Page 274 - Six Sigma Demystified

254 Six SigMa DemystifieD

Saturated designs refer to special cases of FFDs where only the main factors
can be estimated. In a saturated design, the minimum number of experimental
conditions (1 + p) is used to estimate the p main factors. For example, use a 2 3–1
design to estimate three factors in four runs, a 2 7–4 design to estimate seven
factors in eight runs, and a 2 15–11 design to estimate 15 factors in 16 runs. In
saturated designs, the main factors are all confounded with two-factor interac-
tions. In addition, we have no “extra” runs to estimate error, so we cannot deter-
mine which parameters are significant to the regression. We can only calculate
the parameter effects, which provide the coefficients of the regression equation.
Generally, we will add at least one additional run (a degree of freedom) to the
saturated design, resulting in p + 2 runs, to allow an estimate of experimental
error and resulting significance of the model terms. A center point [where each
factor is set to the midpoint between its high (+1) and low (–1) condition] can
be used to provide a rough estimate.
It should be clear that the fewer parameters we need to estimate, the less
costly the experiment will be to run. Often at least one factor in a design is
statistically insignificant. If, after collecting and analyzing the data, we can
remove that factor from the analysis, we are left with a replicated data set that
provides an estimate of error and better estimates of the remaining factors.
See also “Plackett-Burman Designs,” “John’s ¾ Designs,” and “Central Com-
posite Design” in the Glossary and “Response Surface Analysis” topic elsewhere
in Part 3.

Factorial Designs

Minitab

Use Stat\DOE\Factorial\Create Factorial Design\2-level factorial (default genera-
tors). Specify Number of Factors.
Select the “Designs” button to select a design. Replicated screening designs are
usually preferred, so select two corner point replicates; blocks (see “Blocking Fac-
tor” in the Glossary) are not generally needed for an initial screening design; center
points are optional. Select the “Factors” button to specify Numeric (i.e., quantita-
tive) or Text (i.e., qualitative) and real experimental values for each factor level.

Use the “Options” button to randomize experimental trials.
For example, a / fraction two-level replicated design (8 runs × 2 replicates =
1
8
16 runs) was constructed for six factors A through F. Two levels were chosen