Sigma level calculator

Enter the defects you found, the units you checked and the opportunities for a defect in each unit. The calculator returns the DPMO, the yield and the sigma level of the process.

In short

The sigma level expresses how capable a process is of producing without defects, on a scale where 6 sigma means 3.4 defects per million opportunities. It is calculated from DPMO, the defects per million opportunities, with the conventional 1.5 sigma shift.

Defects found

Count every defect, even if one unit has several.

Units inspected

Opportunities per unit

Ways a single unit can be defective. Use 1 if you only count good or bad.

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Sigma level

2.8

DPMO104,167

Yield89.6%

Below 3 sigma, more than one unit in fifteen carries a defect. The process needs its biggest problems found before any fine-tuning: start with a Pareto of the defects to see which few types account for most of them.

The formula

DPMO = defects ÷ (units × opportunities per unit) × 1,000,000
Yield = 1 − DPMO ÷ 1,000,000
Sigma level = Z(yield) + 1.5

Z is the inverse of the standard normal distribution. The 1.5 added at the end is the conventional long-term shift used in Six Sigma tables; without it you get the short-term Z value.

Sigma level, DPMO and yield

Sigma level	DPMO	Yield
2	308,538	69.1%
3	66,807	93.3%
4	6,210	99.38%
5	233	99.977%
6	3.4	99.99966%

Worked example

A team checks 480 units and finds 50 defects, counting one opportunity per unit. DPMO = 50 ÷ (480 × 1) × 1,000,000 = 104,167. The yield is 89.6%, and Z(0.896) + 1.5 gives a sigma level of about 2.8. That is below 3 sigma, so the first step is a Pareto of the defect types.

Related guides

Pareto Ishikawa diagram Control plan

Frequently asked questions

What is DPMO?

Defects per million opportunities: the number of defects divided by the total opportunities for a defect, scaled to one million. It lets you compare processes whose units differ in complexity.

Why add 1.5 to the sigma level?

Six Sigma assumes a process drifts by about 1.5 sigma over the long term, so the tables add that shift to the short-term Z value. It is a convention, which is why 6 sigma corresponds to 3.4 DPMO and not to a far smaller figure.

How do I count opportunities per unit?

List the distinct ways a unit can fail to meet a requirement that matters to the customer, and count them. Keep the list stable over time, because inflating it lowers DPMO without improving anything.

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