# 2 Sigma Control Limits

by Bryan Berg; Updated September 26, 2017The use of sigma, also known as standard deviation, can be confusing. However, it's a great tool for analyzing any set of data. Using two-sigma control limits can benefit your analysis by chopping out the data you don't need and sticking only to the pertinent data at hand. Best of all, since the theory behind control limits is based on standard deviation, there's very little math involved.

## Standard Deviation

Sigma measurements of any kind are based on the standard deviation of a series of numbers. Standard deviation is a measure of variability within a set of figures. A data set with a small amount of difference between the numbers will have a small standard deviation, whereas a data set with all kinds of different numbers will have a higher standard deviation. The standard deviation of a set of numbers is represented by the Greek character sigma, which is where the terms like two-sigma, three-sigma and six-sigma come from.

## Normal Distribution

The use of standard deviation is dependent largely upon a normal distribution, which means the numbers within the data set are relatively compressed. Most of the numbers lie fairly close to the mean, with few outliers skewing the data. If the distribution for a data set is not normal, analysis using standard deviation does not work. However, if the data set does fall within the normal distribution, you can learn a lot about the data by using standard deviation.

## Two-Sigma

The normal distribution shows how numbers will fall based upon the standard deviation of the data set. The rules of the normal distribution dictate that 68 percent of all numbers will fall within one standard deviation of the mean, also known as the average of all numbers in the data set. Adding standard deviations to the equation means more numbers are included; using the normal distribution, 95 percent of all data is within two standard deviations of the mean. This 95 percent is a very common confidence interval used when proving hypotheses, as it excludes outliers and sticks to the main supply of data.

## Two-Sigma in Business

While two-sigma gives a good confidence level for analysis, it is not a good methodology for production. If the control limits of any production process are within two standard deviations of the mean, that process is in serious trouble. It essentially says that out of a million units produced, more than 300,000 will be defective. This is an extremely inefficient way to produce any goods. Producing at even a three-sigma rate would bring that defect level down to 66,000; while this is by no means perfect, it is nearly 500 percent more efficient than producing at two-sigma.