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Three-Sigma Limits

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Three-sigma limits, also called 3-sigma limits, are a statistical calculation used to define quality control limits on a process. In statistical quality control, three-sigma limits are used to set upper and lower control limits on a chart that plot data like a bell curve. This type of chart is called a normal distribution chart, or bell-curve chart. Within these charts 1% of all plot points reside above the average value and above the three-sigma line. This statistic is important for controlling quality in a production system, as it allows to identify points that could indicate a problem before the system begins producing faulty results.

The three-sigma limits are derived from the standard deviation of a dataset and are placed at +3 and -3 standard deviations from the mean. The mean is calculated by totaling all of the data points in the dataset and dividing by the total number of data points. Standard deviation is the sum of the squares of the differences between each data point and the mean, divided by the number of data points minus one. The result of this calculation and the mean are used in a formula to set the 3-sigma limits.

For quality control purposes in production systems, data points outside the three-sigma line are classified as non-conforming and indicate that further investigation is needed. The data points or parts involved in the process may need to be removed from the system and further quality control measures taken. Data points close to the three-sigma line can influence the data points that come after it and indicate that further investigation may be needed before continuing with the quality control.

In summary, three-sigma limits are calculated using the average value of a dataset and its standard deviation to identify points that fall outside of desired quality parameters. Points outside the three-sigma line are classified as non-conforming and warrant further investigation to ensure that quality control is maintained. While three-sigma limits have been traditionally used in production systems, they are now being used in numerous other processes to control quality, such as medicine, engineering, and finance.

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