As a quality control expert with extensive experience in statistical process control, I can provide you with an accurate answer regarding the relationship between sigma levels and defect rates.

In a normal distribution, 3 sigma (three standard deviations from the mean) covers approximately 99.73% of the data. This means that only 0.27% of the data falls outside this range. In terms of defects per million (DPMO), this is a measure used to quantify quality that is based on the number of defects in a large sample.

To calculate the number of defects per million at the 3 sigma level, you can use the following formula:

DPMO = (1 - (1 - (1/(2 * 0.5)) * (1/(2 * 0.5)))) * 1,000,000

This formula accounts for the fact that 3 sigma covers both sides of the normal distribution, and the 1/(2 * 0.5) represents the area under the curve for one half of one standard deviation.

Using this formula, the calculation would be:

DPMO = (1 - (1 - (1/1) * (1/1))) * 1,000,000
DPMO = (1 - (1 - 1)) * 1,000,000
DPMO = (1 - 0) * 1,000,000
DPMO = 1,000,000 * 0
DPMO = 0

However, this calculation assumes a perfect normal distribution, which is a theoretical scenario. In practice, the actual number of defects per million at the 3 sigma level would be very low, but not exactly zero due to the 0.27% that falls outside the 3 sigma range.

So, the answer is:

At the 3 sigma level, theoretically, there would be 0 defects per million (DPMO), but in practice, it would be a very small number close to zero.

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Sigma levelsSigma levelSigma (with 1.5�� shift)DPMO31.566,80742.56,21053.523364.53.43 more rowsread more >>