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DOE: Factor needs to change range within a process after a specific time

martindemel

Hi,

Any ideas/experiences, or confirmatino that there is no way doing this (especially from the modeling perspective) would be helpful.

A customer asked me what would be the best way to design an experiment, where it is necessary to change one factor setting after a given time in a process they run the experiments on. That is, you know that factor A has to be at the beginning of the process at a value within Range1 (let's say 10-20) but after 1h it has to be changed to a higher level (within e.g. range2: 25-30).

One can do two factors, but they want to avoid this (due to the size of the DOE with other factors involved). Is there a good way? Or has someone experienced such a situation in the past?

Besides the setup, I'm wondering how the modeling would work at all in such a scenario with just one factor.

For the setup. I thought about candidate set, or a two step approach (augmentation) however, I still wonder how the model should work then.

Thanks

Accepted answers

Phil_Kay

Interesting question. I think the answer is fairly simple though: there are 2 factors here: A(t0) and A(t1).

That is, unless...

1. Either A(t0) or A(t1) are constant. e.g. A is always 15 at t=0. Or...

2. A(t0) and A(t1) are perfectly correlated. e.g. A always increases by 5 units at t=1.

In those cases you only really have one factor.

But it doesn't sound like that is the case. It sounds like they want to change 2 things but they only want to have 1 factor in their design to keep number of runs low. Not possible unfortunately.

They could define N different "profiles" for A as a function of time and that could be a categorical factor. But then they'll need to estimate N-1 parameters, so the design gets big. Especially if they also need to look at interactions with this factor.

Hope that is helpful.
Phil

Phil_Kay

Absolutely. Sequential experimentation is the tried and tested approach for understanding systems with many potential important factors. They could start with a small screening design and then optimally augment to estimate the RSM model for optimization. Or they could take a Bayesian optimization approach.

All comments

Phil_Kay

Interesting question. I think the answer is fairly simple though: there are 2 factors here: A(t0) and A(t1).

That is, unless...

1. Either A(t0) or A(t1) are constant. e.g. A is always 15 at t=0. Or...

2. A(t0) and A(t1) are perfectly correlated. e.g. A always increases by 5 units at t=1.

In those cases you only really have one factor.

But it doesn't sound like that is the case. It sounds like they want to change 2 things but they only want to have 1 factor in their design to keep number of runs low. Not possible unfortunately.

Hope that is helpful.
Phil

russ_wolfinger

Building on Phil's good comment: Why can't you use two continuous factors and then limit the number of runs to what is affordable?

martindemel

Thanks both, that confirms my thoughts. About two factors, Russ, it would have too many effects including the other factors of interest, that they would not be able to understand all what they want to understand. But I'm with you, you have to pay a certain price for the information and constraints you want to include.

I wonder if we could work around this problem using two factors as Phil described, doing a simple first design and then use bayesian optimization to see, if we can get faster to combinations leading to a better result. That way they do not have to run all combinations but only those who seem to support a better model with less uncertainty.

Phil_Kay

Jed_Campbell

What about designing the experiment with 2 factors, but then removing the second factor from model before creating the design? That should allow the constraint to be made but not increase the number of runs.

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ),
	Add Factor( Continuous, 10, 30, "Factor A", 0 ),
	Add Factor( Categorical, {"Beginning", "End"}, "Time", 0 ),
	Set Random Seed( 261201637 ), Number of Starts( 2087 ), Add Term( {1, 0} ),
	Add Term( {1, 1} ), Add Term( {1, 2} ), Add Alias Term( {1, 1}, {2, 1} ),
	Set Sample Size( 16 ), Disallowed Combinations(
		Factor A > 20 & Time == "Beginning" | Factor A < 25 & Time == "End"
	), Simulate Responses( 0 ), Save X Matrix( 0 ), Set Run Order( Randomize ),
	Make Table}
);

MikeD_Anderson

I've run into this kind of problem in the past with thermal profiles (i.e. for ceramics or heat-treatments for metals). What I did (no comment on whether it was right or wrong, but it did work) was to set up each step/set point as a factor and give all the factors the same range (i.e. 10-30 from your example). I then set up a system of linear constraints so that the setting for the next factor always had to be higher than the setting for the previous one (i.e., factor 1 <= factor2, factor2 <= factor3). This allowed the factors to float and explore the parameter space while still keeping the desired overall profile. If we cared about cooling profiles, we just reversed the rule logic.

If you only have a couple set points, it's not too bad on resources.