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Custom Design: problems with highly correlated factors

Hi all,

Attached the factors and the script to run the custom design with the factors defined in the model. All the factors listed are known to be significant, and can only be accepted with a moderate correlation (<10%?) between them.

A custom DOE platform is used. JMP suggests a minimum DOE of 20runs and default of 36runs.

The problem is in the proposed DOE, some factors are very correlated: up to 85% correlation.

I tried to change the criteria to A-optimal/Alias Optimal, I increased the number of runs. the same parameters remain very – and too – correlated.  Can you tell how to decrease the correlations to <10%.

Could you please help?

Thanks, Valérie

 

Re: Custom Design: problems with highly correlated factors

Thanks Phil, Sam and Don.

 

Re: Custom Design: problems with highly correlated factors

Hi @Valerie_Nedbal ,

I don't think it will be possible to reduce the correlations below 0.1. High correlations between main effects and third-order terms of the same factors should be expected.

The example in chapter 5 of Goos and Jones (in the attached journal) is a good illustration. This is a design for 2 factors including all 3rd order terms. The correlation colour map looks horrible (below) and that is partly because it is an irregular shaped factor space. But it is also because it is not possible to have low correlations between main effects and 3rd order terms of the same factors.

Despite these high correlations, the experiment was a success, and they were able to build a useful model.

 

 

Re: Custom Design: problems with highly correlated factors

Hi Sam and Don,

actually, those high terms are known to be very important and therefore they must stay in the model. Do you know if there are any ways how to reduce the correlations?

Thanks in advance,

Valerie

 

Re: Custom Design: problems with highly correlated factors

@Valerie_Nedbal the effects with high correlation are the higher order effects that are placed into the model because the factor Frequency is specified as a discrete numeric factor.  In order to find the optimal design and force Frequency to be discrete, higher order terms (Frequency^2 and interaction of that with other factors) are placed in the model that is used to find the optimal design.  

I think that mostly likely, the actual model that would fit the data well would not require those higher order terms.  If you remove those higher order terms in the design evaluation then overall the design looks good.  Also, graphing the design out shows that is a nicely balanced design across all the factors.

This also depends on the goals of the experiment.  If this is for screening, I would say that it is a very good design.  For prediction or optimization, it might need some additional design points, or more replication within the existing design points.

 

Remove these in the Model in Design Evaluation:

Design Plot:

 

 

Re: Custom Design: problems with highly correlated factors

All the high correlations involve 3-factor interactions, either with main effects or with other 3 FIs. The 6 level discrete numeric factor seems a bit excessive. Why so many levels? The answer to this might hint at a better approach to creating the design.