# Standard Deviation

Six Sigma – iSixSigma Forums Old Forums General Standard Deviation

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• #28022

Fontanilla
Participant

What is a simple explaination as to why you cannot add standard deviations??

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#69406

Jim Johnson
Participant

Please clarify your question. Is it:”Why can’t standard deviations (1, 2 or 3 from the mean) be summed?” (If this is your question, what are you measuring by summing them?)or is it:”Why can’t standard deviations from sub-processes be combined to make a composite for the entire process?” or is it something else?Jim Johnson

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#69407

kmb
Participant

I think I can guess the practical application which this question is alluding to, namely gage r&r with continous data.  Frequently I find that when people look at the results from Gage R&R output in MINITAB they’re perplexed as to why the repeatability and reproducibility standard deviations don’t add up to 100%.  It’s because we actually inspect the variance components (these will, of course sum to 100%).  There’s more info in a paper on gage R&R via http://www.minitab.com/company/virtualpressroom/Articles/UsingGageRR.pdf and there’s soon to be a tutorial on nested gage r&r (for use in destructive testing) with a fuller discussion on variance components usage, expected mean squares, etc. via the tutorials page at http://www.minitab.com/resources/tutorial/index.htm so stay tuned for that.

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#69433

Ken K.
Participant

The nicest way I’ve seen is to related the standard deviations to the lengths of the sides of a right triangle.
The length of the hypotenuse is equal to the square root of the sum of the squared side lengths.
Clearly the length of the hypotenuse can’t be simply the sum of the side lengths – that just wouldn’t make sense from a visual perspective.
The other nice thing about this analogy is to show the relative effect of measurement error. If the horizontal side is the actual value’s variability (standard deviation) and the vertical side is the inprecision due to measurement error (the standard deviation due to GR&R), then the hypotenuse represents the total variation that you will actually observe.

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#69440

Fontanilla
Participant

Thanks for the question to clarify mine.
Your second question is closer to being correct. “Why can’t standard deviations from sub-processes be added to get an overall SD”?

Thanks.

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#69448

Edwards
Participant

If you are trying to find the total variance in a process that has multiple stages you can do this by squaring the standard deviation from each stage and adding them together then the square root of the sum of these is the tatal variation.

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