Page 271 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 251

Graphically, the design would look as shown in Figure F.12. The trial num-
bers from Table T.8 are shown at the corners of the cube.
When we have five factors, we can estimate all the main factors and interac-
5
tions using a 32-run (2 ) experiment. This will allow us to estimate 5 main
factors (A, B, C, D, and E), 10 two-factor interactions (AB, AC, AD, AE, BC,
BD, BE, CD, CE, and DE); 10 three-factor interactions (ABC, ABD, ABE, ACD,
ACE, ADE, BCD, BCE, BDE, and CDE), 5 four-factor interactions (ABCD,
ABCE, ABDE, ACDE, and BCDE), and 1 five-factor interaction (ABCDE).
Notice how quickly the number of runs increases as we add factors, doubling
for each new factor when there are only two levels per factor. You may notice
that adding a single factor at three levels would triple the number of runs
required.
You may wonder: Do we really need to estimate all these three-, four-, and
five-factor interactions? Fortunately, the answer is no. CFDs are rarely, if ever,
used and are presented only to aid in an understanding of the benefits of frac-
tional factorial designs.

TAble T.8 a Complete Factorial Design for Three

Std. Order Factor A Factor B Factor C
1 + + +
2 + + –
3 + – +
4 + – –
5 – + +
6 – + –
7 – – +
8 – – –

Fractional Factorial Designs
In most experiments, particularly screening experiments, we can ignore the
effects of the higher-order (larger than two-factor) interactions. It’s unlikely
that these higher-order interactions are significant unless the main factors or
two-factor interactions are also significant. Therefore, we can reduce the num-
ber of runs by excluding the higher-order interactions. These fractional factorial
designs are constructed by aliasing (or substituting) the higher-order interac-