Combining Errors for Stress Calculation

[charlesltl]

Hello Everyone,

I am trying to compute the standard error of a stress related calculation.

Let's consider the following:

A \pm \DeltaA
B \pm \DeltaB

where A and B are the mean values while \DeltaA and \DeltaB are the respective standard errors.

The common combination of errors formulas are as follows:

y = A + B then, \Deltay = √(\DeltaA²+\DeltaB²)

y = k. A then, \Deltay = k.\DeltaA

Now my equation is,

y = k₂ . [ A + k₁ . ( A + B + C ) ]

May I know if my following working is correct?

( A + B + C )
= √(\DeltaA²+\DeltaB² + \DeltaC²)

k₁ . ( A + B + C )
= k₁ . √(\DeltaA²+\DeltaB² + \DeltaC²)

A + k₁ . ( A + B + C )
= √[\DeltaA² + (k₁ . √(\DeltaA²+\DeltaB² + \DeltaC²))²]
= √[\DeltaA² + k₁² . (\DeltaA²+\DeltaB² + \DeltaC²)]

k₂ . [ A + k₁ . ( A + B + C ) ]
= k₂ . √[\DeltaA² + k₁² . (\DeltaA²+\DeltaB² + \DeltaC²)]


I am confused because I was suggested that it should be,
k₂ . [ A + k₁ . ( A + B + C ) ]
= k₂ . √ [k₁. \DeltaA² + k₁² . (\DeltaA²+\DeltaB² + \DeltaC²)]

Your input in highly appreciated.

Charles

 

[HallsofIvy]

That last appears to be the "mean square error" rather than the "error".

 

[charlesltl]

Would you suggest that my working to compute the standard error is correct?