Covariates in defined order in custom design

[#1]

Hi, 

In our experiment we have 3-4 continuous controllable factors and the fill height of a reservoir that is gradually reduced with each run as uncontrollable factor .

It is not an option to adjust the fill height for each run.

The reservoir can not be filled to less than 100% at the start of the experiment.

If blocking is used the fill height of the reservoir will decrease within each block.

The reservoir can be refilled to 100% after it is depleted and further runs can be performed.

I hoped to load the fill height as a covariate table with a defined order (Full -> empty), however that seems to be not possible due to randomization of the covariate input.

Any other suggestions how to best tackle that problem are highly welcome.

cheers ben

[#2 · Accepted solution]

Hi @BenGengenbach,

Yes, you already thought about this in your original post with this "defined order". Please find attached the datatable used in my example if you want to see or evaluate some parts in more details.

I did the DoE creation in a very "conventional" way at the beginning : for 3 factors and a model including main effects and 2 factors interaction, the number of runs recommended by JMP is 12. So I created a table for "Run Order" or "Time" (with one column) to be used as a covariate factor, with 14 rows : 12 rows required/recommended for the 3 factors model, and 2 additional runs : 1 to estimate main effect for time, and 1 to estimate quadratic effect for time (recommended by default in the book "Optimal Designs of Experiments : A Case Study Approach" from Peter GOOS and Bradley JONES). These 14 rows represent my "row order covariate" (numeric continuous covariate factor) or time variable.

In the DoE creation, I create the 3 factors, and then add the time covariate factor thanks to the previous covariate table. In the model, I specify main effects and 2 FI for the three X factors, and main effect and quadratic effect for "Time" covariate. I set the number of runs to 14 (as seen previously) and click on "Make Design". Since you have entered "Time" (or "order") as a Factor in your design, you can right click on this factor, and then Sort by Time column ascending (or do it on your datatable).

Since your design already includes this "Time" factor constraint in the model (through its main effect and quadratic term), the restriction on randomization is taken into account and you can sort by this "Time" column to realize your runs. You can check on your table that runs with factor levels in common are well "dispersed" regarding this Time constraint (high number of changes from one experiment to the next one, and if you have replicates like in my example, you'll see they are allocated at the beginning and end of the experiment: rows 2 and 12, 4 and 14, 6 and 10, 1 and 11, 3 and 13, 5 and 9 ("original"/unique rows 7 and 8 are at the middle time of the experiments).

I hope this answer is helpful for you,

[#3]

Hi Victor,

thanks for the clarification.

I overcomplicated things quite a bit. The design remains orthogonal no matter how I resort it as long as the covariate variable was considered during design creation...

cheers ben