DoE when factors can not be changed independently

[#1]

Hi,

Can DoE be used where factors can not be changed independently?  In the illustrative example attached, we want to maintain a response when changing the scale of manufacture from 21 L to 21 m3.  To do this we need to establish which mixing factor to maintain.  The effect of maintaining each mixing factor can in turn be assessed on an intermediate scale (as shown in the table), but the act of changing scale means this is at the expense of all the other factors changing.  That is to say, the interdependence of the factors means that on changing scale, a maximum of only one factor can be kept at the same value as the small scale.

The table attached shows one way of doing this.

Is there a better way?

More generally, can DoE handle factors that can not be varied independently?

[#2 · Accepted solution]

Hi @kjwx109prime,

Not directly related to your specific situation, but yes, DoE can handle factors that can not be varied independently.

These factors can be handled in the design as covariates, factors that you cannot directly control, but that you can measure and know in advance of the experiments (not measured during the experiments).

There are several discussions about the use of covariates in DoE in the Community where you could find informations :

Define a covariate 

DOE custom design with covariates 

How to use covariate factors for space filling design? 

Covariate as a designing factors 

effect of parameter not being part of design, how to evaluate, treat it as covariate or something el... 

[...]

And a tutorial and presentation about how to use them :

I hope this answer will help you,

[#3]

Another approach is to consider nesting.  If the levels of one factor are dependent on the levels of another, this is nesting.  Covariates are used to handle factors you have no control over.

For example: You are trying to figure out what factors affect the quality of a drilled hole.  Two factors are bit materials (High speed steel vs. carbide) and drill speed.  The 2 levels for drill speed are contingent on the bit materials.  In this case, drill speed is nested in material type.  Although there will be 2 levels of speed tested for each material, there are different speeds.  Note, Nesting will not allow for the estimation of interactions.