Sigma value for defect ratio

Allow me to ask you here (since I can't comment yet) why would you choose $6σ$.

Since 99.7% means less than 0.3% defect ratio, maybe if we take an additional $σ$ only we would be in a safe place, in my opinion. Therefore, my answer would be $4σ$ (3 is already safe for your question).

New Information

As I mentioned, since we are talking about defects, it's more about the Six Sigma and the Sigma Level. Therefore, if we go to the wikipedia page, we can see that the value should be between 4 and 5 Sigma Levels.

Now, we go back to our original SIGMAs, which are easier to understand. Our goal is to get 0.3% defect, or 99.7% good. Therefore, we take our table of values we know that within 3σ we get 0.9973. Therefore, the real value should be a bit less than $3σ$. But we can go with $3σ$

Being Very Precise

Table for Z-value if you read the table you will find 2.75 Sigma for 0.99702.

Reference

Quora Difference between Sigma and Sigma Level