Vol. 5, No. 5
from Professor Cleary
Alas, Dinah will continue to
thirst for her black belt ensemble. The control limits vary because the
sample sizes vary in the X-bar and S chart. In the print documentation for SQCpack, p. 287,
you will find the formula
used for X-bar and sigma charts. The upper control limit formula is:
One way to explain the varying width of the control limits is by pointing out how the n in the formula affects the width. If the sample size is always 5, the control limits will not vary. On the other hand, if a smaller sample (such as 2, in this case), the control limits will widen.
One can be less certain about a small sample size than about a larger one. Therefore, the smaller the sample size, the wider the control limits.
A second way to consider this formula is to recall the standard error and the central limit theorem:
= standard deviation of the population
= the sample size of the samples in the distribution of sample means
When I offer this consideration to my students, many of them just smile and wait for me to go on to the next chapter.
Copyright 2003 PQ Systems.
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