Page 407 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 387

subgroups about the X chart center line is a reduction in process variation. But
the range chart fails to confirm this theory.
These data, provided by a major cosmetic manufacturer, represent the fill
weight for bottles of nail polish. The filling machine has three filling heads, so
subgroups were conveniently formed by taking a sample from each fill head.
The problem is that the heads in the filling machine apparently have signifi-
cantly different average values. This variation between filling heads causes the
within-subgroup variation (as plotted on the range chart) to be much larger
than the variation in the subgroup averages (represented graphically by the
pattern of the plotted points on the X chart). The X chart control limits, cal-
culated based on the range chart, thus are much wider than the plotted
subgroups.
The underlying problem, then, is that the premise of a rational subgroup has
been violated: We tried to construct a subgroup out of apples and oranges. But
all is not lost (fruit salad isn’t so bad) because we’ve learned something about
our process. We’ve learned that the filler heads are different and that we could
reduce overall variation by making them more similar. Note the circles that
highlight subgroups 16 through 40 in Figure F.50. The software has indicated
a violation of run test 7, which was developed to search for this type of pattern
in the data (see “Run-Test Rules”).
This type of multistream behavior is not limited to cosmetics filling opera-
tions. Consider the potential for irrational subgroups in these processes:

• A bank supervisor is trying to reduce the wait time for key services. She con-
structs a control chart using subgroups based on a selection of five customers
in the bank at a time. Since she wants to include all the areas, she makes sure

to include loan applications as well as teller services in the subgroup.
• An operator finish grinds 30 parts at a time in a single fixture. He measures
5 parts from the fixture for his subgroup, always including the two end
pieces. His fixture is quite worn, so the pieces on the two ends differ sub-
stantially.

Most likely, each of these examples will result in an irrational subgroup
owing to multistream processes.

Sampling Considerations
Many times, the process will dictate the size of the rational subgroup. For ex-
ample, the rational subgroup size for service processes is often equal to 1. A