Mistakes per million possibilities

Defects per million opportunities (English defects per million opportunities , abbreviated DPMO, also nonconformities per million opportunities ) is a unit of measurement for the frequency of errors, for example in industrial manufacturing processes. The unit of measurement is common in the Six Sigma quality management method . It is defined as follows:

{\ displaystyle 1 \ DPMO = {\ frac {\ mbox {number of errors}} {{\ frac {\ mbox {number of parts}} {1,000,000}} \ times {\ mbox {number of possible errors per part}}}} }

In contrast to the simple error frequency (for example in millionths ), DPMO includes the number of error possibilities per individual part. This makes it easier to compare simple and complex manufacturing processes with one another.

Examples

Simple frequency of errors in light bulb manufacture

For the sake of simplicity, we assume that in the manufacture of light bulbs there is only one possibility of error per light bulb. With an error rate of 3.4 millionths (which in this case corresponds to 3.4 DPMO), there are 3.4 defective lightbulbs for every 1,000,000 lightbulbs produced. Assuming that the errors occur statistically independently of one another, this corresponds to a distance between the mean value and the closest tolerance limit in the amount of six times the statistical standard deviation , which is abbreviated with the symbol σ (sigma). This value 6σ is the origin of the term Six Sigma .

Electronics manufacturing with multiple possibilities for errors

In the first example variant, a component has 2 solder points as sources of error. If exactly every millionth component is defective, the following error frequency is calculated:

{\ displaystyle {\ frac {1} {{\ frac {1,000,000} {1,000,000}} \ times 2}} = 0.5 \ {\ mbox {DPMO}}}

In the second example variant, a chip is fitted with 100 soldering points on a circuit board and each individual soldering point is a source of error. If exactly every millionth circuit board is faulty here, too, DPMO results in a much lower fault frequency:

{\ displaystyle {\ frac {1} {{\ frac {1,000,000} {1,000,000}} \ times 100}} = 0.01 \ {\ mbox {DPMO}}}

In the two example variants, the frequency of defects in the component produced was identical, but the process quality of the individual soldering is much better in the second example.

use

DPMO is used as a measurement unit in quality management as well as in business process optimization. The rule of thumb 3.4 DPMO = 6 Sigma was used to name the Six Sigma method .