Please enter valid positive numbers. Units and Opportunities cannot be zero.
Defects Per Unit (DPU):–
Defects Per Opportunity (DPO):–
DPMO (Defects Per Million):–
Process Yield:–
Sigma Level (Short Term):–
How to Calculate Six Sigma Defect Rates
In process improvement and quality control methodologies like Six Sigma, quantifying performance is crucial. This calculator helps quality managers and Green/Black Belts determine the baseline capability of a process by converting raw defect data into standard metrics like DPMO (Defects Per Million Opportunities) and the Process Sigma Level.
Key Definition: A "Defect" is any instance where a product or service fails to meet customer requirements. An "Opportunity" is any chance for a defect to occur within a single unit.
Understanding the Metrics
To use this calculator effectively, it is important to understand the hierarchy of Six Sigma metrics:
DPU (Defects Per Unit): The average number of defects found on a single unit. It is calculated as Total Defects / Total Units.
DPO (Defects Per Opportunity): A probability metric indicating the chance of a defect occurring in any single opportunity. It provides a more granular view than DPU.
DPMO (Defects Per Million Opportunities): This is the standard Six Sigma metric that normalizes defect rates to a scale of one million. It allows for comparison between different processes with varying complexity.
Process Yield: The percentage of opportunities that are defect-free.
Sigma Level: A statistical determination of process capability. The higher the Sigma level, the less likely the process is to produce defects. A Six Sigma process allows only 3.4 defects per million opportunities.
The Six Sigma Calculation Formulas
If you wish to perform these calculations manually, here are the standard formulas used by this tool:
1. Calculate Total Opportunities:
Total Opportunities = (Total Units Tested) × (Opportunities per Unit)
2. Calculate DPO:
DPO = Total Defects / Total Opportunities
3. Calculate DPMO:
DPMO = DPO × 1,000,000
4. Calculate Sigma Level:
The Sigma Level is typically calculated using the inverse standard normal distribution of the yield, plus a 1.5 shift to account for long-term process variation. Formula: NormSInv(1 – DPO) + 1.5
Example Calculation
Imagine a smartphone manufacturer testing a batch of phones. A phone has 50 different checkpoints (opportunities for failure).
Units Tested: 1,000 phones
Opportunities per Unit: 50
Total Defects Found: 25
First, calculate Total Opportunities: 1,000 × 50 = 50,000.
Then, DPO: 25 / 50,000 = 0.0005.
DPMO: 0.0005 × 1,000,000 = 500 DPMO.
This low DPMO would result in a high Sigma Level (approx 4.8 Sigma), indicating a very capable process.
function calculateSixSigma() {
var units = document.getElementById("totalUnits").value;
var oppPerUnit = document.getElementById("oppPerUnit").value;
var defects = document.getElementById("totalDefects").value;
var errorMsg = document.getElementById("errorMsg");
var resultsDiv = document.getElementById("results");
// Validate Inputs
if (units === "" || oppPerUnit === "" || defects === "" ||
isNaN(units) || isNaN(oppPerUnit) || isNaN(defects)) {
errorMsg.style.display = "block";
resultsDiv.style.display = "none";
return;
}
var unitsNum = parseFloat(units);
var oppNum = parseFloat(oppPerUnit);
var defectsNum = parseFloat(defects);
// Logical validation
if (unitsNum <= 0 || oppNum <= 0 || defectsNum 1) dpo = 1;
// 4. Calculate DPMO
var dpmo = dpo * 1000000;
// 5. Calculate Yield
var yieldVal = (1 – dpo) * 100;
// 6. Calculate Sigma Level
// Formula: NORMSINV(1 – DPO) + 1.5
// If DPO is 0, Sigma is theoretically infinity. We cap at 6.0 or show "6.0+"
// If DPO is 1, Sigma is -Infinity.
var sigmaLevel = 0;
if (dpo === 0) {
sigmaLevel = 6.0; // Perfect score representation
} else if (dpo >= 1) {
sigmaLevel = 0; // Worst case
} else {
// Calculate NormSInv(1 – dpo)
// Using approximation for Inverse Normal Cumulative Distribution
var p = 1 – dpo;
sigmaLevel = getNormSInv(p) + 1.5;
}
// Formatting Results
document.getElementById("resDPU").innerHTML = dpu.toFixed(4);
document.getElementById("resDPO").innerHTML = dpo.toFixed(6);
document.getElementById("resDPMO").innerHTML = Math.round(dpmo).toLocaleString();
document.getElementById("resYield").innerHTML = yieldVal.toFixed(2) + "%";
var sigmaDisplay = sigmaLevel.toFixed(2);
if (dpo === 0) sigmaDisplay = "6.0+ (Perfect)";
document.getElementById("resSigma").innerHTML = sigmaDisplay;
resultsDiv.style.display = "block";
}
// Helper function: Inverse Normal Cumulative Distribution (Acklam's algorithm approximation)
// Converts probability to Z-score
function getNormSInv(p) {
var a1 = -39.6968302866538, a2 = 220.946098424521, a3 = -275.928510446969;
var a4 = 138.357751867269, a5 = -30.6647980661472, a6 = 2.50662827745924;
var b1 = -54.4760987982241, b2 = 161.585836858041, b3 = -155.698979859887;
var b4 = 66.8013118877197, b5 = -13.2806815528857, c1 = -7.78489400243029E-03;
var c2 = -0.322396458041136, c3 = -2.40075827716184, c4 = -2.54973253934373;
var c5 = 4.37466414146497, c6 = 2.93816398269878, d1 = 7.78469570904146E-03;
var d2 = 0.322467129070039, d3 = 2.44513413714299, d4 = 3.75440866190742;
var p_low = 0.02425, p_high = 1 – 0.02425;
var q, r;
if (p < p_low) {
q = Math.sqrt(-2 * Math.log(p));
return (((((c1 * q + c2) * q + c3) * q + c4) * q + c5) * q + c6) /
((((d1 * q + d2) * q + d3) * q + d4) * q + 1);
} else if (p <= p_high) {
q = p – 0.5;
r = q * q;
return (((((a1 * r + a2) * r + a3) * r + a4) * r + a5) * r + a6) * q /
(((((b1 * r + b2) * r + b3) * r + b4) * r + b5) * r + 1);
} else {
q = Math.sqrt(-2 * Math.log(1 – p));
return -(((((c1 * q + c2) * q + c3) * q + c4) * q + c5) * q + c6) /
((((d1 * q + d2) * q + d3) * q + d4) * q + 1);
}
}