Defect Rate Calculator
ANA›Life Services Authority›National Calculator Authority›Defect Rate Calculator
.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }
Defect Rate Calculator
Calculate defect rate, defects per million opportunities (DPMO), yield, and Sigma level to measure and monitor process quality.
Total Units Produced
Number of Defective Units
Opportunities for Defect per Unit
Number of ways a unit can be defective (default: 1)
Calculate
function defCalc() { var totalUnits = parseFloat(document.getElementById('def-total-units').value); var defectiveUnits = parseFloat(document.getElementById('def-defective-units').value); var opportunities = parseFloat(document.getElementById('def-opportunities').value); var resultDiv = document.getElementById('def-result');
// --- Validation --- if (isNaN(totalUnits) || isNaN(defectiveUnits) || isNaN(opportunities)) { resultDiv.style.display = 'block'; resultDiv.innerHTML = 'Please fill in all fields with valid numbers.'; return; } if (totalUnits Total units produced must be greater than zero.'; return; } if (defectiveUnits Defective units cannot be negative.'; return; } if (defectiveUnits > totalUnits) { resultDiv.style.display = 'block'; resultDiv.innerHTML = 'Defective units cannot exceed total units produced.'; return; } if (opportunities Opportunities per unit must be a whole number of at least 1.'; return; }
// --- Core Calculations --- // Defect Rate (proportion) var defectRate = defectiveUnits / totalUnits;
// Yield (good units / total units) var yieldRate = 1 - defectRate;
// Defects Per Opportunity (DPO) var dpo = defectiveUnits / (totalUnits * opportunities);
// Defects Per Million Opportunities (DPMO) var dpmo = dpo * 1000000;
// Rolled Throughput Yield (RTY) — probability a unit passes all opportunities var rty = Math.pow(1 - dpo, opportunities);
// Sigma Level approximation using the standard DPMO-to-Sigma lookup // Formula: Sigma ≈ 0.8406 + sqrt(29.37 - 2.221 * ln(DPMO)) // Valid for DPMO between 3.4 and 933,193 (1-sigma to 6-sigma range) var sigmaLevel = null; var sigmaDisplay = 'N/A'; if (dpmo > 0 && dpmo ' + '' + 'Defect Rate' + '' + (defectRate * 100).toFixed(4) + '%' + '' + '' + 'Yield (Good Units)' + '' + (yieldRate * 100).toFixed(4) + '%' + '' + '' + 'Defects Per Opportunity (DPO)' + '' + dpo.toFixed(6) + '' + '' + '' + 'DPMO' + '' + dpmo.toLocaleString('en-US', {maximumFractionDigits: 2}) + '' + '' + '' + 'Rolled Throughput Yield (RTY)' + '' + (rty * 100).toFixed(4) + '%' + '' + '' + 'Sigma Level' + '' + sigmaDisplay + ' σ' + '' + '' + 'Quality Classification' + '' + qualityLabel + '' + '' + ''; }
#### Formulas Used
Defect Rate: Defect Rate = Defective Units ÷ Total Units Produced
Yield: Yield = 1 − Defect Rate
Defects Per Opportunity (DPO): DPO = Defective Units ÷ (Total Units × Opportunities per Unit)
Defects Per Million Opportunities (DPMO): DPMO = DPO × 1,000,000
Rolled Throughput Yield (RTY): RTY = (1 − DPO)Opportunities per Unit
Sigma Level (approximation): σ ≈ 0.8406 + √(29.37 − 2.221 × ln(DPMO)) Valid for DPMO between 3.4 and ~933,000 (1σ to 6σ)
#### Assumptions & References
- A defective unit is any unit that fails to meet specifications, regardless of the number of defects it contains.
- Opportunities per unit refers to the number of distinct ways a single unit can be found defective (e.g., a circuit board with 5 solder joints has 5 opportunities).
- The Sigma Level approximation uses the Bothe (1997) formula and is accurate to within ±0.03σ for DPMO values between 3.4 and 933,193.
- Six Sigma quality corresponds to 3.4 DPMO, assuming a 1.5σ long-term process shift (Motorola convention).
- Rolled Throughput Yield (RTY) assumes defects at each opportunity are independent and identically distributed.
- This calculator measures unit-level defects. For defect-count-based analysis (e.g., defects per unit, DPU), use a separate DPU/Poisson model.
- References: Montgomery, D.C. (2020). Introduction to Statistical Quality Control, 8th ed.; iSixSigma DPMO & Sigma Level tables.
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