Creating a Statistical Control Chart using Standard Deviation

Control charts were developed by a statistician named Walter Shewhart in the 1920's. He was working for Bell Labs, who, at that time, were rolling out a telephony network across the US. For this network, amplifiers and other such equipments needed to be buried underground, and it was expensive to have to dig it up for repairs. They were worried about the variations in the manufacturing process leading to increased cost in repairs.

Shewhart used control charts to show that variation was normal and reacting to small variations by making changes to the manufacturing process was wrong. As long as the variation was within control limits and not trending in any particular direction, there was nothing to worry about.

A simple control chart uses the mean of the data (or a subset of that data) to draw a center line around which the data varies. Control limits are set at two or three standard deviations (on the basis that under a normal distribution...