How to calculate upper & lower control limits

Updated March 23, 2017

A control chart is a chart used to monitor the quality of a process. The upper and lower control limits are two horizontal lines drawn on the chart. If data points fall outside of these lines, it indicates that it is statistically likely there is a problem with the process. These lines are usually placed three standard deviations from the mean, so there is a 99.73 per cent probability that a data point will be within those limits. To calculate the control limits, you will need to first find the mean and standard deviations of your data set. Then you will calculate the upper and lower control limits.

Find the mean of your data set by adding all the data points and dividing by the number of data points. As an example, take the data set: 2, 3, 5, 5, 7. The mean is 2+2+3+5+5+7 / 6 = 24 / 6 = 4.

Subtract the mean from each data point and square the result. Continuing the example: (2-4)^2, (2-4)^2, (3-4)^2, (5-4)^2, (5-4)^2, (7-4)^2 = (-2)^2, (-2)^2, (-1)^2, (1)^2, (1)^2, (3)^2 = 4, 4, 1, 1, 1, 9.

Find the mean of the result. Again, from the example: 4 + 4 + 1 + 1 + 1 + 9 = 20 / 6 = 3.33.

Take the square root of that mean to get the standard deviation. The standard deviation of the example is sqrt(3.33) = 1.83.

Multiply the standard deviation by 3. From the example = 1.83 x 3 = 5.48.

Add the mean of the original data set to the result. This is the upper control limit. The upper control limit for the example data set is 4 + 5.48 = 9.48.

Subtract the result of Step 1 from the mean of the original data set to get the lower control limit. The lower control limit of the example data set is 4 - 5.48 = -1.48.


Make sure to double-check your calculations.

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Kaylee Finn began writing professionally for various websites in 2009, primarily contributing articles covering topics in business personal finance. She brings expertise in the areas of taxes, student loans and debt management to her writing. She received her Bachelor of Science in system dynamics from Worcester Polytechnic Institute.