Defects Per Million Opportunities (DPMO) Calculator
ANA›Life Services Authority›National Calculator Authority›Defects Per Million Opportunities (DPMO) Calculator
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Defects Per Million Opportunities (DPMO) Calculator
Calculate the number of defects per million opportunities (DPMO) and the corresponding Six Sigma level for any process.
Number of Defects
Number of Units Inspected
Opportunities for Defect per Unit
Calculate
function defCalc() { const resultDiv = document.getElementById('def-result');
const defects = parseFloat(document.getElementById('def-defects').value); const units = parseFloat(document.getElementById('def-units').value); const opportunities = parseFloat(document.getElementById('def-opportunities').value);
// --- Validation --- if (isNaN(defects) || isNaN(units) || isNaN(opportunities)) { resultDiv.innerHTML = 'Please fill in all three fields.'; return; } if (defects Number of defects cannot be negative.'; return; } if (units Number of units must be at least 1.'; return; } if (opportunities Opportunities per unit must be at least 1.'; return; } if (defects > units * opportunities) { resultDiv.innerHTML = 'Defects cannot exceed total opportunities (Units × Opportunities per Unit).'; return; }
// --- Core Calculations --- const totalOpportunities = units * opportunities;
// Defect Rate (proportion defective) const defectRate = defects / totalOpportunities;
// DPMO const dpmo = defectRate * 1_000_000;
// Yield (percentage of defect-free opportunities) const yieldPct = (1 - defectRate) * 100;
// Sigma Level using the standard approximation: // Sigma = 0.8406 + sqrt(29.37 - 2.221 * ln(DPMO)) // Valid for DPMO > 0; for DPMO = 0 the calculator reports > 6 Sigma. let sigmaLevel, sigmaDisplay; if (dpmo 6.0 (Perfect)'; sigmaLevel = null; } else if (dpmo >= 1_000_000) { sigmaDisplay = '0.0 (100% defective)'; sigmaLevel = 0; } else { const lnDPMO = Math.log(dpmo); const inner = 29.37 - 2.221 * lnDPMO; if (inner { if (sl === null || sl >= 6) return '🏆 World-Class (Six Sigma)'; if (sl >= 5) return '✅ Excellent'; if (sl >= 4) return '👍 Good'; if (sl >= 3) return '⚠️ Average'; if (sl >= 2) return '❌ Below Average'; return '🚨 Poor'; };
const label = sigmaLabel(sigmaLevel);
resultDiv.innerHTML = `
Total Opportunities ${totalOpportunities.toLocaleString()}
Defect Rate ${(defectRate * 100).toFixed(4)} %
DPMO ${dpmo.toLocaleString(undefined,{maximumFractionDigits:2})}
Process Yield ${yieldPct.toFixed(4)} %
Sigma Level ${sigmaDisplay} σ
Quality Rating ${label}
`; }
#### Formulas Used
Total Opportunities (TOP): TOP = Units × Opportunities per Unit
Defect Rate (p): p = Defects ÷ TOP
DPMO: DPMO = p × 1,000,000 = (Defects ÷ TOP) × 1,000,000
Process Yield: Yield (%) = (1 − p) × 100
Sigma Level (short-term approximation): σ = 0.8406 + √(29.37 − 2.221 × ln(DPMO)) (Valid range: DPMO 3.4 to ~933,000; capped at 6σ)
#### Assumptions & References
- DPMO assumes a stable, in-control process over the inspection period.
- Each unit must have the same number of defect opportunities.
- A "defect" is any non-conformance to specification; a unit may have multiple defects.
- The Sigma Level formula includes the standard 1.5σ shift used in Six Sigma methodology (long-term vs. short-term capability).
- Six Sigma benchmark: 3.4 DPMO ≈ 6σ (99.99966% yield).
- Sigma approximation formula source: Pyzdek & Keller, The Six Sigma Handbook, 4th Ed.
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