DoE follow-up

Question

Dear,

I performed a first DoE (i-optimal) with 6 factors (main effects, quadratic effects, interactions).

Among these factors, temperature has a major effect and I would like to add new experiments to test the other factors in a narrower range of temperature.

The initial tested conditions for temperature were between 35 and 80°C. I would like to add runs only in the 70-80°C range.

The objective of this follow-up experiment is to increase the statistical power to detect the effect of the other factors in this range of temperature.

How should I do this in JMP?

Thank you for your help!

Victor_G · Answer

Ok I understand better.

I think augmenting the design is still a better idea than starting again from scratch, as some prior information about influence of factors can be leveraged and help reduce the required number of experiments.

When augmenting, you can check "Group new runs into separate blocks". I really recommend checking this option as a safeguard measure, as it helps you take into account and mitigate risks of having shifts or difference of variance for your responses between the initial set of experiments and the augmented one.

Then, if you want to add blocks in your augmented design, it may be possible but not straightforward :

* Augment the design with the total number of runs expected (a multiple of 3, in the example recreated here, I started from a 34 runs I-optimal RSM design, and I add 12 runs thanks to augment design platform) :

* On your datatable, create a table with only your augmented runs with the option Create a Subset Data Table :

* Using the platform Custom Design on your subset table, use the option "Select Covariate Factors" to enter your factors from the subset table (but not the Block factor if you have checked the option "Group new runs into separate blocks" as the only value will be 2 and you'll be rearranging these augmented runs into random blocks of 3 runs). The augmented runs will be used as a Candidate set. You can then add a blocking factor (3 runs per block) in your factors list :

You can also check the option "Include all selected covariate rows in the design" to make sure the augmented runs created previously are all considered and used. This step is only used to re-arrange the order of your augmented runs into random blocks respecting your experimental constraints.

* You can then change the Design Role property of the blocking factor to "Random Block" if needed (you can also change it when setting the model for analysis in the Fit Least Squares platform using Attributes options) and copy paste the design with the augmented runs from the custom design (with the order from the random block effect) to your original complete augmented design datatable to replace the order of the augmented runs :
I would recommend not combining the "block factors" into one column, as you have different objectives and use for them :
- The block from the augmentation is useful to assess if you have any shift or variance differences in your responses from first to second set of experiments (might be dropped in the analysis if not statistically and practically significant/meaningful),

- The random block from the experimental constraint might not be used in the analysis directly, but help mitigate the risk that an effect might be confounded/aliased with the day of the experimentations ("unlucky randomization"). If you already had a random block from your first set of experiments, you can then expand the use to the new set and use it in the analysis.

There might be more elegant option to take your experimental constraints into considerations, but this practical work-around should work for your use case.

Hope this makes sense for you and may help you,

PYS · Answer

Dear Victor,

Thank you for your reply.

The thing is that we suspect that (for technical reasons) only the data at high temperature are valid.

Therefore; we would like to improve our knowledge at these high temperatures without losing the information we gathered.

Maybe the augmentation is not the correct option? If we decide to perform another DoE with temperature in a narrower range (70-80), may we add the previous runs we performed at only 80°C?

The next DoE will contain different random blocks (we can only perform 3 experiments/day), how should I handle the previous experiments (that were also obtained in different random blocks). Should I create two random variables (1 for the day blocks and 1 for the "DoE" blocks)?

I am a bit lost

PY

Victor_G · Answer

Hi @PYS,

You can do this very easily by using the platform Augment Designs.

One your factors and responses have been specified, you can change the ranges of your factors to reduce (or augment) the ranges of your factors, before choosing the augmentation strategy :

I don't know how relevant and possible this option can be, but have you considered expanding the ranges of the other factors ?
Hope this answer will help you,