Replicates in a RSM design table

[#1]

I would like to create a DoE to obtain an optimised recipe to achieve maximum yield. Usually I go to custom design, input my variables and click on RSM in the model.

In this scenario, what are the best practices for replicates? By replicates I mean the repeated runs to evaluate experimental error.

Suppose we decide for 5 replicates. Is there a smarter way to repeat the design table 5 times instead of stacking them? Additionally, what would you suggest to do with the replicates? Average them by run or add a random effect on replicate to model it and use the number of observations?

Thanks in advance and bye winter!

[#2]

Hi @Enormous_PValue,

Welcome in the Community !

I'm not entirely sure you differentiate replicates (stacked table) from repetitions (splitted table).

Difference between repetition and replication : Repetition is about making multiple response(s) measurements on the same experimental run (same sample/row in the datatable, several columns for each measurement done on this sample), while replication is making multiple experimental runs (multiple samples/rows in the datatable) for each treatment combination. 

• Replications are used in order to estimate more precisely pure error and parameters estimates more accurately. A replicate is a new run. Replication reduces all sources of variation (experimental + measurement).
• Repetitions may be used to lower the measurement variance and increase measurement precision/accuracy. Repeating Measurements reduces only the variation from the measurement.

You can read more about this important difference here : https://cdn.statease.com/media/public/documents/2021-08_Replicates_vs_Repeats.pdf 

Concerning your use case, if you are mentioning replicates, you can replicate your design using the Augment Designs platform. See Replicate a Design example. However you're right, using this platform to augment it will create a table with replicate runs ordered in the same way as the original design (it's only copying and stacking the original runs the number of times you have specified). I see two options that may be interesting to use to improve the randomization :

• Either you create the design with replicates, and if you're able to run the experiments at the same time, you can randomize the whole datatable. @jthi found a nice trick for me yesterday to randomize a datatable using the "Table Subset" feature with a random subset of sampling size 1 : Randomize rows from a datatable 
• If you're not able to run the experiments at the same time, it could be great to add a blocking random effect to identify the replicate number, and randomize the runs inside each replicate. This way, you can account for variation from replicate-to-replicate in your model.

Do not average the replicate by "run"/treatment combinations. Replicates are individual new runs, and they enable to increase the degree of freedom to detect more easily some effects. Averaging them would delete this important benefit.

If your question was oriented towards repetitions and not replicates, you can read more about how to handle them in various posts :

Can i include a standard deviation of replicates into DOE Analyses ? 

How to add multiple measurements of a sample into my experimental design? 

How do I write the data table with repeats and replicates 

DOE - replicates vs. repetitions 

How to Include Repeats in DOE Response Data 

Basically in repetition scenario, you add a measurement colum for each repetition of the measurement, and you can fit a model to the mean value of these measurements, as well as the standard deviation if it may be interesting for you. 

Hope this response will help you,