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

[Totumfrog]

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]

Originally Posted by Totumfrog

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]

Remember also that the whole "Six Sigma" system is set up with the mystical "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

[Totumfrog]

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.Scott]

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

[D.Scott]

Figures I would mess up the formatting

I am attaching a doc file that should be easier to read.

Dave

[Govind]

Here is a link from isixsigma which can be useful to you:
Six sigma Calculator
Regards,
Govind.
Note: Donot forget to read the formula rationale and assumptions.
Process Sigma Calculator Assumptions

[Arvind]

http://elsmar.com/Forums/showthread....131#post114131