what is a three sigma limit 
a three sigma limit is a statistical calculation in which the data are within three standard deviations from a mean three sigma refers to processes in business applications that operate efficiently and produce items of the highest quality three sigma limits are used to set the upper and lower control limits in statistical quality control charts control charts establish limits for a manufacturing or business process that s in a state of statistical control understanding three sigma limitscontrol charts are also known as shewhart charts named after walter a shewhart an american physicist engineer and statistician 1891 1967 1 control charts are based on the theory that a certain amount of variability in output measurements is inherent even in perfectly designed processes control charts determine if there s a controlled or uncontrolled variation in a process 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 statisticians and analysts use a metric known as the standard deviation to measure variations also referred to as sigma it s a statistical measurement of variability showing how much variation exists from a statistical average sigma measures how far observed data deviates from the mean or average investors use standard deviation to gauge expected volatility consider the normal bell curve which has a normal distribution the farther to the right or left a data point is recorded the higher or lower the data is than the mean low values indicate that the data points fall close to the mean high values indicate that the data is widespread and not close to the average example of calculationlet s consider a manufacturing firm that runs a series of 10 tests to determine whether there s a variation in the quality of its products the data points for the 10 tests are 8 4 8 5 9 1 9 3 9 4 9 5 9 7 9 7 9 9 and 9 9 