Adding to Jeff's response, I suggest you read Dr. Wheeler's papers/books regarding the incorrect assumption of normality when using control charts (Shewhart's charts).
Wheeler, Donald, and Chambers, David (1992) “Understanding Statistical Process Control” SPC Press (ISBN 0-945320-13-2)
You can also read Shewhart's original book:
Shewhart, Walter A. (1931) “Economic Control of Quality of Manufactured Product”, D. Van Nostrand Co., NY
Bill Woodall also has an excellent paper:
Woodall, William H. (2000), "Controversies and Contradictions in Statistical Process Control", Journal of Quality Technology, Vol. 32, No.4 October 2000.
Also go here:
https://community.jmp.com/t5/JMPer-Cable/Designing-Insightful-Process-Behavior-Charts/ba-p/21332
"All models are wrong, some are useful" G.E.P. Box