How Do I Do Three Sigma Calculations?

Naresh Kilokov asked 9 months ago

Please explain the three sigma calculation to me with an example. Thanks

1 Answers
Expert Staff answered 9 months ago

What is Three Sigma Rule?

If you navigate to the glossary page, you will find the basic definition of the three sigma rule.  But to make your work easier, the three sigma rule is a statistical rule that uses three standard deviations to measure how far the data is from the mean. In the manufacturing and business industry, the word ‘three-sigma’ is used to represent a process that operates efficiently to produce the highest quality products.  In short, three sigma is the middle ground between “normal” and “abnormal goods”. Three sigma is an important concept in quality control.

Bell Curve of the Three Sigma Rule
Bell Curve of the Three Sigma Rule

Step by Step guide to calculating three-sigma:

Step 1# Calculate the mean

The first step to a three-sigma calculation is to get the mean.  You can get the mean by dividing the sum of all points and diving it with the number of data points.  For instances,  if there were four data points of 4, 5.7, 8.9 and 9.7 then the statistical mean of these points would be [(5.7+ 8.9 + 9.7 +4)/ 4] which is 7.075.

Step 2# Calculate the variance

Variance definition:

Variance is the measure of spread between data points.
The variance is calculated after generating and squaring new data points by subtracting each number from the mean. For example in our previous example, the variance of the first number would be {[7.075 – 5.7]}2 or 1.89. Repeat the same process for all other data points.
After finding the variance of each data point, add them together and divide the sum by the number of data points.
For example, if the first variance was 1.89 and the second variance 2.4 etc then you should add these two numbers and divide by 4

Step 3# Calculate the three-sigma

Sigma is another term for standard deviation.  To get the standard deviation, you need to calculate the square root of the variance. Let’s assume that the variance is 27. To get the sigma we use the square root of 27 which will be 3. Besides, to get the six-sigma, you need to calculate 3 times the square root of 27 which is 9.  From our previous data points, only one data point of 9.7 has reached the expected quality level.

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