Sigma in the control chart.

Steve Simon

2000-01-27

Dear Professor Mean, I ran a control chart in SPSS for individual values, and the control limits don’t correspond with what I would expect from the descriptive procedure that I ran first. In particular, the value of sigma in the control chart appears to be an approximation of what I computed earlier. Why would SPSS use a different calculation for sigma?

Dear Reader, The use of the word “sigma” in quality control circles is different than how it is used in other circles. So the sigma limits that you get in your control chart are different than what you would get in any other descriptive statistics procedure. In particular, sigma represents neither the sample standard deviation, nor the standard error of the mean.

The reason the sigma in a control chart differs from any of the numbers you might get in a descriptive summary is that:

Further reading

Donald Wheeler has authored or co-authored three excellent books that explain this material far better than I can.

You can find an earlier version of this page on my original website.