# Combination of Errors

1. Mar 18, 2013

### 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)]

Charles

2. Mar 18, 2013

### HallsofIvy

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

3. Mar 18, 2013

### charlesltl

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