Authors: Marilyn & Robert Hart
Q: How do I use a control chart to compare
measurement data taken from samples from different
applications?
A: The Xbar and s control chart is an
excellent way to compare both the average (mean)
and the variability (standard deviation) of
samples from different applications in order
to compare their performance. This is called
the use of rational subgroups, rather than the
time-order of data usually associated with control
charts. Since there are typically few subgroups
involved, subgroups of at least 25 measurements
are recommended.
Example:
It is desirable to compare the performance of
two shifts making similar product. Fifty measurements
from each of the two shifts are taken to be
analyzed on an Xbar & s chart. Since only
two subgroups are being used, it is desirable
to use 1.5 sigma limits to keep the alpha risk
in the desired range (close to 0.07). (See the
previous month's Quality Practice Tips.) The
resulting Xbar & s chart is shown in Figure
1. The s chart is out of control which means
that the difference in s between the two shifts
is statistically significant. Note that this
is similar to hypothesis testing on the means
(and variances) or analysis of variance in classical
statistics.
Figure 1. Xbar & s Chart, 1.5-Sigma Limits
