Three-Sigma Limits

What is 'Three-Sigma Limits'

A statistical calculation that refers to data within three standard deviations from a mean. Three-sigma limits (3-sigma limits) are used to set the upper and lower control limits in statistical quality control charts. Control charts are used to establish limits for a manufacturing or business process that is in a state of statistical control.


Control charts are based on the theory that even in perfectly designed processes, a certain amount of variability in output measurements is inherent. Variations in process quality due to random causes are said to be in-control; out-of-control processes include both random and special causes of variation. Control charts are intended to determine the presence of special causes.


Control charts are also known as Shewhart charts after Walter A. Shewhart, an American physicist, engineer and statistician (1891-1967).

BREAKING DOWN 'Three-Sigma Limits'

Shewart set 3 standard deviation (3-sigma) limits as "a rational and economic guide to minimum economic loss." 3 sigma limits set a range for the process parameter at 0.27% control limits. A standard deviation is a statistical measurement of variability, showing how much variation exists from a statistical average. Low values indicate that the data points fall close to the mean (average); high values indicate the date is widespread and not close to the mean.


Investors use standard deviation to gauge expected volatility - this is known as historical volatility.