# Understanding Sigma Levels

### What Is Sigma ?

Sigma or standard deviation is a statistical measure of dispersion in data. It is a measure which uses the characteristic of past data to make judgements about how the process will perform in the future. If a given set of data has normal probability distribution then the number of defects that will occur in the process over a period of time can be known depending upon the sigma level of the process.

### What Are Sigma Levels ?

The sigma (standard deviation) is multiplied with the numbers 1, 2, 3 etc to come up with a range. For example lets assume that the average of a data set is 10, while the sigma is 2. Hence 1 sigma will include all the data points between 10 +/-2 i.e. between 8 and 12. A 2 sigma measure would include 10+/-2(2) i.e. all data points between 6 and 14. So on and so forth.

However, it is a known fact that in a normal distribution the points tend to be around the mean. Therefore all the points will be closer to the average. Hence as one goes to farther and farther sigma levels the additional gains in terms of productivity are less.

### Observations

• Sigma levels which are less than 3 are not desirable. Companies with less than 3 sigma levels will not be able to survive in a competitive marketplace.
• After Sigma Level 3 the gains are very small. But these gains make a considerable difference to the overall cost of quality as explained in costs of poorly performing processes.

To be a six sigma organization, the processes of an organization must be able to support this kind of efficiency sustainably. Building such robust processes requires a lot of intelligence and effort.

 Sigma Level Defects/Million Percentage Defects 1 691462 69% 2 308538 31% 3 66807 6.7% 4 6210 0.62% 5 233 0.023% 6 3.4 0.00034% 7 0.019 0.0000019%

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