3 sigma and 1 sigma values

[NDEngineer]

I have what seems to be a simple statistics question, but has stumped everyone in my office (including me)...

I did a tolerance stack analysis on an assembly by doing a RSS (root sum squares) analysis. From what I understand, this results in a 3-sigma value. Is there a way to convert this number to a 1-sigma value? If so, how is it accomplished?

 

[IRstuff]

divide by 3?

TTFN

 

[IRstuff]

However, your understanding is incorrect. RSS of 1-sigma values results in a 1-sigma value

TTFN

 

[NDEngineer]

There isn't really a sigma distribution associated with the individual tolerances. A small example...

tol 1: +-.005
tol 2: +-.010
tol 3: +-.010

RSS = sqrt((.005^2)+(.010^2)+(.010^2)) = .015

All of the information I could find regarding RSS analyses for tolerance stack applications concluded that the result (.015 in this example) is a 3-sigma value.

This being the case, can I simply divide by 3 to get a one sigma value? Using the same logic, would I multiply the result by 2 to get a six sigma value?

 

[CESSNA1]

NDENGINEER: Go to a basic statistics book. The 1 sigma value is considered to be one standard deviation. 2 sigma id 2 standard deviations. 3 sigma is 3 standard deviations, and so on.

In a standard normal distribution about 68.3% of the data lie within 1 standard deviation of the mean. 95.5% or the data lie within 2 standard deviations of the mean. 99.73% of the data lie with 3 standard deviations of the mean.

Regards
Dave

 

[NozzleTwister]

I think this is a good question for a 6th Sigma Black Belt.

NozzleTwister
Houston, Texas

 

[GregLocock]

Approximating a RSS to a normal distribution sort of works because of the central limit theorem. Since the original tolerances are likely to be based on the process, they will be around the 3-4 sigma mark, for most processes.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[tygerdawg]

This has been discussed before, you may want to search for it.

In a previous life we had a tolerance stackup question. The Quality Department referred to Juran's Quality Manual. It indicates that RSS applies ONLY if all of your individual tolerances are normal distributions with Cpk of >= 1.33. Otherwise your tolerance stackup is arithmetic summation. You probably ought to verify this "fact" because I'm going on memory.

The summation, in reality, isn't very practical because the total tolerance could be very unreasonable. So where's the balance? Dunno. We just muddled through using so-called "engineering judgement".

TygerDawg