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 $\pm$ $\Delta$A
B $\pm$ $\Delta$B

where A and B are the mean values while $\Delta$A and $\Delta$B are the respective standard errors.

The common combination of errors formulas are as follows:

y = A + B then, $\Delta$y = √($\Delta$A²+$\Delta$B²)

y = k. A then, $\Delta$y = k.$\Delta$A

Now my equation is,

y = k₂ . [ A + k₁ . ( A + B + C ) ]

May I know if my following working is correct?

( A + B + C )
= √($\Delta$A²+$\Delta$B² + $\Delta$C²)

k₁ . ( A + B + C )
= k₁ . √($\Delta$A²+$\Delta$B² + $\Delta$C²)

A + k₁ . ( A + B + C )
= √[$\Delta$A² + (k₁ . √($\Delta$A²+$\Delta$B² + $\Delta$C²))²]
= √[$\Delta$A² + k₁² . ($\Delta$A²+$\Delta$B² + $\Delta$C²)]

k₂ . [ A + k₁ . ( A + B + C ) ]
= k₂ . √[$\Delta$A² + k₁² . ($\Delta$A²+$\Delta$B² + $\Delta$C²)]


I am confused because I was suggested that it should be,
k₂ . [ A + k₁ . ( A + B + C ) ]
= k₂ . √ [k₁. $\Delta$A² + k₁² . ($\Delta$A²+$\Delta$B² + $\Delta$C²)]

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?