# Six sigma and defect rate (6 sigma = 3.4 PPM)

#### sushant_kulkarni

##### Involved In Discussions
Dear All,

Can anyone will explain me that six sigma level i.e. 6 sigma = 3.4 PPM,

Logical analysis behind those things.

How they arrived that 6 sigma= 3.4. PPM

K

#### kaikai

It is very simple.

Assuming the Normal Distribution.
Cp is in the 6-sigma level.
Cpk is in the 4.5-sigma level.
(The case that the process mean drift 1.5 sigma in either direction is considered)

The area of a normal distribution beyond 4.5 sigma from the mean is 3.4 ppm.

#### Jim Wynne

Dear All,

Can anyone will explain me that six sigma level i.e. 6 sigma = 3.4 PPM,

Logical analysis behind those things.

How they arrived that 6 sigma= 3.4. PPM
The idea is that a process that has a 4.5-sigma "cushion" will produce ~4.5 "DPMO" or defects per million opportunities. The six-sigma number comes by adding an imaginary, illogical 1.5-sigma to account for process drift in the long term. In other words, if you set your process to +/- 6-sigma limits, over time it will drift or deteriorate and you'll be left with 4.5 sigma in the long term. You will hear many SS advocates confidently state that the 1.5-sigma drift is empirically derived, but the only evidence is anecdotal and mostly nonsensical. Thus the entire edifice of SS is constructed on a foundation of voodoo statistics.

#### bobdoering

Trusted Information Resource
Thus the entire edifice of SS is constructed on a foundation of voodoo statistics.
Yes, it is practicing the rite of normalcentricty. Bring along your chicken claw.

#### Jim Wynne

Yes, it is practicing the rite of normalcentricty. Bring along your chicken claw.
It's not just your well-founded distaste for flinging the normal distribution around indiscriminately; it's the idea that SS, at its base, is a way of institutionalizing statistical ignorance in general. We have a few conscientious SS devotees here, and they'll always argue for the application of rationality (and good on them for that), but it's a runaway train at this point. The good news, if there is any, is that runaway trains can't run away forever.

#### Stijloor

Super Moderator
Friends,

Statistical snake oil is an extremely strong poisonous potion...:mg:

Stijloor.

U

#### Umang Vidyarthi

Dear All,

Can anyone will explain me that six sigma level i.e. 6 sigma = 3.4 PPM,

Logical analysis behind those things.

How they arrived that 6 sigma= 3.4. PPM
Jim has given you good response. From your question I feel you are new to six sigma. If so, then I recommend you visit the site "New to Lean Six Sigma".

Umang

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