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# Statistical Solutions, LLC

Defects Per Million (DPM) and Process Sigma Calculator

Use the form below to perform Defects Per Million and Process Sigma calculations. If you have questions or problems you can contact Statistical Solutions via E-mail by clicking the following link . Contact Us

 Here you can calculate a Process Sigma-Metric by entering the number of defects in a sample. *Note that this calculator rounds-up to the nearest Sigma-Metric. Reference the table below. Enter the number of defects observed (n) Enter the total size of the sample or population (N) Sigma Metrics* Defects Per Million (DPM) Short-Term Process Sigma-Metric (σst) Long-Term Process Sigma-Metric (σlt) σlt includes the 1.5 sigma shift ...read more

 DPM and Process Sigma Table DPM Short-Term Process Sigma (σst) Long-Term Process Sigma (σlt) Yield 2 6.0 4.5 99.99966 5 5.9 4.4 99.99954 9 5.8 4.3 99.99915 13 5.7 4.2 99.9987 21 5.6 4.1 99.9979 32 5.5 4.0 99.9968 48 5.4 3.9 99.995 72 5.3 3.8 99.993 108 5.2 3.7 99.989 159 5.1 3.6 99.984 233 5.0 3.5 99.98 337 4.9 3.4 99.97 483 4.8 3.3 99.95 687 4.7 3.2 99.93 968 4.6 3.1 99.90 1,350 4.5 3.0 99.87 1,866 4.4 2.9 99.81 2,555 4.3 2.8 99.74 3,467 4.2 2.7 99.65 4.661 4.1 2.6 99.5 6,210 4.0 2.5 99.4 8,198 3.9 2.4 99.2 10,724 3.8 2.3 98.9 13,903 3.7 2.2 98.6 17,864 3.6 2.1 98.2 22,750 3.5 2.0 97.7 28,716 3.4 1.9 97.1 35,930 3.3 1.8 96.4 44,565 3.2 1.7 95.5 54,799 3.1 1.6 94.5 66,807 3.0 1.5 93.3 80,757 2.9 1.4 91.9 96,801 2.8 1.3 90.3 115,070 2.7 1.2 88.5 135,666 2.6 1.1 86.4 158,655 2.5 1.0 84.1 184,060 2.4 0.9 81.6 211,855 2.3 0.8 78.8 241,964 2.2 0.7 75.8 274,253 2.1 0.6 72.6 308,538 2.0 0.5 69.1 344,578 1.9 0.4 65.5 382,089 1.8 0.3 61.8 420,740 1.7 0.2 57.9 460,172 1.6 0.1 54.0 500,000 1.5 0.0 50.0 539,828 1.4 -0.1 46.0 579,260 1.3 -0.2 42.1 617,911 1.2 -0.3 38.2 655,422 1.1 -0.4 34.5 691,462 1.0 -0.5 30.9 725,747 0.9 -0.6 27.4 758,036 0.8 -0.7 24.2 788,145 0.7 -0.8 21.2 815,940 0.6 -0.9 18.4 841,345 0.5 -1.0 15.9 864,334 0.4 -1.1 13.6 884,930 0.3 -1.2 11.5 903,199 0.2 -1.3 9.7 919,243 0.1 -1.4 8.1 933,193 0.0 -1.5 6.7

An Explanation Of The 1.5 Sigma Shift

6 sigma actually translates to about 2 Defects Per Billion Opportunities (DPBO), and 3.4 Defects Per Million Opportunities (DPMO), which we normally define as 6 sigma and corresponds to a sigma value of 4.5. Where does this 1.5 sigma difference come from? Motorola has determined, through years of process and data collection, that processes vary and drift over time - what they call the Long-Term Dynamic Mean Variation. This variation typically falls between 1.4 and 1.6.

By offsetting normal distribution by a 1.5 standard deviation on either side, the adjustment takes into account what happens to every process over many cycles of manufacturing… Simply put, accommodating shift and drift is our 'fudge factor,' or a way to allow for unexpected errors or movement over time. Using 1.5 sigma as a standard deviation gives us a strong advantage in improving quality not only in industrial process and designs, but in commercial processes as well. It allows us to design products and services that are relatively impervious, or 'robust', to natural, unavoidable sources of variation in processes, components, and materials. The reporting convention of Six Sigma requires the process capability to be reported in short-term sigma -- without the presence of special cause variation. Long-term sigma is determined by subtracting 1.5 sigma from our short-term sigma calculation to account for the process shift that is known to occur over time.

After a process has been improved using the Six Sigma DMAIC methodology, we calculate the process standard deviation and sigma value. These are considered to be short-term values because the data only contains common cause variation -- DMAIC projects and the associated collection of process data occur over a period of months, rather than years. Long-term data, on the other hand, contains common cause variation and special (or assignable) cause variation. Because short-term data does not contain this special cause variation, it will typically be of a higher process capability than the long-term data. This difference is the 1.5 sigma shift. Given adequate process data, you can determine the factor most appropriate for your process.