SC QUALITY GUILDSigma, DPMO and yield
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Drag the sigma level and watch the tails. The 1.5 shift applied the way the examinations apply it.
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Q-BotClick for an explanation of this calculator.Sigma level, DPMO and yield
1.5σ LONG-TERM SHIFT APPLIEDFor educational use. This page is a study aid. The method behind it has far more depth and detail than one page and one tool can cover, and what you see here is not everything the method offers or everything this site offers. For full understanding and application, use the governing standards and texts, and seek further education, training or qualified advice. Results depend on the data you enter, so check them before relying on them.
What a sigma level actually counts
A sigma level is a way of restating a defect rate as a distance. If the process output is normal and the specification limits sit six standard deviations from the mean, the process is at six sigma. Nothing more mystical than that.
The unit underneath it is DPMO — defects per million opportunities. Not defects per million parts. That distinction is where most of the arguments start, and we will come back to it.
The 1.5 sigma shift, and why the numbers look wrong without it
Six sigma from the mean to each limit gives about two defects per billion (one in each tail). Yet every reference says six sigma is 3.4 defects per million. The gap is the 1.5 sigma shift.
The reasoning is that no real process holds its mean perfectly over the long run. Tools wear, batches vary, setups drift. The convention allows the mean to wander up to 1.5 sigma either way and reports the defect rate at that worst case. So a "six sigma" process is being scored as though it were running at 4.5 sigma on its bad day.
| Sigma level | DPMO with 1.5 shift | DPMO centered (both tails) | Yield (shifted) |
|---|---|---|---|
| 2 | 308,538 | 45,500 | 69.15% |
| 3 | 66,807 | 2,700 | 93.32% |
| 4 | 6,210 | 63 | 99.379% |
| 4.5 | 1,350 | 6.8 | 99.865% |
| 5 | 233 | 0.6 | 99.977% |
| 6 | 3.4 | 0.002 | 99.99966% |
The two columns differ by more than three orders of magnitude at six sigma. Whenever somebody quotes you a sigma level, the first question is which column they used. A supplier reporting "4.5 sigma" means 1,350 DPMO if they shifted and 6.8 if they did not — a factor of two hundred.
The shift is a convention, not a law of nature. It came out of Motorola's experience with long-term drift and it was never claimed to be universal. A tightly controlled process may drift far less; a poorly controlled one may drift more. It is applied because it makes numbers comparable, not because every process actually moves 1.5 sigma.
Opportunity counting decides the answer
DPMO has a denominator, and you choose it. A wiring harness with 400 solder joints can be counted as one opportunity per harness or four hundred. Same defects, same harnesses, and the DPMO differs by a factor of four hundred — which moves the sigma level by roughly one and a half to two full points.
This is the single easiest metric in quality to game, and it is usually gamed without anyone intending to. Somebody counts opportunities generously during a good quarter, the number improves, and nobody re-derives it.
- Fix the opportunity definition in writing before the first measurement, and keep it fixed. A sigma level is only comparable against its own history if the denominator never moved.
- Count opportunities that can genuinely fail independently. If a single setup error puts the same defect on all four hundred joints, they were never four hundred opportunities.
- Never compare DPMO across companies without comparing their opportunity definitions first. The comparison is almost always meaningless and occasionally deliberate.
Where sigma levels mislead
- The output is not normal. The whole conversion assumes a normal distribution. Applied to a skewed or bounded characteristic — flatness, roundness, anything with a hard floor at zero — the tail estimate can be wrong by orders of magnitude.
- One number for a process with several characteristics. Rolling them together hides the one that is actually failing.
- It says nothing about the customer. A process can sit at five sigma against a specification that was never right in the first place.