Page 270 - Six Sigma Demystified

250 Six SigMa DemystifieD

Factorial Designs

Factorial designs include complete factorial designs (CFDs) and fractional facto-
rial designs (FFDs). They serve as the basis for most design of experiments
(DOE).

When to Use

Analyze Stage

• Use fractional factorial designs as screening designs to understand sources
of variation and discover the process drivers

Improve Stage

• Supplement fractional factorial designs with center points to estimate
curvature effects

Methodology

Refer also to “Design of Experiments (DOE)” above for a general discussion of
the methodology for conducting a designed experiment.

Complete Factorial Designs
Complete factorial designs are capable of estimating all factors and their inter-
actions. We can calculate the number of experimental runs needed to estimate
all the factors and interactions using this simple formula, where b is the number
of levels of each factor and f is the number of factors:

Number of experimental runs = b f

For example, with three factors at two levels each, we calculate that we need
at least eight (2 ) experimental runs to estimate the main factors (A, B, and C),
3
the two-factor interactions (AB, AC, and BC), and the three-factor interaction
(ABC). One degree of freedom is needed to estimate the overall mean.
The complete factorial design for three factors at two levels each is presented
in Table T.8. Note the pattern in the design, where a positive sign indicates the
high level of the factor and a negative sign indicates the low level of the factor.
The actual run order of the design will be randomized when implemented, but
the pattern is useful for seeing how the design is generated.