Six Sigma DPMO Calculator

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Six Sigma DPMO Calculator

Calculate Defects Per Million Opportunities (DPMO), Sigma Level, and Process Yield to measure and improve process quality using Six Sigma methodology.

Number of Defects Found

Number of Units Inspected

Opportunities for Defect per Unit

Calculate

DPMO —

Sigma Level —

Process Yield —

Defect Rate (DPO) —

function sixCalc() { var errEl = document.getElementById('six-error'); var resEl = document.getElementById('six-result'); errEl.style.display = 'none'; resEl.style.display = 'none';

var defects = parseFloat(document.getElementById('six-defects').value); var units = parseFloat(document.getElementById('six-units').value); var opportunities = parseFloat(document.getElementById('six-opportunities').value);

// --- Validation --- if (isNaN(defects) || isNaN(units) || isNaN(opportunities)) { errEl.textContent = 'Please fill in all three fields.'; errEl.style.display = 'block'; return; } if (defects units * opportunities) { errEl.textContent = 'Defects cannot exceed total opportunities (Units × Opportunities per Unit).'; errEl.style.display = 'block'; return; }

// --- Core Calculations --- // DPO = Defects / (Units × Opportunities) var totalOpportunities = units * opportunities; var dpo = defects / totalOpportunities;

// DPMO = DPO × 1,000,000 var dpmo = dpo * 1000000;

// Process Yield = (1 - DPO) × 100 var yieldPct = (1 - dpo) * 100;

// Sigma Level using the inverse normal CDF approximation // Sigma = NORMSINV(1 - DPO) + 1.5 (includes 1.5 sigma shift) // This calculator uses the Abramowitz & Stegun rational approximation for NORMSINV function normsinv(p) { if (p = 1) return Infinity; var a = [0, -3.969683028665376e+01, 2.209460984245205e+02, -2.759285104469687e+02, 1.383577518672690e+02, -3.066479806614716e+01, 2.506628277459239e+00]; var b = [0, -5.447609879822406e+01, 1.615858368580409e+02, -1.556989798598866e+02, 6.680131188771972e+01, -1.328068155288572e+01]; var c = [0, -7.784894002430293e-03, -3.223964580411365e-01, -2.400758277161838e+00, -2.549732539343734e+00, 4.374664141464968e+00, 2.938163982698783e+00]; var d = [0, 7.784695709041462e-03, 3.224671290700398e-01, 2.445134137142996e+00, 3.754408661907416e+00]; var pLow = 0.02425; var pHigh = 1 - pLow; var q, r, x; if (p = 1) { sigmaLevel = 0; } else { sigmaLevel = normsinv(1 - dpo) + 1.5; sigmaLevel = Math.max(0, Math.min(sigmaLevel, 6.0)); }

// --- Quality Label --- var label, color, bg; if (sigmaLevel >= 6.0) { label = '🏆 World Class — Six Sigma Quality (≤ 3.4 DPMO)'; color = '#166534'; bg = '#dcfce7'; } else if (sigmaLevel >= 5.0) { label = '✅ Excellent — Five Sigma Quality'; color = '#14532d'; bg = '#f0fdf4'; } else if (sigmaLevel >= 4.0) { label = '👍 Good — Four Sigma Quality'; color = '#1e40af'; bg = '#eff6ff'; } else if (sigmaLevel >= 3.0) { label = '⚠️ Average — Three Sigma Quality'; color = '#92400e'; bg = '#fffbeb'; } else { label = '❌ Poor — Below Three Sigma — Immediate Improvement Needed'; color = '#991b1b'; bg = '#fef2f2'; }

// --- Display Results --- document.getElementById('six-dpmo').textContent = dpmo.toLocaleString('en-US', {maximumFractionDigits: 2}); document.getElementById('six-sigma').textContent = sigmaLevel.toFixed(2) + ' σ'; document.getElementById('six-yield').textContent = yieldPct.toFixed(4) + '%'; document.getElementById('six-dpo').textContent = dpo.toFixed(8);

var ql = document.getElementById('six-quality-label'); ql.textContent = label; ql.style.color = color; ql.style.background = bg;

resEl.style.display = 'block'; }

#### Formulas Used

DPO (Defects Per Opportunity): DPO = Defects ÷ (Units × Opportunities per Unit)

DPMO (Defects Per Million Opportunities): DPMO = DPO × 1,000,000

Process Yield: Yield (%) = (1 − DPO) × 100

Sigma Level (with 1.5σ long-term shift): Sigma Level = NORMSINV(1 − DPO) + 1.5 where NORMSINV is the inverse of the standard normal cumulative distribution function.

Sigma Benchmarks (with 1.5σ shift):

Sigma LevelDPMOYield 6σ3.499.99966% 5σ23399.977% 4σ6,21099.379% 3σ66,80793.319% 2σ308,53769.146%

#### Assumptions & References

The 1.5 sigma shift is applied per the Motorola/industry standard to account for long-term process drift. Short-term sigma = NORMSINV(1 − DPO); long-term sigma adds 1.5.
All defect opportunities within a unit are assumed to be independent and equally likely.
The inverse normal CDF is approximated using the Abramowitz & Stegun rational approximation (maximum error < 1.5 × 10⁻⁵).
Sigma level is capped at 6.0σ for display purposes when zero defects are observed.
This calculator measures attribute data (defective/non-defective). Variable data requires a different approach (process capability indices Cp, Cpk).
References: Motorola University (1986) — Six Sigma origin; Montgomery, D.C. — Introduction to Statistical Quality Control; ASQ Six Sigma Body of Knowledge.

Six Sigma DPMO Calculator

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