Quality worked example

Sigma Level with defects of 9 defects: a worked example

This worked example runs the sigma level numbers for a tougher week than the baseline: defects of 9 defects instead of the typical 18 defects. Convert defects, units, and opportunities into DPMO, quality rate, and an approximate sigma level.

The inputs for this scenario

  • Defects: 9 defects (the input this scenario stresses; the baseline uses 18)
  • Units inspected: 12,000 units (held at the documented default)
  • Opportunities per unit: 4 opportunities (held at the documented default)
  • Sigma shift: 1.5 sigma (held at the documented default)

Working through the calculation

  • The calculation starts from the formula this tool documents: DPMO = defects ÷ (units × opportunities) × 1,000,000.
  • Sigma level works out to 5.06 sigma at these inputs, and this is the headline figure for the scenario.
  • DPMO works out to 188 DPMO at these inputs.
  • Quality rate works out to 99.98 % at these inputs.
  • Opportunities works out to 48,000 opportunities at these inputs.

How this compares with the baseline

  • Against the tool's baseline example, where defects sits at 18 defects and the headline result is 4.87 sigma, this scenario comes in 3.83% above the baseline at 5.06 sigma.
  • Use it to baseline a process, benchmark across lines or sites, and quantify improvement after a Six Sigma project. A result at this level usually justifies acting on the stressed input before touching anything else, because every other figure in the table is downstream of it.

Results at a glance

  • Sigma level: 5.06 sigma (headline result)
  • DPMO: 188 DPMO
  • Quality rate: 99.98 %
  • Opportunities: 48,000 opportunities

Run it with your numbers

  • To rerun this with your own numbers, open the live Sigma Level calculator, set defects to your actual value, and adjust the remaining inputs to match your operation.

Last reviewed 2026-05-12.