Unexpected change in controlled variable in DOE

[#1]

Hi,

I made a custom design to understand the impact of caoting temperature and speed on performance. I kept all the parameters same. However, unexpectedly I had to vary the nozzle air pressure for different runs as it was not possible to make the coatings at same air pressure. So, my question here is that how can i include the change in air pressure in the DOE. I cannot afford any more runs.

Is there any possibility to consider the different air pressure or should I just assume that it does not have any affect on final performance(which I am not sure).

Is my question clear?

Thanks in advance

[#2]

Thank you @Victor_G  for your answer.

Just in case I am also exchanging about this subject in this thread: Solved: Define a covariate - JMP User Community

I explained there that I am confused because I have a variable (powder humidity) that I know in advance of my experiments and that it is in a certain way uncontrolled. I was confused because it is said that covariates are variables that are know in advance (like in my case). However, my variable (powder humidity) does not really co-varies with the change in the factor levels from one treatment to the next (as explained by @Mark_Bailey in the the other thread).

I am therefore more inclined to treat my variable as an uncontrolled one, but I am not completely sure of making the right choice.

regards,

Julian

[#3]

I'm not sure I agree with the distinctions made.  A covariate is a measurable noise variable (a variable you are not willing to control for what ever reason).  Since you can put a value in for each treatment, this random variable can be assigned in the model typically with 1 DF) and thus reduces the estimate of the MSE.  You will be writing a mixed model.

Now there are issues with using covariates.  For example, you are limited as to how many covariates you can account for.  What value to you use for the covariate?  Let's say the covariate is a chemical property as Victor alludes to.  Realize the chemical property varies and the value you use may not be exactly correct.  You have additional measurement errors measuring the covariate....

[#4]

I may be wrong, but the distinction between Uncontrolled variable and covariate relates to two aspects for me:

• Time-dependancy : covariates can be measured or calculated in advance, before running the experiments, whereas Uncontrolled variable are measured only during the experiments.
• Use of this variable : covariates can be used to select/filter the most promising conditions to optimize an experiment, whereas an Uncontrolled factor is just a source of variability, but to no interest for the practitioner.

In my example, temperature and pression may also have some measurement errors like any measured input factors, so I don't think this could make a distinction between covariates and uncontrolled factors. Besides, I was referring the molecular properties used as covariates as the properties you can calculate (also called "molecular descriptors" so no measurement errors involved, but still some inaccuracies/deviations are possible).

[#5]

I'm not sure about right and wrong, but I don't think your time dependency is required to use covariates.  Only that you can take a measure of the covariate for each treatment.  Also I don't think I understand your Use of this Variable statement.  The covariate is a random variable in an otherwise fixed effects model.  Thus you have a mixed model.  Accounting for the covariate reduces the MSE estimate (if this was not accounted for, the MSE would include the effect of the covariate).  One could argue this increases the precision of the experiment.  As a random variable, I typically start with adding the first order effect, but there may be additional effects you can estimate (interactions and non-linear).  If the covariate is indeed significant, the user may be able to input the covariate value in the model and solve for remaining significant factors (elect levels) in the model to improve the results.

I am always interested in determining causal relationships.  It is our hope (wish) that we can develop a useful model using factors that we are willing to manage, but that is not required of nature.  It may be in the noise which is extremely useful to the practitioner.  Knowing the significant variation is from noise leads one to broaden their investigation.  One may find they are willing to manage factors they previously did not or one may desire to become robust to the noise both choices are important to the practitioner.

[#6]

Thank you @Victor_G  and @statman for all your views on the subject. They contribute to better understanding the topic. Still, I see that sometimes the line between Covariate and Uncontrolled variables is very fine.

[#7]

You are confusing the nature of the variable (e.g., uncontrolled or noise) with how it can be handled in an experiment.  One way to handle an uncontrolled variable that can be measured is to treat it as a covariate.  There are other ways to handle noise in an experiment.