Bill: You’ve been fooled by the dirty little “secret” of six sigma. If you also look at the probability for being outside of 6 std dev’s (6 sigma) you won’t find 3.4 ppm, but rather less than 1 in a billion. The difference is that back in the “old days” when it was difficult to take data and virtually all data that was taken was considered short-term, folks wanted to protect against longer term shifts/drifts, so they adjusted the data by 1.5 sigma. This has been perpetrated through numerous summaries of defect rates and their sigma equivalents. If you look in a Z-table or use Normsdist function in Excel, you will get the actual value. If you subtract 1.5 from the number of std dev’s (sigma) and look that up in the table (or use Normsdist in Excel) you will get the often advertised values.
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