nav[aria-label="Primary Navigation"] { padding: 0; & ul { list-style: none; width: 100%; display: flex; flex-direction: row; justify-content: start; align-items: start; gap: 30px; padding: 0; & li { margin: 0; } & ul li { list-style: none; } } }

Randomness in DOE Factors

Jasean

I am designing a 3 factor experiment with all factors continuous. For one of the factors (of most interest for predicting the response), I cannot SET the values of the levels. Instead I have to choose from a sample of values that are "close" to the desired level. For a given level of this factor, I should be able to confine the actual value to within about 5% of the range across the levels. Is that close enough to consider it "set," or should the randomness be accounted for (in the design or the analysis)? If the latter, how? Is there general guidance for when a factor can be considered set versus random? What is it? If you look closely enough, every real world factor setting includes some component of randomness.

Thanks

Accepted answers

MathStatChem

I think in your situation, it doesn't matter practically that the target factor setting has some small amount of noise when you execute the experiment. One way to check the impact of the variation in the factor settings is to use the design evaluation tools in JMP.

For instance, I generated a 3 factor design in Custom Design, and then modified one of the factor settings to have +/- 5% uniform random noise around the factor setting. Here are the two designs

The design comparison of these two designs shows that they are practically the same, as far as their statistical properties are concerned:

All comments

Mark_Bailey

I think that there are possibly two issues in your question but I can't be sure.

Randomness in a designed experiment has to do with producing a run:

You randomly select the treatment (conditions) and the experimental unit.
You reset all of the factor settings before each run.

If you have a hard to change factor that is difficult or even impossible to reset every time, then you should indicate that fact when you specify the factor (Changes) in Custom Design. This change makes a split-plot experiment.

On the other hand, you might not have the control necessary to achieve the desired factor setting. If that is the case, then simply update the data table so that the actual factor level replaces the original design value.

Jasean

Mark, Thanks for the response. I think I didn't ask my question well. As an example, I have a factor that is a property of my experimental unit, like bulk resistivity. It is practically impossible to have multiple experimental units with exactly the same bulk resistivity. However, I can collect a sample of experimental units that have "high" bulk resitivity, and a sample that have "low" bulk resitivity. The range within one level of the bulk resistivity factor is about 5% of the difference between "high" and "low."

Randomizing runs and changing bulk resistivity between runs are easy, but getting multiple samples with exactly the same bulk resistivity is practically impossible.

MathStatChem

For instance, I generated a 3 factor design in Custom Design, and then modified one of the factor settings to have +/- 5% uniform random noise around the factor setting. Here are the two designs

The design comparison of these two designs shows that they are practically the same, as far as their statistical properties are concerned:

Jasean

Ah, that's a good idea. Thanks. Why didn't I think of that?