----- Original Message -----
From: "Nigel Marriott" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Tuesday, October 28, 2003 7:42 AM
Subject: QUERY: Shouldn't 6-Sigma be 4.5-Sigma?
> As someone who is about to get involved in the whole industrial quality
control, I have been reading up on a lot of material related to this area.
Naturally 6-Sigma is one such area. On looking at the General Electric
website (who seemed to have started the whole thing off), they stated that
6-Sigma is so called because there stated tolerance level of 3.4 defects or
less million parts equates to 6 standard deviations under a normal
distribution. Idly, I decided to verify this by looking up the one tailed
probability of the normal distribution in EXCEL and STATISTICA. But I
found that the stated probability level is in fact 4.5 standard deviations
> NOT 6 standard deviations!
>
> What have I done wrong?
Nothing - you just forgot to add in the missing "corporate constant" that
allows the nice PR slogan "Six Sigma" to exist instead of the clumsy "4.5
sigma" - I just love the justification! Ok - I'm being a bit harsh - but
the first paragraph below makes me squirm!
From: the GE MEdical Healthcare Site
http://healthcare.isixsigma.com/library/content/c010701a.asp
1.5 Sigma Process Shift Explanation by Zack Swinney
I'm not going to bore you with the hard core statistics. There's a whole
statistical section dealing with this issue, and every green, black and
master black belt learns the calculation process in class. If you didn't go
to class (or you forgot!), the table of the standard normal distribution is
used in calculating the process sigma. Most of these tables, however, end
at a z value of about 3 (see the iSixSigma table for an example). In 1992,
Motorola published a book (see chapter 6) entitled Six Sigma Producibility
Analysis and Process Characterizationbuy it now!, written by Mikel J. Harry
and J. Ronald Lawson. In it is one of the only tables showing the standard
normal distribution table out to a z value of 6.
Using this table you'll find that 6 sigma actually translates to about 2
defects per billion opportunities, and 3.4 defects per million
opportunities, which we normally define as 6 sigma, really corresponds to a
sigma value of 4.5. Where does this 1.5 sigma difference come from?
Motorola has determined, through years of process and data collection, that
processes vary and drift over time - what they call the Long-Term Dynamic
Mean Variation. This variation typically falls between 1.4 and 1.6.
After a process has been improved using the Six Sigma DMAIC methodology, we
calculate the process standard deviation and sigma value. These are
considered to be short-term values because the data only contains common
cause variation -- DMAIC projects and the associated collection of process
data occur over a period of months, rather than years. Long-term data, on
the other hand, contains common cause variation and special (or assignable)
cause variation. Because short-term data does not contain this special
cause variation, it will typically be of a higher process capability than
the long-term data. This difference is the 1.5 sigma shift. Given adequate
process data, you can determine the factor most appropriate for your
process
Regards ... Paul (black belt supreme master!!)
_____________________________________________________________________
Paul Barrett DDI: +64-(0)9-238-6336
email: [log in to unmask] Fax: +64-(0)9-353-1681
[log in to unmask] Mobile: +64-021-415625
[log in to unmask] Web: www.pbarrett.net
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