Which approach to use for designing my experiments (DoE)?

Hi all and welcome to my first post.

I am new to the field of DoE and did a lot of background reading. Now, I need to design a series of experiments: I want to fabricate a specific part on a machine and investigate the influence of about 15 factors on the mechanical strength of that part. Some of the parameters have two levels, for which a factorial design would be fine, but some don't. They might even have a 'random' behavior: for example the position on the machine's table, the age of the material (e.g. degradation) and the relative humidity in the room. I don't expect interference between the (most) parameters, which probably makes it a little bit easier. However, due to the large amount of factors and the relatively high costs of the experiments, I am trying to reduce to number of experiments to a minimum.

Some questions might sound trivial, please take my apologies me for that.

1) What would be the best approach in general?
1.1) .. would that be to build one group for the factors with two levels (factorial design) and investigate the ones with multiple levels individually (individual experiments method)?
1.2).. or would that be to investigate even all parameters individually (individual experiments), because I don't expect interference?
1.3) .. or does it make sense to reduce the factors with multiple levels to two levels (e.g. say max and min position on the table and neglect everything in between) and do a factorial design with all parameters?
2) How many tests of the same factor and level (repetitions) are needed to get statistically correct results?

With this question I also want to make sure, that I didn't oversee certain methods which might be more appropriate.

Thank you all so much!
Best regards


TS Contributor
just a few quick points that could help: you have several choices besides taking a variable as a factor. If the variable is very hard ro control but might have an influence on your outcome a possibility could be to record its values during the experiment and use it in the analysis as a covariate.Wome others vould be used as blocking variables, like possibly age of the material ( one block with aged and one block with younger material)? Others you might just randomize, according to the old DoE wisdom - block what you can and randomize what you can't.

More specifically 1. the best approach will depend on the number of factors you are left with. In general, you should plan a screening type of design first and adapt your experiment based on what you learn. A good rule of the thumb is to spend about 20% of your budget for the first run amd reserve the rest for follow-ups whete you will be a lot more informed. For screening designs I would always use two levels per factors, as I do not know yet which factors will be important, so there is a high risk of wasting runs.

2. That depends in theory on the effect size and the variation of you tesults. I personally prefer to run one replication first and get an upper limit on the effect size in case I find nothing. Then in the secon set of experiments we can decide to replicate the experiment and search for smaller effects or look somewhere else where we have a more promising situation.

kind regards and good luck


TS Contributor
I would start with a fractional factorial screening design. If you are very confident that there are no interactions, try a Plackett-Burmann design or one of Douglas Montgomery's No-Alias Screening Designs. I also recommend adding 3 - 5 center points. This will allow you to test for curvature and provide an estimate of experimental error without performing replications. Regarding table position and age of material, I would use worst/best case levels. Record relative humidity and treat it as a covariate, not as a factor.

Regarding the number of replicates required, start with specifying the delta (change) that is of "practical" significance. Estimate the process standard deviation by measuring a number of parts. You will then need to specify the desired Power and Alpha risk. Then calculate the required number of replicates. However, due to sparsity of effects, you can usually count on some hidden replication as you remove factors from the model.

Many industrial practitioners are only interested in strong effects and run unreplicated experiments for screening designs. You may miss some weaker effects, but these are usually of little practical value.