DoE and multivariate analysis with a time factor

[#1]

Hi all,

This is a two part question:

I need to do a DoE that has 5-6 factors and measuring 6-8 variables. Two of the factors are time in weeks (numeric, nominal) and temperature (numeric nominal). The other factors are continuous numerics of concentrations of different materials. How do I create a DoE that takes into account the dependency of measurements that were taken during a time course and temperature gradient? How should I account for the dependency between samples during DoE creation and Analysis?

Thank you

[#2]

Just making a correction that both time and temperature are ordinal, not nominal.

[#3]

I'll start, but it is impossible to provide specific advice with the limited information you provided.  For example, "concentrations of different materials" sounds like you may need a mixture design? I can't say for sure what the "right" way to handle these factors is as I don't understand the situation at all.  I perhaps can offer some general comments and questions.

What is the purpose of the DOE?  Explanatory, prediction or "pick the winner"?

What is the hypothesis about weeks?  Are you concerned with X's that may change over weeks?  Have you studied week-to-week variation?  How?  Is the week-to-week variation consistent? Have you done any CoV studies?  You obviously can't treat week as a design factor (Week will not be part of the model).  That is, you can't finish the experiment and conclude week is significant and week 1 is best as you can never have week 1 again.  To me, week is a place holder for x's that change week-to-week.  It would be better to identify what those x's are and then determine if any are design factors or noise and treat them accordingly. Often folks in the experiment world would treat week as a block.  How many weeks do you need to include in the study?  Why?

For temperature, why can't you treat it as a continuous variable set at different levels?  Or do you mean ambient conditions that change over time?

Another thought is to question your response variables.  Can you capture the time series of the responses?  Are you interested in the rate of change of the response variables over some period of time?  You collect the max, min, slopes, etc. to use as response variables for the experiment.

[#4]

Thank you for your response, these are important questions and I will do my best to provide context and answers.

The different components that make up this "mixture" do not necessarily add up. It's just a list of possible materials that could be added at different concentrations. For example I might add two amino acids at a specific concentration, and for another experiment there might be a third amino acid that is being added. I could translate the concentrations to volumes and then they would add up to a similar total volume, and hence make it a mixture experiment but I'd appreciate your advice on that.

The purpose of the DoE by order of importance:

1. Pick a winner, where the winner is decided by evaluating multiple variables.

2. Evaluate which of the measured variables contribute the most to finding a winner.

3. Design set of experiments that will enable building a ML classifier that could help predict results of future experiments.

Weeks: Some properties of the tested materials change over time. We are not looking for optimal time point, just to show stability. Historically, we've been testing the materials at 0,1,2,4,8,12 weeks and note their properties. Some variables do not change (at least from what we've seen in previous experiments, some change verry little, and some have considerable change). Those materials that change (degrade) over time are immediately flagged as failed materials.

Temperature: Historically we test the material at 4,25,40 c. The reason for these is that we need to show stability at these temperatures. We do not look for optimal temperature.

I could translate the response variables to the difference between time points (rate), if you think it is more valuable. Do you have an advice how to accomplish that and embed it within the design, and later on the analysis?

Please let me know if you have more questions / comments!! and Thank you so much for your time and help!!!

[#5]

Sorry, there is just  not enough insight into the process.  I'll try my best to offer some response.

"The different components that make up this "mixture" do not necessarily add up. It's just a list of possible materials that could be added at different concentrations. For example I might add two amino acids at a specific concentration, and for another experiment there might be a third amino acid that is being added. I could translate the concentrations to volumes and then they would add up to a similar total volume, and hence make it a mixture experiment but I'd appreciate your advice on that."

I don't understand the process well enough to provide specific advice.  Is this a "batch" process? If you add a material at "x" concentration, does the concentration of the others change in the "batch"?  You should decide if a mixture design is appropriate:

https://www.jmp.com/support/help/en/18.0/?os=mac&source=application#page/jmp/mixture-designs.shtml

"The purpose of the DoE by order of importance:

1. Pick a winner, where the winner is decided by evaluating multiple variables.

2. Evaluate which of the measured variables contribute the most to finding a winner.

3. Design set of experiments that will enable building a ML classifier that could help predict results of future experiments."

IMHO, your number 1 purpose is not the purpose of experimental design.  Experimental design is an effective method for understanding causal structure.  This is likely an iterative process.  You might start with a screening type experiment and build on the that experiment through iterations (e.g., fractional factorial with lots of factors, select a subset of interesting factors, reduce the design space and increase inference space, etc.)  I don't have much advice for a "pick the winner" strategy.

"Weeks: Some properties of the tested materials change over time. We are not looking for optimal time point, just to show stability."

Do you want to understand the impact of materials on your product? DOE is not really the tool to assess stability (this is a sampling idea).

"Historically, we've been testing the materials at 0,1,2,4,8,12 weeks and note their properties."

Why? Why those intervals? From this testing do you know the extremes of material variation?

"Some variables do not change (at least from what we've seen in previous experiments, some change verry little, and some have considerable change). Those materials that change (degrade) over time are immediately flagged as failed materials."

Do you want to be robust to those variations?

"Temperature: Historically we test the material at 4,25,40 c. The reason for these is that we need to show stability at these temperatures. We do not look for optimal temperature."

OK, so you want to be robust to temperature?

"I could translate the response variables to the difference between time points (rate), if you think it is more valuable. Do you have an advice how to accomplish that and embed it within the design, and later on the analysis?"

You need to figure out how to quantify the phenomena you are studying, I can't tell you from what you've given me.  If you are concerned with the product changing in time, then you might want to find factors that affect the rate of change.  I would calculate the slope over some given time period and use that as one of the responses in the experiment.