3 factor - 3 level experiment with DoE and Minitab



Hey guys,

I just started using DoE and Minitab and my first project is to design an 3?-experiment.

Repeating each three times I get a total of 3?x3 = 81 experiments to perform. Problem is that I only have 48 slots and it takes 6 months for one run.

What would be the right approach to optimize my DoE? I need all main effects and can't really exclude any possible interactions except for the three factor one (ABC). Minitab is apparently able to create an optimal design based on different key factors, but how do I know if this design gonna give me the desired information after I have performed the experiment?

I attached the full factorial design.

Happy for every piece of advice


Elsmar Forum Sponsor


Forum Moderator
Re: 3 factor - 3 level experiment

Since I know nothing about your process and factors, I am going to ask some basic questions.

First, a beginners mistake in DOE is to jump into full factorials with a lot of factors at many levels. Three factors are fine, but do you really need three levels in your first DOE? Are these factors continuous or discrete? If they are continuous, you could try a full factorial at two levels with a few center points and two replicates instead of three.

Now, if your factors are discrete and you absolutely must run three levels, I would reduce the number of replicates to two. Most experimenters are after strong effects. If the effect is indeed strong, you should see it with minimal replication. If you need 3 replicates to see the effect, it is most likely a weak effect that will be of minimal use.

Either of these recommendations should get you into 48 slot goal.

Bev D

Heretical Statistician
Super Moderator
Miner is correct (as always:D)

it would be helpful if you could explain your process and what you are actually trying to learn from the experiment.


Hey, thanks for your fast responds.

Yes I need the 3 levels of all 3 factors because they are discrete. Let me explain the experiment in a few words.

A special steel coating has to be tested and compared. This is the first factor. The other two are pre damage and the pre treatment of the surface before applying the new coating, which has to be compared to two different coatings. Hope that was clear enough :)
After the six months the coating is tested.

For what i got so far the D-Optimal design created by Minitab is the way to go. Another option would be to convert a discrete factor into a continues one in order to reduce the level to 2 (high and low level).

Can I use the Box-Behnken-Design for discrete factors?


Forum Moderator
Would you expect setup to setup to be a large source of variation for any of these factors? If not, you can eliminate the replicated runs and take repeat measurements within a single replicate.

Regarding Box-Benken, it requires a minimum of three continuous variables. Additional discrete variables may be added, but the design cannot be three discrete variables alone.


So the Box-Behnken is not an option. Thats good to know. Could you explain your first point? I dont really understand what you are trying to say. Thanks.


Forum Moderator
In DOE there is a distinction between the terms replicate and repeat.

  • Replicate = multiple experimental runs made under the same conditions. Replicates include variation from unit to unit AND from setup to setup because other experimental runs were made between each replicate.
  • Repeat = multiple measurements made within a single experimental run. Repeats include unit to unit variation but do not include setup to setup variation.
If setup variation is large a weak factor may show as significant in a design run without replicates and as not significant in a design run with replicates. A strong factor should show as significant either way. Also, if setup variation is small, a weaker factor will still show as significant.

Weak factors combined with large setup variation and un-replicated designs is a major cause for promising results that later fail to live up to expectations.

Back to my comment: If your setup variation is small, you have no need for replicates (or as many replicates). This will reduce your experiment size.


Thanks a lot, I got it now.

For as far as I can tell the Taguchi design could be interesting as well. If I choose the three factors with three levels in a L27 design Minitab still seems to be able to detect possible AB, AC, BC interactions.

Do you have experience with this special design? Is it usable for discrete levels?


Forum Moderator
Yes, I am familiar with these designs (trained by Shin Taguchi and Yuin Wu).

Yes you can take this approach, and it works for discrete factor levels. Be careful how you specify the design in order to obtain these interactions. Minitab makes it fairly painless.

Note that it does not use replicates. Taguchi methods use repeats, and Minitab reproduces it faithfully. The Taguchi methods do work. I no longer use them because I have found classical approaches to be more efficient, and I do not like the S/N Ratio approach.


You were trained by the guy himself...wow :D
I think I gonna go with 2 replicates and convert the third factor into a continuous one in order to have only 2 levels.
Like that I get 3*3*2*2 = 36 experiments.
The alternative would be to convert the factor and do the full 48 experiments with a D-optimal design excluding the ABC interactions.

Of these two, which would be your preference?
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