Don’t Replicate Fractional Factorial Designs when Designing Experiments

Don’t Replicate Fractional Factorial Designs when Designing Experiments

Some experimenters are of the view that it is always necessary to replicate designs in order to test for significant effects. As a consequence, some experimenters will replicate fractional factorial designs. This doesn’t make sense.

Consider the case of a quarter fraction, 2-level design of 6 factors in 16 runs. There is considerable aliasing among the two factor interactions, about which we will be concerned. See the alias structure here reproduced from Minitab:

Alias Structure

I + ABCE + ADEF + BCDF

A + BCE + DEF + ABCDF
B + ACE + CDF + ABDEF
C + ABE + BDF + ACDEF
D + AEF + BCF + ABCDE
E + ABC + ADF + BCDEF
F + ADE + BCD + ABCEF
AB + CE + ACDF + BDEF
AC + BE + ABDF + CDEF
AD + EF + ABCF + BCDE
AE + BC + DF + ABCDEF
AF + DE + ABCD + BCEF
BD + CF + ABEF + ACDE
BF + CD + ABDE + ACEF
ABD + ACF + BEF + CDE
ABF + ACD + BDE + CEF

Replicating this design will require 32 runs, but the additional 16 runs won’t assist in breaking up the aliases among the two factor interactions. After the replication we will have a more powerful test for significance of effects, but we will continue to have the same degree of aliasing as before the replication. Instead, if there are resources available for 32 runs, it makes much more sense to use the 32 runs to design a half fraction, in which, in this particular case, there won’t be aliasing among the two factor interactions. The power to test for significant effects will be much the same as that achieved from the replicate on the quarter fraction, because the additional insignificant effects that are likely to be produced using a half fractions can be converted to sums of squares, and will perform much the same role as the replicate on the quarter fraction. That is; you will have much the same ability to detect significant effects, while avoiding aliasing among the two factor interactions, for the same 32 experimental runs.

Learn more about the correct use of fractional designs by attending our Design of Experiments courses. The next public Design of Experiments course is a three day course scheduled for 5th – 7th June in Dublin. This course can also be run on an in-house basis. We also have a six day Design of Experiments for R&D course. The latter is run as an in-house course.