Page 413 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 393

special causes, including the type of control chart, its options, the use of run test
rules, and the method by which we sample from the process.
Once we have differentiated between the variation owing to special causes
and the variation owing to common causes, we can separately reduce the varia-
tion from each. To reduce the variation owing to common causes, we look to
all elements of the system and process for clues to variation. We generally can
ignore the point-to-point variation because it represents a combination of fac-
tors that is common to all the subgroups. We’ll typically use designed experi-
ments and multiple regression analysis to understand these sources of
variation.

Transformation

Transformation creates a new variable using one or more original variables, usu-
ally to make an analysis more useful.
When to Use

Analyze Stage

• To stabilize variance to meet the assumptions required for ANOVA tech-
niques (a constant level of variance at each response level)
• To calculate parameters based on a measured response or responses (For
example, cost may be the preferred response, even though labor time was
measured. The effect of the parameter on process variation can also be
calculated when there are repeat runs at each operating condition.)

Methodology

Variance Stabilization
Once the condition of nonconstant variance is detected using the F test for
equality of variance (discussed earlier), we can plot the log of the standard
deviation at each experimental condition with the log of the mean of the ex-
perimental condition. The resulting slope of the line will provide an indication
of a useful transformation, as shown in Table T.20 (Box, Hunter, and Hunter,
1978). Note that slopes lying between those indicated in Table T.20 should be
rounded up or down to the levels provided.
For example, a plot of the log of the averages (of the replicated trials) versus