process DOE which option is better and why - small batch or split plot for larger batch

[#1]

Hi,

i would like to design DOE for the following situation:

The process has 3 steps. 

option A - in step 1 prepare a small batch of 100g and continue with that to the next steps. each batch per one DOE run. this means that all the parameters would be easy to change

option B - in step 1 prepare a small batch of 500g and continue with 100g out of this Big batch to the next steps - this batch will last for 5 DOE runs. this means split plot design

in both cases, there is no way to check QC for the product of the first step.

please advise,

Thank You!

[#2]

Hi @YanivD,

It may be hard to find a definitive answer to your question, without knowing your goal, factors, supposed model, experimental budget, etc...

Both options could have an interest depending on your goal study:

• Option A with one batch per run : This option is interesting if you want to have a realistic assessment of the total variability of your inputs on your process. Since you'll "create" one batch per run, your batch-to-batch variability could be estimated quite precisely, perhaps at the expense of a larger design, but it may be cofounded with other factors...
• Option B with one big batch per 5 runs : This option is interesting if you are not specifically interested in the variability of your inputs, but still want to take into account a part of it. You may be able with this option to differentiate process variation from batch variation (thanks to blocking factor), which might not be possible with Option A (since you use one batch per run).

If you're interested in evaluating your process (and not your "product" input, since you can't check QC of it anyway), option B sounds good to me.
I would be interested to know what other members of this community think about this use case.

[#3]

Thank you @Victor_G and @statman for your reply. I have 7 factors all of the continues. The first process step has 2 factors.

The goal is classic - to find the process conditions for the highest product yield. of this goal including knowing the best conditions for each step in the process.

For option A - 15 runs would be enough with a power of 80%+

For option B - 15 runs will result in a power of 30% for the first step factors and a power of 80%+ for the other 5 factors.

@Victor_G could you please explain if with these inputs you would suggest option B and why? what to check in comparing the different designs besides power?  

please advise,

[#4]

As Victor eludes to, you have not provided enough information.  What subsequent DOE has 5 runs?  How many factors?  Are you experimenting on factors to make the "batch"?  If so, this experiment makes up the whole plot.  Then you can experiment on subsequent factors in the sub plot.  You will likely increase the precision of both the WP and the SP with this type of experiment and potentially reduce resources.

[#5]

Thank you @statman i added the details and goals (in upper reply please) - may be with this information it will help to decide. appreciate your time and assistance 

[#6]

I may not be the one to provide advise as I do not hold much weight in the Power estimates for experiments.  Most of the statistical comparisons of experiments require knowledge you do not have, so they are just not too reliable.  I use the following criteria to determine what experiments to run:

1. Constraints: Time, money, material availability, measurement/equipment capability, etc. How many treatments canbe made (this will likely need to be negotiated)?
2. How many factors are to be manipulated (the number of hypotheses to be compared)?
3. How will noise be managed or partitioned?
4. Are some factors harder to change than others?  Are there other restrictions on randomization?
5. What are the prioritized effects you want to estimate?
6. Are higher order effects suspected/predicted (e.g., interactions, curvature)?

• What is the desired resolution? (What effects do you want to estimate/separate?)
• What order polynomial is necessary?

You can run a factorial of the 2 factors to make the 4 batches (full resolution) and you run either a res III (8 treatments) or V (16 treatments) of the sub plot factors by splitting the 4 batches.  Entire experiment Uses 4 batches and both the WP and SP have increased precision over a factorial off the 7 factors without the split.

[#7 · Accepted solution]

Lots of good discussion below. I would just add when I am placed in this situation I ask myself what will happen in the plant. Will you make matched batch sizes in the plant or will you be making a large batch and using it in many subsequent steps. I always strive to experiment in the lab to mimic the variation I will see in the plant. So if one batch on step 1 will be made for step 2 in the plant then that is what I would model in the lab. By making one large batch of step 1 you will be diluting your variation in real life perhaps.