Enter the total number of defects found in a sample, the sample size, and the number of defect opportunities per item to calculate the sigma level.

Sigma Level Formula

The following table lists the sigma level on a defects per million basis and a percentage yield.

Sigma LevelDefects Per Million
Yield %

Sigma Level Definition

What is sigma level? A sigma level is a term used in both statistics and manufacturing to describe the rate of defects per million opportunities as a function of the number of standard deviations from a mean of a sample. For example, in a standard mean data set of 1 million objects, only 3.4 out of a million would fall within the sixth standard deviation.

Sigma Level Example Problem

How to calculate sigma level?

  1. First, determine the total number of defects in the sample.

    For this example, there were 100 defects found in the sample.

  2. Next, determine the sample size.

    These defects were found in a sample size 5,000.

  3. Next, determine the number of opportunities for defects in each item.

    There are 10 total possible spots of failure in the object.

  4. Next, calculate the DPMO.

    Using the formula DPMO = Total defects / (sample size*opportunities for failure per item) * 1,000,000. This yields 2,000 DPMO.

  5. Finally, determine the sigma level.

    Using the table above, the sigma level is found to be 4 sigmas.

About Sigma Level

What is a good sigma level? In manufacturing, the gold standard of quality is reaching a six sigma level. In fact, there are entire fields of study that go into reaching a six sigma quality level. However, lower sigma levels can be acceptable depending on the operation or product.

Can a sigma level be negative? No, sigma levels cannot be negative by definition. (At least in terms of manufacturing). The most possible failures are 100% failure or 0% yield. This would simply equate to a sigma level of 0.

How many sigma levels are there? There is an infinite number of possible sigma levels, but most studies only consider sigma levels of 1 through 6, with six being the highest sigma level.