Batch of material - how to treat it in DoE?

[#1]

Hello everyone,

This is my first post so I hope that my question is not found in other posts. If this is the case please guide me to the relevant post

I saw in the "Optimal Design of Experiments - A Case Study Approach" book that in Chapter 4 the supplier of raw material, a categorical factor, is treated as a blocking factor for which interactions with the continuous main factors were accounted for. My question is: Why did they treat the supplier as a blocking factor rather than a normal categorical factor for which interactions with the continuous factors can also be specified, but in this case the variable would be randomized in the whole experiment. What would be the main differences? I understand that blocking is used for nuisance variables and that you should "Block what you can, randomize what you cannot" but is the supplier really a nuisance variable? The batch of raw material should also be treated as a nuisance variable?

This question is related to a DoE that I'd like to create. It should have 3 runs per day, 21 runs in total. My idea is to introduce a Random Block for Day to account for possible day-by-day variations. The experiment should be done with 3 batches of raw material. If I'd block, I should have 7 runs per batch for an I-Optimal Design, but in this case I'd change the lot in some days. Is there any problem that arises from such a design?

And another question that I have: how could I specify from the Custom Design that I want multiple random blocks? Should I create the design without the random block designation and change it to random block after the creation of the DoE? 

Hopefully I stated my problem in a clear manner

[#2]

Lots to comment on in your post. I'll just deal here with your first paragraph and let others comment on your actual design construction. I no longer have my copy of Goos and Jones so I'm not sure if they wrote about their thinking wrt to handling the supplier as a blocking variable...but here's how I always thought about an issue such as this. It boils down to how you want to treat the noise source from a system design point of view. In this case the source is the 'supplier'. If I'm intent on designing a system where the supplier is a conscious decision wrt to the overall system design...then I'd be very tempted to treat the supplier as categorical factor because I want to be able to model the effects of supplier and any interactions that might involve supplier effects. For example, suppose I have multiple suppliers that I am considering specifying in the system design and I will ultimately pick one or more for that system design. Then I'm tempted to treat suppliers as a categorical factor.

On the other hand...suppose I am really ambivalent wrt to the supplier...but I happen to have multiple supplier's materials on hand for this experiment...but the supplier choice is outside the scope of the system design. Then as insurance against any supplier differences that might exist that could influence system performance...then I want to treat the supplier as a blocking factor.

I hope this helps?

[#3]

Yes, it was very useful and it makes a lot of sense. Thank you very much! I'll remember this line of thinking

[#4 · Accepted solution]

Here are my thoughts:

1. Do you have any idea from past experience or previous data collection how much the batch-to-batch variation there is?  Is it consistent?  Can you represent the future variation in the batches in just a couple of batches during your experiment?

2. Do you have any hypotheses as to why there is/may be batch-to-batch variation?  Are you interested in studying this?

3. Here are some answers to your questions:

Blocking is a strategy to handle noise.  You do NOT want to confound design factors with the block. The strategy is to keep the noise "constant" within the block thereby increasing the precision and then purposely varying THAT noise between blocks to increase the inference space.  If you can assign what factors are confounded with the block (that is you know what those factors are), then it seems reasonable to treat the block as a fixed effect and then be able to estimate the block effect and all block-by-design factor interactions.  The later are extremely useful for robust design.  If you want to be robust to noise (in this case supplier material batches), then determining if your design factors have a consistent effect over changing noise is critical (this is estimated by the block-by-factor interactions).  If you cannot assign the noise, then likely you treat the block as a random effect and you will not be able to estimate noise-by-factor interactions.  As is always the case, the more you understand about effects such as Batch or Day, the better your options.

Can you control the batch effect?  I think not. This by definition is noise (a factor you are unwilling or unable to manage).

4. As I see it you have the following options:

• Use sampling to understand the batch-to-batch component of variation.  This would be quite useful in determining the strategy to handle this in an experiment.  I would add this strategy to understand Day variation as well.  
• Confound the batch with the block and treat as a random effect.  This will increase the precision of the design and increase the inference space, but will not allow estimation of the robustness of your process to batch variation.  There is still the question of how representative are the batches in your experiment of future batch variations (thus randomly select batches)
• Confound the batch with the block and treat as a fixed effect (this is Box's quote you have included in your post "Block what you can..." means what you can identify and manage for the experiment).  The benefits of the first strategy as well as getting some estimate of robustness. In industrial experiments, I seldom use more than 2 "exaggerated" blocks as we don't want to model a non-linear (e.g., quadratic) block effect (it is non-sensical).

• If you have a good relationship with the supplier, you could have them experiment on factors associated with making the batches and then do split-plots on your design factors (Batch experiment in the whole plot and your design factors in the sub plot...very efficient and effective).  The most information for the least resources.

[#5]

As always your answers are very informative. Your questions (that I should have asked myself from the beginning) are spot-on and you managed to make me better understand which option among the 4 you presented should I choose.

Thank you very much for your thorough post