Page 387 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 367

the list of designs, and optionally choose Randomize Runs and add Design Rep-
licates and Center Point.
A Central Composite or Box-Behnken design is chosen with Design Replicates set
to 2 to produce a design similar to Minitab’s (shown above). Use New Chart\
Designed Experiment to edit the existing design and add axial points.

Interpretation

In the ANOVA shown in the following example, the F statistic is used to com-
pare the sum of squares variation owing to curvature with the sum of squares
variation owing to pure error. The low p value (0.000; much less than 0.05)
indicates that curvature is significant, suggesting that we are near a stationary
point (such as a local minimum, maximum, or saddle point).
When the stationary point is outside the experimental region, the experi-
mental region should be expanded with new data, where possible. When new
data cannot be generated because the stationary point lies in a region where the
factors cannot exist, then we can use the steepest ascent techniques with con-
strained optimization.
When the stationary point is a saddle point, we also can use the steepest
ascent with constrained optimization techniques.
Axial points are added to the current design (at the new centerpoint), and
the full results are analyzed (to make maximum use of the data). The locations
(values) of the axial points are chosen to achieve rotatable orthogonal designs
based on the number of parameters (see further discussion under Central Com-
posite Design in the Glossary). In the following example, there are three param-
eters (B, E, BE), so the axial points are chosen at a value of 1.682, which is

applied to factor B’s level of 10 to achieve an axial level of 16.82 and to factor
E’s level of 8.74 to achieve an axial level of 14.7.
Once the optimal point has been defined, additional data always must be
collected at this new operating region to verify the predicted results.

Response Surface Designs

Minitab

The results of the first-order design with centerpoint at local maximum are
analyzed using the Stat\DOE\Factorial\Analyze Factorial Design option.
(Continued)