They were kidding about published tables, surely. My 1970 copy of
Biometrika tables for statisticians, vol 1, Table 1 goes up to 6.
Martin
Paul Barrett wrote:
>
> ----- 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
--
***************************************************
J. Martin Bland
Prof. of Health Statistics
Dept. of Health Sciences
University of York
Heslington
York YO10 5DD
Email: [log in to unmask]
Phone: 01904 321334
Fax: 01904 321382
Web site: http://www-users.york.ac.uk/~mb55/
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