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.
- DPMO Calculator (Defects Per Million Opportunities)
- Rate Per 1000 Calculator
- CPK Calculator
- Ppk (Process Performance Index) Calculator
- System Reliability Calculator
- Defect Rate Calculator
Sigma Level Formula
The Sigma Level Formula is a statistical measure used to determine the quality and effectiveness of a process. It is computed by analyzing the number of defects or errors in a process relative to the number of opportunities for defects to occur.
The following table lists the sigma level on a defects per million basis and a percentage yield.
| Sigma Level | Defects Per Million DPMO | Yield % |
| 1 | 690,000 | 30.85% |
| 2 | 308,000 | 69.15% |
| 3 | 66,800 | 93.32% |
| 4 | 6,210 | 99.38% |
| 5 | 230 | 99.977% |
| 6 | 3.4 | 99.99966% |
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?
- First, determine the total number of defects in the sample.
For this example, there were 100 defects found in the sample.
- Next, determine the sample size.
These defects were found in a sample size 5,000.
- Next, determine the number of opportunities for defects in each item.
There are 10 total possible spots of failure in the object.
- 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.
- 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.
