Hi,
The short answer is that the calculations below are looking at both tails of
the normal distribution, but the 'standard' method of calculation just looks
at one tail. In other words you should calculate A as simply F(n-1.5)
(taking s as 1).
Personally I find it hard to get through the gobbledegook surrouding six
sigma, but my understanding of what's going on here is that the specifiction
limit you're supposed to worry about is just on one side of the mean. In
other words, the idea is that things (say) six sigma above the mean are out
of specification, but things six sigma below the mean, or even ten sigma
below the mean, are not out of specification. This might or might not make
sense in any given context, I think.
Regards,
Kevin McConway
Senior Lecturer in Statistics
Department of Statistics
The Open University
Walton Hall
Milton Keynes MK7 6AA, UK
Phone: +44-1908-653676
Fax: +44-1908-652140
email: [log in to unmask]
-----Original Message-----
From: Concerned with the initial learning and teaching of statistics
[mailto:[log in to unmask]] On Behalf Of Romesh Juneja
Sent: 19 March 2003 14:59
To: [log in to unmask]
Subject: DPMO and Six Sigma Calculation
Hello,
We are trying to determine why the calculation below gives a different
answer that what the books state. Could someone please indicate the
inaccuracies in the calculation below? Thank you. Romesh
Curious about the derivation of 3.4 defects/million. I wanted to explain
this concept to my team, but calculated a different number using the
statistical concepts in a college text of mine (I did include the 1.5s
shift). In short, I calculate that the DMPO is off by a factor of 2 by my
methods.
In short, my calculation is:
DPMO = 1e6 * [1 - A]
where A = F[(n-1.5)s] - F[-(n-1.5)s]
with s = arbitrary (set to 1, so it will be standard normal)
n = sigma level (eg. 6)
F = cummulative distribution function for standard normal
Note, most texts to not have F(x) greater than for x=3. I wrote a numerical
integration spreadsheet to calculate F at any x, but the spreadsheet matches
my text with x up to 3.
Example: n=4
so A = F(2.5) - F(-2.5) = 0.9938-0.0062 = 0.9876
DPMO = 1e6*[1-0.9876] = 12400
our handouts, the six sigma calculator, and the website all have 6210. The
difference is a factor of 2.
Todd
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