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What is the conversion for PPM defects vs. Sigma Equivalents?

T

Totumfrog

#1
I'm trying to figure out if a chart or cross-reference exists that compares PPM rates to sigma levels. I.E. How is it calculated that 6 sigma is 3.4 parts per million defects? What is 5 sigma? What is 4 sigma? How many sigma is 230 ppms? If anyone has any ideas, please let me know.
 

Al Rosen

Staff member
Super Moderator
#2
Totumfrog said:
I'm trying to figure out if a chart or cross-reference exists that compares PPM rates to sigma levels. I.E. How is it calculated that 6 sigma is 3.4 parts per million defects? What is 5 sigma? What is 4 sigma? How many sigma is 230 ppms? If anyone has any ideas, please let me know.
You can find the answer in the attachment, DPMO to Sigma conversion, in the cove.
 

Tim Folkerts

Super Moderator
#3
Remember also that the whole "Six Sigma" system is set up with the mystical
magic.gif
"1.5 sigma shift" built in. That is why you can't simply look up the numbers in standard Z tables.

For 6 sigma, you would look up the Z table for 6-1.5 = 4.5 and find 1-0.9999966 = 3.4 x 10^(-6) = 3.4 PPM are in the upper tail. Then look up Z = -6-1.5 = -7.5 and find that basicallly none are in the lower tail. (OK, OK, I'm sure some of you are dying to know. The actual number is 3.2 x 10^-(14) = 32 PPQ (thats parts per quadrillion, at least in the US).)

Tim F
 
T

Totumfrog

#4
Thank you all.

I'm thoroughly impressed. I've looked for this conversion on and off over the years. I even asked a professor from a college in Dayton and he could only quote the emperical rule. Thank you for your help. I only hope that I can help someone else someday.

Totumfrog
 
D

D.Scott

#5
Here is a quick comparison of what Tim is talking about -

Comparison of Process Fallout

Based on Cpk values with 1.5 sigma allowance for normal shift (modern)
Vs
Cpk values assuming no process shift (traditional)

Both methods assume a stable process with normal distribution.


Sigma Cpk PPM Fallout
Modern Traditional
6 2.0 3.4 2 ppbillion
5 1.67 230 2 ppm
4 1.33 6,210 96
3 1.0 66,800 2,700
2 .66 308,000 71,860
1 .33 690,000 >134,000

Dave
 

Statistical Steven

Statistician
Staff member
Super Moderator
#9
Oh wise 6 Sigma gurus...why a 1.5 sigma shift? What does that shift apply to all processes and products? In some applications, a 1.5 sigma shift is critical. I just do not understand why when we say 6 sigma it means 6 sigma and not 4.5 sigma!
 

Jim Wynne

Super Moderator
#10
Statistical Steven said:
Oh wise 6 Sigma gurus...why a 1.5 sigma shift? What does that shift apply to all processes and products? In some applications, a 1.5 sigma shift is critical. I just do not understand why when we say 6 sigma it means 6 sigma and not 4.5 sigma!
The 1.5 sigma shift is a theoretical abomination which assumes that operators measuring things in production will not react until hit over the head, or that reactions only occur after changes in the process are actually charted, neither of which is true. IMO, the shift is the prime problem with SS, and a sure indication that SS advocates don't understand what production workers do for a living.
 
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