Where does 3.4 parts per million come from?
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 This topic has 3 replies, 4 voices, and was last updated 19 years, 11 months ago by John Twist.

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November 6, 2002 at 3:22 pm #30700
How is this number derived?
0November 6, 2002 at 3:26 pm #80345November 6, 2002 at 4:11 pm #80347Convert 3.4 DPMO to percent (i.e. 3.4/1,000,000) and look up the right tail area in a Standard Normal Table (most tables don’t go this far, so you will probably need one asscociated with Six Sigma). You will get 4.5 standard deviations.
Now add 1.5 to this and you get 6 Sigma. We add 1.5 because the general assumption for calculating sigma level is that you have long term data (it represents most of the systems variation) but want to estimate short term Sigma (i.e. what the customer is likely to see at any given time… from a batch or run or order). Past studies have shown that short term sigma level is general 1.5 Sigma better then long term.
This is how 3.4 DPMO equates to Six Sigma.
Jamie
0November 6, 2002 at 6:05 pm #80349
John TwistParticipant@JohnTwist Include @JohnTwist in your post and this person will
be notified via email.Taken from: http://www.lmu.ac.uk/lis/imgtserv/tools/sixsigma.htm
A Six Sigma quality level is said to equate to 3.4 defects per million opportunities. This is actually a little strange since if a normal distribution table is consulted (very few go out to six sigma), one finds that expected nonconformances are 0.002 parts per million (two parts per billion). The difference between this figure and the ‘official’ six sigma figure of 3.4 defects per million parts is because, when the concept was established, it was assumed that a typical process mean could drift 1.5 sigma in either direction. The area of a normal distribution beyond 4.5 sigma from the mean is indeed 3.4 parts per million. Because control charts will easily detect any process shift of this magnitude in a single sample, the 3.4 parts per million represents a very conservative upper bound on the nonconformance rate.0 
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