This Six Sigma Defect Rate Calculator helps quality assurance professionals, manufacturing engineers, and project managers determine the baseline performance of a process. By inputting the total units produced, the number of opportunities for error per unit, and the actual defects found, you can calculate critical metrics like DPMO and Sigma Level.
How is the Sigma Level Calculated?
The calculation is based on the standard normal distribution. The logic follows the standard industry practice of including a 1.5 Sigma Shift to account for long-term process variation. The formula steps are:
Calculate DPU (Defects Per Unit): Total Defects ÷ Total Units.
Calculate DPO (Defects Per Opportunity): Total Defects ÷ (Total Units × Opportunities per Unit).
Calculate DPMO: DPO × 1,000,000.
Determine Sigma Level: This is calculated using the inverse standard normal cumulative distribution function of the yield (1 – DPO), plus the 1.5 shift.
Definitions of Key Terms
Opportunities for Defect per Unit: The number of specific things that could go wrong on a single unit. For example, if you are manufacturing a circuit board with 10 components, and each component could be placed incorrectly, that represents 10 opportunities per unit.
DPMO (Defects Per Million Opportunities): A standardized measure of error that allows for comparison between processes of different complexities.
Process Yield: The percentage of opportunities that are defect-free.
Sigma Level: A statistical term indicating how far the process mean is from the specification limits. A 6 Sigma process produces only 3.4 defects per million opportunities.
Common Sigma Levels and DPMO
Use the table below to interpret your results:
6 Sigma: 3.4 DPMO (World Class)
5 Sigma: 233 DPMO
4 Sigma: 6,210 DPMO (Industry Average)
3 Sigma: 66,807 DPMO
2 Sigma: 308,537 DPMO
1 Sigma: 691,462 DPMO
Why is this important?
Reducing variation and defects leads to cost savings, higher customer satisfaction, and better bottom-line results. Moving from a 3 Sigma level to a 4 Sigma level represents a massive improvement in quality and a significant reduction in waste.
function calculateSixSigma() {
// Clear previous error
var errorDiv = document.getElementById("errorMsg");
errorDiv.style.display = "none";
errorDiv.innerText = "";
// Get Inputs
var units = document.getElementById("totalUnits").value;
var oppsPerUnit = document.getElementById("oppsPerUnit").value;
var defects = document.getElementById("totalDefects").value;
// Validate Inputs
if (units === "" || oppsPerUnit === "" || defects === "") {
errorDiv.innerText = "Please fill in all fields.";
errorDiv.style.display = "block";
return;
}
units = parseFloat(units);
oppsPerUnit = parseFloat(oppsPerUnit);
defects = parseFloat(defects);
if (isNaN(units) || units <= 0) {
errorDiv.innerText = "Total Units must be greater than 0.";
errorDiv.style.display = "block";
return;
}
if (isNaN(oppsPerUnit) || oppsPerUnit <= 0) {
errorDiv.innerText = "Opportunities per Unit must be greater than 0.";
errorDiv.style.display = "block";
return;
}
if (isNaN(defects) || defects totalOpportunities) {
errorDiv.innerText = "Total Defects cannot exceed Total Opportunities.";
errorDiv.style.display = "block";
return;
}
var dpu = defects / units;
var dpo = defects / totalOpportunities;
var dpmo = dpo * 1000000;
var yieldVal = (1 – dpo) * 100;
// Sigma Calculation (Using Inverse Normal Distribution Approximation + 1.5 Shift)
// If 0 defects, theoretically infinity, but we cap it or show >6.0
var sigmaLevel = 0;
if (defects === 0) {
// Perfect score handling
sigmaLevel = 6.0; // Or technically higher, but usually capped for calculators
// Let's calculate based on a theoretical 1 defect if 0 to show a "Max" or just return "6.0+"
// For standard practice, we can treat 0 defects as slightly less than 1/TotalOpps for calculation or just display "6.0+"
} else if (dpo >= 1) {
sigmaLevel = 0; // Or -Infinity
} else {
// Approximation for NORMSINV(1 – DPO)
// Using a standard approximation for the inverse cumulative normal distribution
var p = 1 – dpo;
sigmaLevel = normsinv(p) + 1.5;
}
// Display Results
document.getElementById("resDPU").innerText = dpu.toFixed(4);
document.getElementById("resOpps").innerText = totalOpportunities.toLocaleString();
document.getElementById("resDPMO").innerText = dpmo.toLocaleString(undefined, {minimumFractionDigits: 0, maximumFractionDigits: 2});
document.getElementById("resYield").innerText = yieldVal.toFixed(4) + "%";
var sigmaText = sigmaLevel.toFixed(2);
if (defects === 0) sigmaText = "6.00+"; // Indicate perfect or near perfect
document.getElementById("resSigma").innerText = sigmaText + " σ";
document.getElementById("ssResults").style.display = "block";
}
// Inverse Standard Normal Distribution Function (Acklam's approximation)
function normsinv(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 = 2.445134137143, d4 = 3.75440866190742;
var q, t;
if (p 1 – 0.02425) {
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);
} else {
q = p – 0.5;
t = q * q;
return (((((a1 * t + a2) * t + a3) * t + a4) * t + a5) * t + a6) * q /
(((((b1 * t + b2) * t + b3) * t + b4) * t + b5) * t + 1);
}
}