# Converting DPMO to SIGMA - Seeking Forumula

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R

#### rivet guy

JimDad

Motorola has a book with tables.

sigmas DPMO(npmo) non-conformities or ppm
1 317,400
2 45,400
3 2,700
4 63
5 0.57
6 0.002
7 0.000003

This data above doesn't include a 1.5 sigma shift on either side of the median.

The book title is The Nature of 6 Sigma Quality from the Motorola University Press.

J

#### Jimdad

Thanks for the feedback folks, I really need to find the formula. Unfortunately, the table does not produce a sigma for a specific DPMO and I do not have the entire 2000 office suite to utilize Pyzdek's converte page.

Still seeking directions,,
Jim

J

#### Jimdad

Folks, I am deserately seeking a formula for converting DMPO to sigma...

Anyone??

K

#### Ken K.

Here is a formula (ready?)

Sigma =SQRT(LN(1/(1-EXP(-B24/1000000))^2))-(2.55155+0.802853*SQRT(LN(1/(1-EXP(-B24/1000000))^2))+0.010328*SQRT(LN(1/(1-EXP(-B24/1000000))^2))^2)/(1+1.432788*SQRT(LN(1/(1-EXP(-B24/1000000 ))^2))+0.189269*SQRT(LN(1/(1-EXP(-B24/1000000))^2))^2+0.001308*SQRT(LN(1/(1-EXP(-B24/1000000))^2))^3)+1.5

where B24 is DPMO

This formula is accurate to two decimal places between Sigma = 3.2 - 9.0, and one decimal between 2.5 & 3.2, and shouldn't be used for Sigma < 2.5

If you're using Excel you can use:
Sigma =NORMINV(1-B24/1000000,1.5,1)

The Excel function is accurate to 2 decimal places between Sigma = 1.4 - 5.7, and to 1 decimal place for Sigma = 5.7 - 6.1

S

#### stefanson

Check out: ***DEAD LINK REMOVED****

Last edited by a moderator:
J

#### Jimdad

Been there, I don't have the complete MS 2000 suite to utilize the converter.

Thanks for the feedback.

Jim

G

#### GaryC

DPMO to sigma is simple. Go to normal tables with your DPMO, get the z value and add 1.5. That is your sigma value.

Use the paste function in Excel for the most accurate normal tables.

GaryC

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