Sigma Level ↔ DPMO ↔ Yield
Converts between the three common ways of stating a process’s defect rate: defects per million opportunities (DPMO), yield, and the Six Sigma process sigma level. Enter any one and the page gives the other two. Six Sigma belts and quality engineers use it to put a measured defect rate on the sigma scale, or to turn a sigma target into a defect rate [1]–[3].
Equations
Yield = 1 − DPMO / 106
Z = Φ−1(Yield) Sigma level = Z + 1.5
DPMO is defects ÷ (units × opportunities per unit) × 106. Yield is the share of opportunities with no defect. Φ−1 is the inverse of the standard normal cumulative distribution, so Z is the number of standard deviations from the mean to the one specification limit that would leave that tail. The page treats all defects as one tail. The 1.5 is the conventional shift: Six Sigma assumes a process mean drifts by about 1.5σ over the long term, so a process that is “6 sigma” short term makes 3.4 DPMO long term [1], [2]. Choose No for Apply 1.5σ Long-Term Shift and the sigma level equals Z.
Limits and common mistakes
- The 1.5σ shift is a convention, not a measurement. If you know your process’s own drift, use the Process Capability calculator instead.
- Count opportunities honestly. Inflating them lowers DPMO and raises the sigma level without any real improvement.
- Yield here is per opportunity. A unit with many opportunities has a lower first-pass yield; see the Rolled Throughput Yield calculator.
- Zero DPMO, or 100 % yield, has no finite sigma level, and the page says so.
Worked example
Final inspection of 4,500 circuit boards finds 27 defects, with 6 defect opportunities on each board. That is 27 ÷ 27,000 × 106 = 1,000 DPMO. What sigma level is the process at?
- Choose Known Value DPMO (defects per million opportunities).
- Enter DPMO 1000.
- Choose Apply 1.5σ Long-Term Shift Yes (conventional Six Sigma metric).
- Press Solve. The Solution shows:
DPMO: 1,000
Yield: 99.9 %
Long-term Z (true Z): 3.09023
Process sigma level (with 1.5σ shift): 4.59023
Check: a one-sided tail of 0.1 % lies 3.09 standard deviations from the mean, as any normal table shows, and 3.09 + 1.5 = 4.59. Going the other way, a sigma level of 6 gives the familiar 3.4 DPMO (3.39767 on the page).