5, No. 11
from Professor Cleary
should be happy, since LaMal’s theory is dead wrong.
Control limits become wider because of the A2 value used to calculate
them, and the R-bar changes, not because of variability within the sample.
Sample #8 has a sample size of 5. The calculation of control limits
for that sample (and all other samples with a size of 5) follows. The
proper A2 value when n = 5 is
#9 has a sample size of 2. The control limits are wider than those of
Sample #8. The proper A2value
when n = 2 is 1.88.
is also to be noted that the R-bar changes as the sample size changes.
It is easy to see in this example that when the sample size becomes
smaller, the control limits become wider. A logical explanation is that
with a smaller sample, the estimate of the mean is less likely to be
accurate, so control limits must become wider. On the other hand, with
a larger sample—say, 10—the control limits would be tighter
because of more accurate prediction of the mean.
For a more detailed explanation, refer to the documentation for SQCpack
2000. By clicking here http://www.sqcpack.com/support.htm,
you will find a link to this documentation. Refer to pages 302-304.
2003 PQ Systems.
direct questions or problems regarding this web site to the Webmaster.