# When Six Is Really 4.5

Folks,

In teaching Six Sigma workshops at Dartmouth, we ensure that everyone understands that “Six Sigma,” as presented in the industry, is in fact mathematically 4.5 sigma. So when folks say Six Sigma is 3.4 defects per million (dpm), they are in fact not referring to plus-and-minus six standard deviations from the mean (even though they may not know it), as 3.4 dpm is only 4.5 sigma.

The true six sigma defect rate is 2 defects per billion. The figure shows this error.

Where does this confusion come from? When Six Sigma was developed, it was defined as a Cp of 2 and a Cpk of 1.5. These process capability indices are where the confusion lies. A Cpk of 1.5 permits a shifting of the process mean of 1.5 sigma, hence the true statistical measure of Cpk = 1.5 is 4.5 sigma (or 3.4 ppm). True statistical six sigma (Cpk = 2) is elusive indeed at 2 dpb!

Cheers,
Dr. Ron

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Materials expert Dr. Ron Lasky is a professor of engineering and senior lecturer at Dartmouth, and senior technologist at Indium Corp. He has a Ph.D. in materials science from Cornell University, and is a prolific author and lecturer, having published more than 40 papers. He received the SMTA Founders Award in 2003.

## One thought on “When Six Is Really 4.5”

1. The Degradation of “Six Sigma”

It seems “six sigma” is more of a marketing license to try to get by with lower quality while fooling people you are adhering to high quality.

In the current company I work for they are now using Cp=1.5
and assuming the process mean will not shift much (Cpk will stay close to Cp=1.5).

I keep warning them, however, that we will get burned by this policy.

I was trained under the Deming Quality philosophy in the early 1990’s and the degradation of quality I now see happening is frustrating to me.