Quality calculator
Normal-Equivalent Sigma Level Calculator
Translate an observed failed-opportunity proportion into a normal-equivalent Z value, with any declared reporting shift shown separately.
What this calculator does
- Translate an observed failed-opportunity proportion into a normal-equivalent Z value, with any declared reporting shift shown separately.
Formula used
- Total opportunities = inspected units × opportunities per unit
- DPMO = failed opportunities ÷ total opportunities × 1,000,000
- Unshifted Z = −inverse standard normal(failed-opportunity proportion)
- Reported sigma = unshifted Z + declared reporting shift
- Passing opportunity percentage = (1 − failed-opportunity proportion) × 100
Inputs explained
- Failed Opportunities: Count binary opportunity failures once each in this study.
- Inspected Units: Whole units inspected under the same opportunity definitions.
- Opportunities per Unit: Same whole number of binary checks performed on each unit.
- Declared Reporting Shift: Explicit reporting convention; zero adds no assumed shift.
How to use the result
- Best suited to fewer observed defects raise Z, more observed defects lower z.
- Normal-equivalent Z does not establish process normality, capability or long-term performance. Zero or complete observed failure has no finite plug-in Z estimate.
Current U.S. benchmarks
- U.S. manufacturing runs at 75.7% of capacity (Federal Reserve, Aug 2026). New factory orders are up 8.5% year over year (Census).
Common questions
- Why is the default shift zero? A fixed shift is a reporting convention, not an observed process property. Enter one only when your reporting method explicitly requires it.
- Why is sigma undefined with zero observed defects? The empirical defect probability is exactly zero, whose normal-equivalent tail is infinite. More inspection or an uncertainty analysis is needed for a finite statistical bound.
- Can sigma be negative? Yes. The unshifted normal-equivalent Z is negative when more than half the defined opportunities fail. Clamping it would hide the observed rate.
- Does this measure Cpk? No. It maps an observed binary failure proportion to a standard-normal percentile. Cpk requires measurements, specification limits and a defensible within-process SD.
Related guides
Last reviewed 2026-10-06.