Sc.pp.calculate_qc_metrics

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Quality Control (QC) Metrics Calculator

Analyze production performance with DPMO, Yield, and Sigma Level calculations.

How many ways can one single unit fail?

Performance Analysis

0% Process Yield
0% Defect Rate
0 DPMO
0 Sigma Level

Understanding Quality Control Metrics

In manufacturing and service delivery, tracking quality metrics is essential for continuous improvement. These metrics provide a mathematical snapshot of how well a process is performing relative to its requirements.

Key QC Metric Definitions

  • Process Yield: The percentage of products that are produced correctly without rework or scrap. A 100% yield indicates a perfect process.
  • Defect Rate: The inverse of yield, representing the percentage of units that do not meet quality standards.
  • DPMO (Defects Per Million Opportunities): A standardized metric used in Six Sigma to compare different processes. It accounts for the complexity of a product by looking at how many opportunities for error exist in each unit.
  • Sigma Level: A statistical measurement of process capability. A higher Sigma level indicates a process that is more robust and less likely to produce defects. "Six Sigma" corresponds to 3.4 DPMO.

The Formula for DPMO

The calculation for DPMO is as follows:

DPMO = (Total Defects / (Total Units × Opportunities per Unit)) × 1,000,000

Example Calculation

Suppose a factory produces 5,000 printed circuit boards. Each board has 20 solder points (opportunities for defect). During inspection, they find 10 defective boards.

  • Total Units: 5,000
  • Defects: 10
  • Opportunities: 20
  • Calculation: (10 / (5,000 * 20)) * 1,000,000 = 100 DPMO.
  • Result: This process would have a Yield of 99.8% and a Sigma Level of approximately 5.2.
function calculateQCMetrics() { var totalUnits = parseFloat(document.getElementById("qc_total_units").value); var defects = parseFloat(document.getElementById("qc_defects").value); var opps = parseFloat(document.getElementById("qc_opps").value); if (isNaN(totalUnits) || isNaN(defects) || isNaN(opps) || totalUnits <= 0 || opps (totalUnits * opps)) { alert("Number of defects cannot exceed the total number of opportunities."); return; } // 1. Defect Rate var defectRate = (defects / totalUnits) * 100; // 2. Yield var yieldVal = 100 – defectRate; if (yieldVal < 0) yieldVal = 0; // 3. DPMO var totalOpp = totalUnits * opps; var dpmo = (defects / totalOpp) * 1000000; // 4. Sigma Level (Approximate) // Formula for Sigma Level with 1.5 shift: 0.8406 + sqrt(29.37 – 2.221 * ln(DPMO)) // We use a simplified linear/log approximation for common DPMO ranges var sigma = 0; if (dpmo <= 0) { sigma = 6.0; // Cap at 6 for 0 defects } else { // NORMSINV(1 – (defects/totalOpp)) + 1.5 var p = defects / totalOpp; // Approximation of Inverse Normal Distribution var t = Math.sqrt(Math.log(1 / Math.pow(p, 2))); var z = t – (2.30753 + 0.27061 * t) / (1 + 0.99229 * t + 0.04481 * Math.pow(t, 2)); sigma = z + 1.5; } // Display Results document.getElementById("res_defect_rate").innerText = defectRate.toFixed(2) + "%"; document.getElementById("res_yield").innerText = yieldVal.toFixed(2) + "%"; document.getElementById("res_dpmo").innerText = Math.round(dpmo).toLocaleString(); document.getElementById("res_sigma").innerText = sigma.toFixed(2); document.getElementById("qc_results_box").style.display = "block"; }

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