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# If You Run at 6 Sigma How Come You Test at 4.5 Sigma?

## If You Run at 6 Sigma, How Come You Test at 4.5 Sigma?

If you believe you have a 6 Sigma process, in other words 3.4 defects per million opportunities (DPMO), do you test at 4.5 Sigma? I’ve always wondered what the value of the test is when you never exceed the test value. The test doesn’t tell you where you’re at instead, it tells you where you’re not at. If you believe you have a 6 Sigma process how do you monitor whether you are really at 6 Sigma?

Let’s say your process was designed to deliver 6 Sigma performance.  All processes that include machinery degrade over time. If you think you are running at 6 Sigma but you are getting closer to 4.5 Sigma then your defect rate is significantly greater than you may expect. A 4.5 Sigma defect rate is about 1300 DPMO which is a far cry from 3.4 DPMO.

### Cp, Cpk, Pp, Ppk

When you look at Cp do you see a negative deviation from 2.0? Is this real or an artifact of not measuring enough data?  Cp, Cpk and Pp, Ppk only differ by how the sample standard deviation is estimated. Assuming randomize sampling from the same population then really the value of the standard deviation is only going to more solid with the more data points you collect. Of course, any calculation of sample standard deviation is only an estimate of the population deviation. So use it in either formula.

Cpk then becomes your best standard of the normal distributions mean deviating from the desired mean.

To determine your deviation over time from a six Sigma process you will need to look at the change in variance and the movement of the mean with the assumption that the distribution is normal. So Cp gives you sample variance information, Cpk gives you movement of the sample mean from the specified mean and SK which is a skew calculation based on the difference of the sample mean and sample median.

If you are not reaching 6 Sigma then maybe the process was never designed as a 6 Sigma process.  Then it is time to look at Design for Six Sigma and redesign the process.

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