How to use it
- Choose what you start from: Defects (counts), DPMO, Yield or Sigma level.
- Enter the numbers. For counts: units inspected, the number of defect opportunities on each unit, and the defects found.
- Leave Apply the 1.5 sigma shift on for the usual Six Sigma tables, or turn it off for the plain short-term Z value.
- Read the sigma level, DPMO and yield; with counts you also get DPO and DPU.
Formulas
- DPO = defects / (units × opportunities); DPU = defects / units
- DPMO = DPO × 1,000,000
- Yield = 100 % − DPMO / 10,000
- Sigma level = Φ⁻¹(1 − DPMO / 10⁶) + shift, shift = 1.5 or 0
- From a sigma level: DPMO = 10⁶ × (1 − Φ(sigma − shift))
Φ is the standard normal cumulative distribution and Φ⁻¹ its inverse. The yield here is the share of opportunities without a defect.
Worked example
You inspect 1,000 units, each with 5 opportunities, and find 27 defects. DPO = 27 / 5,000 = 0.0054, DPU = 0.027 and DPMO = 5,400. The yield is 100 − 0.54 = 99.46 %. The standard normal value with 0.54 % above it is 2.549, so the process runs at 4.05 sigma with the 1.5 shift (2.55 without).
Going the other way, 6 sigma with the shift gives 1 − Φ(4.5) = 3.4 × 10⁻⁶, the famous 3.4 DPMO.
Tips
- Define opportunities once and keep them fixed. Inflating the count of opportunities lowers DPMO without improving anything.
- Compare like with like: a sigma level with the shift and one without differ by exactly 1.5.
- Capability from measurements: if you have the data and specification limits, Cp and Cpk tell you more than a defect count.