May  2003

Vol. 5, No. 5

Quality Quiz from Professor Cleary

You're right!


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:

  • The number of sigmas ( ) is traditionally 3.
  • is the estimated sigma
  • is the square root of the sample size.

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 error

=  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.

Please direct questions or problems regarding this web site to the Webmaster.