# Six Sigma = 3.4 DPMO … Why?

I have often been asked, why do we have 3.4 Defects Per Million Opportunities (DPMO) for a Six Sigma process?

Before I talk about Six Sigma, let's talk about the process control with plus-minus three sigmas. Historically processes were controlled in ​$$\pm 3\sigma$$, and this was the basis of control charts.

When you have a process, which is centered around the mean, it will have 99.73% items within ​$$\pm 3\sigma$$ and will have 0.27% items outside the ​$$3\sigma$$ limits. Out of this 0.27 %, you will have half of the rejection (0.135%) on the lower end and another half rejection on the upper end. See the Normal Distribution curve below:

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Now instead of ​$$\pm 3\sigma$$, you look at the Normal Distribution curve, with ​$$\pm$$6​$$\sigma$$ you will see that the rejection area is 0.000000197% (or 0.00197 DPMO), and not 3.4 DPMO.

Now the question is, why do we get 0.00197 DPMO for a Six Sigma process instead of 3.4 DPMO?

The answer to that lies in ​$$1.5\sigma$$ shift allowed in the process over a long time. A Six Sigma process is allowed to move ​$$1.5 \sigma$$ on both sides from the mean.

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