Page 408 - Six Sigma Demystified

388 Six SigMa DemystifieD

Figure F.51 Larger shifts are easier to detect because there is a larger percentage of the process outside the control
limits.

larger subgroup taken over a short interval would tend to contain dependent
data; taken over a longer interval, the subgroup could contain special causes of
variation.
The safest assumption for maintaining a rational subgroup is to use a sub-
group size of 1. Since data usually have some cost associated with them, smaller
subgroups generally are cheaper to acquire than larger subgroups. Unfortu-
nately, smaller subgroup sizes are less capable of detecting shifts in the
process.

As seen in Figure F.51, it is easier to detect larger process shifts than to detect
smaller process shifts. The larger shift, shown by the k = 3σ shift on the far
right, has much more area outside the control limits, so it is easier to detect
than the k = 1σ shift.
Table T.19 shows the average number of subgroups necessary to detect a
shift of size k (in standard deviation units) based on subgroup size n. For exam-
ple, if we observe the process a large number of times, then, on average, a sub-
group of size n = 3 will detect a k = 1σ shift in 9 subgroups. As you can see from
the table, small subgroups will readily detect relatively large shifts of 2σ or 3σ
but are less capable of readily detecting smaller shifts. This demonstrates the
power of the X chart.