# Defects per million opportunities (DPMO)

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In Six Sigma, Defects per Million Opportunities (DPMO) is the measure of the process performance.

Defects per Million Opportunities (DPMO)
##### Defect vs Defective:

Let's first understand the difference between the defect and defectives.

Defect:

A defect is the non-conformance on one of many possible quality characteristics of a unit that causes customer dissatisfaction.

ISO 9001:2015 defines a defect as the nonconformity related to an intended or specified use.

Defective:

A unit which has one or more defects is a defective unit.

Example: In the image shown below, each mistake on the page is a defect. However, the whole unit (the page) is the defective unit. Here in this example, we have one defective which has multiple defects. The term DPMO uses the count of defects and not the defectives.

defect vs defective

##### Defects per Unit:

Defects per Unit (DPU) is a measure of the average number of defects per unit. Let's assume that a page is a unit in the example we used above. When we checked 10 pages (or units), we found a total of 2 defects in those 10 pages.

One defect was related to the spelling mistake and another related to the grammar.

Hence DPU = 2/10 = 0.2

##### Defect Opportunity:

Defect Opportunities are the circumstances in which the Critical to Quality parameter fails to meet the customer requirement. Remember that defect opportunity is the "potential defect" and not the actual defect.

The number of defect opportunities in a unit (product, process or service) is related to the complexity of the unit. More sophisticated units will have more opportunities of defects as compared to simpler units.

Examples: A unit has 5 parts, and in each part, there are 3 opportunities of defects – Total defect opportunities are 5 x 3 = 15

##### Defect per Opportunity (DPO)

Defects per opportunity (DPO) is the number of defects identified in a sample divided by the total number of defect opportunities.

Examples: In the previous example we identified 15 defect opportunities per unit. Let's assume that on inspecting 10 such units we found out 2 defects in those.

DPO = 2 / (15 x 10) = 0.0133333

##### Defect per Million Opportunities (DPMO)

Defects per Million Opportunities is calculated by multiplying DPO by one million.

Examples: Continuing with the previous example

DPMO = 0.013333333 x 1,000,000 = 13,333

##### Sigma Level

There is a relationship between the DPMO and the Sigma Level of the process. Six Sigma performance is equivalent to 3.4 DPMO. Click here for the detailed calculation.

13,333 DPMO found in the example shown here is equivalent to 3.7 Sigmas.

## DPMO Calculator

``` function calculateDPMO1() { const defectsInput = document.getElementById('defects'); const unitsInput = document.getElementById('units'); const opportunitiesInput = document.getElementById('opportunities'); const output = document.getElementById('output'); const defects = parseInt(defectsInput.value); const units = parseInt(unitsInput.value); const opportunities = parseInt(opportunitiesInput.value); if (isNaN(defects) || isNaN(units) || isNaN(opportunities)) { alert('Please enter valid values for defects, units, and opportunities.'); return; } const DPMO = (defects / (units * opportunities)) * 1_000_000; const p = DPMO / 1_000_000; const zValue = -jStat.normal.inv(p, 0, 1) + 1.5; const sigmaLevel = zValue.toFixed(2); output.innerHTML = ` <p>DPMO: \${DPMO.toFixed(2)}</p> <p>Sigma Level: \${sigmaLevel}</p> `; } ```

## DPMO to Sigma / Sigma to DPMO Calculator

DPMO to Sigma Level / Sigma Level to DPMO Converters

``` function calculateSigmaLevel() { const dpmoInput = document.getElementById('dpmo'); const resultContainer = document.getElementById('result-dpmo'); const dpmo = parseInt(dpmoInput.value); if (isNaN(dpmo) || dpmoInput.value.trim() === '' || dpmo < 0) { alert('Please enter a valid DPMO value.'); return; } const zValue = jStat.normal.inv(1 - (dpmo / 1000000), 0, 1); const sigmaLevel = zValue + 1.5; resultContainer.textContent = 'Sigma Level: ' + sigmaLevel.toFixed(4); } function calculateDPMO() { const sigmaLevelInput = document.getElementById('sigma-level'); const resultContainer = document.getElementById('result-sigma'); const sigmaLevel = parseFloat(sigmaLevelInput.value); if (isNaN(sigmaLevel) || sigmaLevelInput.value.trim() === '') { alert('Please enter a valid Sigma Level value.'); return; } const zValue = sigmaLevel - 1.5; const dpmo = (1 - jStat.normal.cdf(zValue, 0, 1)) * 1000000; resultContainer.textContent = 'DPMO: ' + Math.round(dpmo); } ```

Sigma Level

(with 1.5 sigma long term shift)

Defects per Million Opportunities (DPMO)

Percentage Yield

1.5 Sigma

500,000

50%

2 Sigma

308,538

69%

3 Sigma

66,807

99.3%

4 Sigma

6,210

99.38%

5 Sigma

233

99.977%

6 Sigma

3.4

99.99966%

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