How this calculator works
A defect is one failure in one unit; an opportunity is one place where a failure could occur. A unit with ten inspection points offers ten opportunities. DPMO scales the defect count to a million opportunities, so a line making a thousand units and a line making a million can be compared on the same scale. The Sigma level converts the DPMO into the number of standard deviations between the process mean and the nearest specification limit, and the usual Six Sigma convention adds a 1.5 sigma shift for long-term drift. A classic Six Sigma process has 3.4 defects per million opportunities, which is a 4.5 sigma short-term capability and 6.0 after the shift.
Formula
DPMO = defects / (units x opportunities per unit) x 1,000,000. DPU = defects / units. yield = 1 - DPMO / 1,000,000. sigma level = inverse standard normal of (1 - DPMO / 1,000,000) + 1.5.
Worked example
A batch of 10,000 units has 621 defects and ten opportunities per unit. DPMO = 621 / (10,000 x 10) x 1,000,000 = 6,210. DPU = 621 / 10,000 = 0.0621 and yield = 1 - 0.00621 = 0.99379, or 99.379 percent. The inverse normal of 0.99379 is about 2.50, so the sigma level is 2.50 + 1.5 = 4.00. A DPMO of 3.4 gives 4.5 + 1.5 = 6.0 sigma.
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Frequently asked questions
What is the 1.5 sigma shift?
In the Six Sigma framework, a process observed over time drifts by about 1.5 standard deviations from its short-term position. The reported sigma level therefore adds 1.5 to the short-term capability calculated from the defect rate. It is a convention from Motorola's methodology, not a law of statistics, and some organisations report the unshifted figure.
How do I choose the number of opportunities?
Count each place in a unit where the customer could notice a failure, such as one per critical dimension or one per inspection step. More opportunities lower the DPMO for the same defects, so define the count before you start measuring and keep it stable. Changing the definition mid-programme makes trends meaningless.
Is yield also the proportion of good units?
Only when each unit can hold at most one defect. Otherwise 1 - DPMO/1,000,000 is the expected share of defect-free opportunities, not the share of perfect units. Rolled throughput yield, which multiplies the yields of each step, is the right figure for whole-unit conformance.
Why does a DPMO of 1,000,000 fail?
At that rate every opportunity fails and the yield is zero, so the inverse normal is undefined. Real processes use DPMO figures well below a million. Enter a smaller rate to get a Sigma level.