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11/09/2007: "Example Sigma Levels"

We are working to implement Six Sigma, and would like to use your diagram to better explain it to upper management. We just want to fully understand what the sigma levels represent. I have attached a copy of the diagram.

My specific questions are 1) is this actual data or illustrative? 2) what does the bogey golf number represent? 3) what about the airline fatality (is that plane crashes, individual fatalities, etc.)

The IRS data is based on a hypothetical 40% error rate, but is in line with what has been reported by some surveys published in the press over the years. Most of the other data points are based on data published on the web, such as by the NTSB and FBI.
The general technique for calculating the sigma level is to determine the error rate, which can then be directly converted to a sigma level. When calculating the error rate from a given sample, the denominator is the number of opportunities. In the IRS tax advice example, each question was considered an opportunity, and if the question was incorrectly answered then it was counted as an error. So in this case, 40% of the questions were incorrectly answered. This is converted to a 1.75 Sigma Level.
The NTSB numbers, if I remember correctly, were defined based on an opportunity being a passenger trip. In fact, that's a good example of how reported Sigma Levels can be manipulated to achieve a particular agenda. I cover this more in my book, and in the training materials, but basically when the number of opportunities is inflated, then the error rate goes down and the Sigma Level goes up. For the NTSB, you could consider a passenger mile as your opportunity, rather than a passenger trip. Since each trip is many miles, that inflates the number of opportunities, even if there is no increased risk from a 2000 mile trip over a 200 mile trip. (Experts tend to say that the risks in air travel are dominated by takeoff and landing, rather than miles).
I was not able to find the original calculations I used to come up with the bogie golf sigma level, but a reasonable approach is to assume that there are 72 opportunities in a golf game if one is to achieve par. Of these, 18 would be sufficiently errant to require an additional shot or a penalty stroke, resulting in a error rate of 25% or a Sigma Level of about 2.2. Of course there are many ways to achieve bogie golf, so there is some presumed error in that estimate. Honestly, it was only included to add some levity to the topic.
You may be wondering how to convert the error rate to a Sigma Level. That's a more involved discussion, requiring the use of the Normal distribution and a 1.5 sigma shift that is customarily applied. Generally, you can use a table, such as provided in my Six Sigma Demystified book, or you can calculate it directly in Excel using the formula =(NORMSINV(1-$D2))+1.5, where the data in cell D2 is entered as a decimal (for example, 30% error rate = 0.3 which calculates as 2.02 Sigma Level).