C) (the response decrease from 4 to 9). Is it possible that this is only a local optimum?

[#7]

I am sure that is possible. I don't really know anything about steepest ascent methods.

I do still think that it would be worth looking at your complete data set with your screening and CCD experiments combined.

(I am assuming that the screening experiment data is not part of the data that you shared - from your description it sounds like you carried out a complete CCD on a different factor region versus the screening experiment.)

Maybe you would also include your steepest ascent data.

[#8]

Sure!

This model seems to be relevant with a non-significant lack of fit, p-value significant and R2, Radj and R pred also high

So I did steepest ascent to know how to increment each factors . This second experiment bring out the curvature area between experiment 4 and 5.

[#9]

Interesting.

How do factors A, B, C, D relate to the factors in your CCD?

Which of factors A, B, C, D are not varied in the CCD and what is the setting?

What is the level of factor E for the steepest ascent and CCD experiments? (From your screening design this seems to be the most important factor by far)

Is the response the same across screening, steepest ascent, and CCD? (You achieved much higher values before the CCD)

Thanks,

Phil

[#10]

• Factor D is not varied in CCD due to its low implication in the response, I've set it constant at 0.24.
• E was categorical factor so SA was selected instead of SB (despite showing better result...., SA is greener)
• So, removing the value of SB, higher values are achieve in screening experiment