# derivation of the 5.15 of measurement system

Six Sigma – iSixSigma Forums Old Forums General derivation of the 5.15 of measurement system

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• #34121

tata
Member

Hi all,
I’m a newly trained blackbelt and I tried to ask my master blackbelt on where did they got the 5.15 from the formula of precision of measurement system.
thanks,
tata

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#93644

Chris L.
Participant

tata,
The 5.15 sigma figure used in the gauge R&R computations is set at this level as it is the sigma level which includes 99.0% of the area under the curve. It seems to me to be an attempt to limit the total variation calcs within minitab etc. to a realistic level. i.e. if you used 6 sigma the area under the curve would be greater and therefore the calc of total R&R variation in the measurement system would be unrealistically inflated, in real life there is no practical difference in 99% & 99.9997% inclusion for measurement system variation.
Chris L.

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#93645

Hemanth
Participant

If you look at the measurement error, it also follows a normal curve with center at zero and std deviation of “R&R std deviation”. In order to convert the standard deviation into a more meaningful term of “error band due to R&R” 5.15 is multiplied to std deviation (+/- 2.575 std deviation on either side). This basically represents the 95% width of a normal curve. Thus 95% of the time your R&R error will not go beyond this band. However, recently AIAG has modified this value to 6 (i.e +/- 3 std deviations this makes more sense right..?)
Hope this was helpful.

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#93646

Hemanth
Participant

Correction..replace 95% with99%
Sorry for the error..:)

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#93647

kivantsy
Participant

this is coming from the 99% CI, used in R&R studies. If you want to cover the 99% of a normal distribution, your covered area will be 5.15 sigma wide.

K.

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#93661

jediblackbelt
Participant

When did they change to 6sigma?  I had not heard this was to be reported this way.

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#93670

tata
Member

Thanks, yes it’s in the training module that under normal distribution, 99% of the area fall under 5.15 sigma. But why 99% why not 98% or 97% or 99.5% or 99.75%, who decided to use 99% CI and what made them decide. Is there an explanation for this?

tata

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#93674

kivantsy
Participant

I think there is no special reason behind this, but I might be wrong.
K.

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#93681

Mikel
Member

The 5.15 is a historical artifact from the guys at GM who first put the methods together in the 1960’s. The engineers did not think they needed to represent 99.73% but thought 99% was okay. Ford used 6 until the combined AIAG standards were first published.

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#93789

tata
Member

Thanks Stan

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