Assume that we have 8 factors and want to design experiments using 2-level fractional factorial design. At the same resolution for 1/8 fraction and 1/16 fraction, we can run partly a same number of experiments:
37 runs with 1 replicate (32 + 5 center points)
42 runs with 2 replicates (16X2 + 5X2 center points)
Considering that we can do not more than 42 experiments, which ones give the better estimation - with replication or without?
Dear Selvaraju,
In the link below it was mentioned that there is no need to replicate fractional factorial design. The replication doesn't make sens. Instead, if there are resources available for more runs, it makes much more sense to use those runs to design a higher fraction.
http://sqt.ie/wordpress/?p=2498
Yes, replication is not required for FFD. It is required only for OFAT and factorial designs.
Interesting question. Which is best, the 1/16 with replication or the 1/8 without? Both have advantages and disadvantages. There are two considerations –
1) The power to detect an effect.
The power to detect effects is higher with the 1/16 w, reps, though not by a lot, than the 1/8 without reps. The probability of detecting a 0.5 Std Dev difference is 27.1 vs. 21.1 for the 1/8, and 76.9% vs. 62.3% for detecting a 1 SD difference. Based on 5% alpha.
2) Degree of confounding.
Confounding is higher with the 1/16 than the 1/8, and this is not corrected by replication. The 1/16 main effects are not confounded, but ALL 2-factor interactions are confounded with 3 other 2-factor interactions, but the 1/8 only SOME of the 2-factor interactions are confounded. For example, the 1/16th AC interaction = AC + BE + DG + FH, and the 1/8th AC = AC + BF + EGH.
Selecting the “best” design probably comes down to what is known about how the factors potentially interact. If interactions between any of the factors is considered unlikely then the 1/16th design could work well. However, if there are potential interactions then the 1/8th might be a better choice because the potential for confounded effects is reduced.
I would be curious to know what you decide.
One thing I forgot to mention - the 1/16 fraction with 5 centerpoints requires 37 runs, not 42 - multiple centerpoints are already replicated.
Therefore -
1/8 fraction - 37 runs with 1 replicate (32 + 5 center points)
1/16 fraction - 37 runs with 2 replicates (16X2 + 5 center points)
Replication is one of the most conditions for Factorial experiments. You must have at least two replicates for each reading. Please refer to Design and Analysis of Experiments, Douglas Montgomery.
Best of luck!
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