Hi @Mathej01,
Your explanations help a lot.
Concerning if your treatments need to be treated as repetitions or replications, it depends on what is considered to be your experimental unit : are your experimental units your 6 "big" samples, or the 30 parts of the big samples ?
- If your experimental unit is the "big sample", then your 5 measurements per sample correspond to different measurement points, and the runs should be treated as repetitions. You can enter the mean (or median, ...) of these 5 repeated measurements for each response, as well as an information on the variance of the measurement (variance, standard deviation, etc...) and use both responses' informations (mean and stddev for example) in the modeling to achieve a robust optimum.
- If you consider your experimental unit to be the "subset" parts, then you can consider your runs as replicates, and use a mixed model approach for this case of randomized restriction. The Whole plot will correspond to the "big" sample, and will help you in the analysis understand the variability from "big" sample to "big" sample as a random effect.
It could be also interesting to compare the two approaches and see how/where they differ or complement each others. I would go with the first option as it seems more appropriate for your experimental setup.
Another option (before any analysis or modeling) could be to visualize your data, and see for example some heatmaps for your responses on the 6 different parts and 5 related subsets, to better visualize and assess the measurement variance (I have done it on my design with 8 whole plots and 3/4 subplots) :
You could also use the Variability Gauge Charts (jmp.com) to better evaluate and compare your variance measurement (error) vs. signal. Use the "whole plot" (or big sample) as your "Part, Sample ID" and the subsets (repetitions) as grouping variable, and specify the response(s) you have. From this platform, you can then evaluate if your "part-to-part" signal (the differences you would like to see between your samples) is relatively high/sufficient compared to the sources of variation from your repeated measurements :
This analysis may help and complement what you can obtain with the modeling done through the Fit Model platform.
I hope this answer will help you,
Victor GUILLER
L'Oréal Data & Analytics
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)