| May 2003 |
Vol. 5, No. 5 |
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Quality Quiz
from Professor Cleary
Congratulations!
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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:
Where
When I offer this consideration to my students, many of them just smile and wait for me to go on to the next chapter.
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Copyright 2003 PQ Systems.
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) is traditionally
3.
is the estimated sigma
is the square root of the sample size.
=
standard error
= the sample size of the samples in the
distribution of sample means