Calculation of the baseline value requires conversion of the defects or variations in a given sample into Defects per Million Opportunities (DPMO).
The formulae for defects per million calculation is:
DPMO = Number of defective items / (Number of Defect Opportunities per Unit x Number of Units) x 1,000,000
In a straightforward example, assuming an assembly line produces a million units of a product, and of these, 691,463 fall within acceptable limits, and the specifications of 308,537 units go beyond the specified limits, in other words the 308,537 units are defective. The baseline measure for the Six Sigma intervention is 308,537 or 2 sigma level. The Six Sigma approach tries to find ways to reduce the number of units not conforming to specifications from 308,537 to 3.4 per million.
In a real life scenario, assume the postal department delivers 378,564 letters a day, and misplaces 17,789 of them, on average. This defect rate of 17,789 for 378,564 needs conversion to one million. (17,789/378,564 x 1,000,000) = 46,990.73. The postal department thereby misplaces 46990.73 letters per million letters delivered, which is the baseline measurement. The sigma level of this baseline value is 3.17.
Now assume the number of possible errors per letter is two, displacement, and wrong delivery. If 17,789 errors fall into any of these two error categories, the defects per million opportunities changes
= 17,789/(2 x 378,564) x 1,000,000 = 23,495.37 defects per million opportunities.
Using any Sigma conversion calculator available online, this translates to a Sigma level of 3.49.