nav[aria-label="Primary Navigation"] { padding: 0; & ul { list-style: none; width: 100%; display: flex; flex-direction: row; justify-content: start; align-items: start; gap: 30px; padding: 0; & li { margin: 0; } & ul li { list-style: none; } } }

Split plot DoE (limiting number of trial runs per day)

Bertelsen92

Hello everyone,

New case:

3 variables (factors)

Factor 1 (Continuous) = 0 - 225

Factor 2 (Continuous) = 0 - 10

Factor 3 (Discrete - 2 level) = 60 and 90 (process step)

Factor 3 can be considered as a final processing step for the mixture of the first 2 factors. So as an example:

Factor 1 (225) combined with Factor 2 (10) - this batch would ideally be treated both at 60 and 90 the same day.

The limiting/challenging part is the number of batches that can be done pr. day. There is only time to mix 2 batches per day with a 8 days of trial in total. Meaning up to 16 batches and "32 unique runs".

I have tried different solutions with blocking/hard to change factors. However the power analysis comes out quite poor if I set both continuous factors as hard to change.

I am interested in a model that can explain the following:

The 3 main factors

All interaction terms

Factor 1 X Factor 1

My current setup can be seen in the pictures attached.

There might be several some solution I have not considered. Could really use some inputs.

Looking forward to your response. Currently using JMP 17 - not capable of writing/working with JSL scripting.

Current setup (DoE).PNG

Accepted answers

Victor_G

Hi Kristian,

One possible option is to consider the two factors 1 and 2 as "Hard to change", and factor 3 as "Easy to change" :

Then, create your model with main effects, interactions and quadratic power for factor 1. Specify the number of Whole plot to 16 and the number of runs to 32 :

You'll have 2 runs per whole plot (for a total of 2 batches/4runs per day, so 2 whole plot per day) in which only the factor 3 will vary :

You can find the datatable for the design attached to evaluate the design and see if it fits your needs.

Split-plot_Custom_Design.jmp

All comments

Victor_G

Hi Kristian,

One possible option is to consider the two factors 1 and 2 as "Hard to change", and factor 3 as "Easy to change" :

Then, create your model with main effects, interactions and quadratic power for factor 1. Specify the number of Whole plot to 16 and the number of runs to 32 :

You'll have 2 runs per whole plot (for a total of 2 batches/4runs per day, so 2 whole plot per day) in which only the factor 3 will vary :

You can find the datatable for the design attached to evaluate the design and see if it fits your needs.

Split-plot_Custom_Design.jmp

Phil_Kay

Hi @Bertelsen92 ,

@Victor_G 's solution makes sense to me and it seems to meet your requirements.

In your example you had specified 7 whole plots and 26 runs total, which would be strange.

The number of whole plots is the number of groups of runs within which the hard-to-change factors remain constant. Hence, Victor set this to 16 because you can execute 2 combinations of your hard-to-change factors each day, over 8 days, 32 runs total.

You were worried about the power. The power will be lower when you set factors as hard-to-change. In designed experiments we learn about the effect of a factor on the response by changing the factor and observing the effect on the response. If we make fewer changes to the factor, we learn less. It is no more complicated than that.

Having said this, the absolute number that you see for power is only meaningful if you have good numbers for the noise (RMSE) and signal you need to detect (anticipated coefficient). Most times we don't have these. So if you are just using the JMP defaults (RMSE = 1, coefficient = 1), there is no sense in worrying about whether the power is > or < 0.8.

I hope this helps.

Phil

Victor_G

Hi @Phil_Kay,

Thanks for the support and explanations provided for the design proposed.
In its original design, Kristian defined 7 plots and 28 runs, in order to respect and realize the 4 runs/day condition. It could have been possible, since the highest possible number of runs is 32, to also use 8 plots and 32 runs to realize the 4 runs/day condition.

But if doing this design, that means the runs in each plot will be similar for the "hard-to-change" factors, so there will be 4 identical batches per day, at 2 conditions for the factor 3. This situation may not impact the power (comparatively to the design I have proposed earlier) for factor 3 since there is a randomization possible for factor 3 in each block (easy to change factor), but due to the "hard to change factors" which imply a severe restriction on randomization for these factors, it will affect the power of the "hard-to-change" factors 1 and 2, as well as the prediction variance for these 2 factors, precision of these parameters estimates, and aliases in the design :

Comparison of power between designs with 8 plots and 16 plots:

Comparison of prediction variance between designs with 8 plots and 16 plots:

Comparison of relative standard error of estimates between designs with 8 plots and 16 plots:

Comparison of correlations between terms in the model for both designs :

I hope this answer will help and complement the great explanations of Phil,

Phil_Kay

Makes sense, @Victor_G . Sorry, I had misread the 28 runs as 26. In any case, your 16 whole plot design will clearly be "better" than 7 or 8 whole plots. The relative difference in power is a useful indicator here: more changes to the factors => more power. But, again, I would stress that the absolute value of power is meaningless unless you have meaningful numbers for the size of the noise and the signal you need to detect.

Bertelsen92

Thank you so much for all your input Victor and @Phil_Kay. Really good explanation and solution to the case I proposed.
I think I might have overestimated the importance of the "power score" since I do only use the JMP default (RMSE = 1, coefficient = 1).

I will go with your solution with the 32 runs and 16 plots. Really good with the comparison feature of the two designs, will definitely try that out next time myself.

Have a nice weekend both.

Bertelsen92

Hi @Victor_G and @Phil_Kay ,

The trial has now been conducted, and I am looking into the Fit model platform for several responses measured. I have one question regarding the WholePlot*Random effect.

So for one of the responses, I get the following:

So the Whole Plots (Pct of total = 81,229). It is correctly understood that 81% of the variance of this data cannot be explained by the factors we have changed, but is more likely to come from something else. In this case, it does make really good sense. Just wanted to make sure I understood it correctly.

Secondly, does it then make sense to use the Prediction Profiler if only 18% of the data is "valid"?

Thank you in advance. Have a great weekend.