Handling a response measure over multiple days

[#1]

Dear all, 

I have a question, for which I cannot find an answer online an I doubt what's the right approach would be. Hopefully you can help me

In short, I am making a protein dough by mixing various ingredients together. After being prepared, the dough rests for 5 days and than it's processed into a protein bar. During this 5 days the texture of the dough changes. 

My research question is how the mixing process affect the texture development over the 5 days.

My goal is to optimize the mixing process so that the right texture is achieved within 24 to 48 hours

My doubt is:

1. Should I create my design, with 5 responses, one per each day?

2. Should I duplicate my design 5 time, adding an extra factor called days, where I record the moment in which I measured the response?

In the first case, I lose the possibility of modelling the effect of "days" on the texture of the dough, hence being able to optimize for this factor.

In the second case, I have the feeling I am cheating, as it is not true that I am replicating the model. I am just analyzing the same subject/run, multiple time across different days. 

What would be your approach for this design?

Thanks for your inputs,

Kind regards,

Elia

[#2]

I suggest that you treat the response as functional data. That is, the response is the entire curve over time.JMP can use functional data as a response in a DOE. See the documentation about defining a functional response and then analyzing the DOE with the Functional Data Explorer.

[#3]

Dear mark,

Thanks for you answer. I will further look into functional responses;)

[#4]

Hi @EliaDF,

Welcome in the Community !
There may be several options available, depending on which version of JMP you are using (JMP or JMP Pro) and the measurement process.

About the measurement process, is the measurement representative ? I mean : do you measure texture on a single point or on several points ? If it's on a single point, is this point representative of the whole dough texture ?
Is the measurement destructive or not with the sample ? I mean : can you monitor and measure the texture over the days on the same sample, or do you need to prepare several doughs in order to have at least one measurement per day ?

About the version/licence of JMP you have, there are several options :
- With JMP, you could model the texture (Y) vs. Day (X) for each experiment of your DoE with the "Fit Y by X" platform, and extract the parameters of the curve to use it as response in the modeling of your DoE.
- With JMP Pro, you could use the Functional Data Explorer, specify Day as X, Texture as Y, and your DoE factors as "supplementary" variables. You can then specify your target curve or optimization target, and see how the factors affect the shape of the texture curve vs. day. An example of the use of Functional Data Explorer for DoE dataset can be found here : https://www.jmp.com/support/help/en/17.1/index.shtml#page/jmp/example-of-functional-doe-analysis.sht...

If you can use the Functional Data Explorer, the second option may be best, and labelling your rows from the same experiment with the same ID will prevent to consider the "duplicate rows" as new replicate runs. In case you have JMP, analyzing the curve experiment by experiment (single analysis or create an "ID experiment" in your datatable and use it as "by" variable in the Fit Y by X platform) should also avoid falsely "creating" replicate runs.

I hope this answer will help you,

[#5]

Hey Viktor,

Thanks for your answer. Unfortunately I have JMP pro but I will try approaching the problem using a sample ID.

The method is not destructive but I make a batch big enough so that I can make three replicates a day for 5 days.
The value i use for the response is the average of the three replicates (measured on different points).

[#6]

Ok, Functional Data Explorer is unfortunately not available in JMP, only JMP Pro.
I would recommend doing the analysis in two ways :
- With a response column for each day like you mentioned, create your models on these 5 responses, and use the Profiler to optimize all responses at the same time,
- Use the "Fit Y by X" platform (or other platform) to model each curve independantly (with an ID column to spot each independent experiment from the DoE), extract the coefficients of each curve, and use them as responses for your DoE. If you can create a "fake" golden curve that looks like what you're trying to achieve, it might be easier to define optimization goals and target values on the curve coefficients when trying to optimize them with the model from the DoE.

Combining and comparing these two approach could be very interesting and informative.

As a last note/remark, it might be interesting also to take into account variability of the texture over the different measurement points, and not only the mean, if you see that you may have a non-uniform or non-constant variability of texture values depending on the experiment.

[#7]

Just to add some thoughts...I'm confused do you have JMP Pro or not? "Unfortunately I have JMP pro". I agree with Victor regarding looking at the mean and some estimate of variation for your repeated measures (those are not considered replicates) for each day.  Realize you will capture both within batch and measurement error confounded within those 3 samples.  How confident are you in the measurement system?  The other analysis you can do is multivariate for the multiple responses over the 3 days (Analyze>Multivariate Methods>Multivariate).