Six-Sigma Conversion Table
The following table will convert Defects Per Million Opportunities to a Sigma Level.
Also shown is a direct conversion to a Cpk level based on the area under a Normal Curve. By convention established at Motorola, where the Six Sigma program originated, the Sigma level is adjusted by 1.5 sigma to recognize the tendency of processes to shift over the long term.
In essence, the 1.5 sigma shift indicates that if you intend to have 3 DPMO over the long term, the process must be more capable than the 4.5 sigma (Cpk) indicated by a normal curve in order to accommodate instability or process shifts that occur over time.
The 1.5 sigma shift may or may not be an accurate estimate of the actual long-term instability of your process.
Note: the conversion of Sigma Level to Cpk is only an approximation because Cpk is based only upon the specification limit closest to the process mean. The other side of the process distribution, which may have a tail beyond the farther specification, is ignored by the Cpk calculation.
* The table assumes a 1.5 sigma shift because processes tend to exhibit instability of that magnitude over time. In other words, although statistical tables indicate that 3.4 defects / million is achieved when 4.5 process standard deviations (Sigma) are between the mean and the closest specification limit, the target is raised to 6.0 standard deviations to accommodate adverse process shifts over time and still produce only 3.4 defects per million opportunities.