Combination of Errors

charlesltl

Hello Everyone,

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

Let's consider the following:

A [itex]\pm[/itex] [itex]\Delta[/itex]A
B [itex]\pm[/itex] [itex]\Delta[/itex]B

where A and B are the mean values while [itex]\Delta[/itex]A and [itex]\Delta[/itex]B are the respective standard errors.

The common combination of errors formulas are as follows:

y = A + B then, [itex]\Delta[/itex]y = √([itex]\Delta[/itex]A²+[itex]\Delta[/itex]B²)

y = k. A then, [itex]\Delta[/itex]y = k.[itex]\Delta[/itex]A

Now my equation is,

y = k₂ . [ A + k₁ . ( A + B + C ) ]

May I know if my following working is correct?

( A + B + C )
= √([itex]\Delta[/itex]A²+[itex]\Delta[/itex]B² + [itex]\Delta[/itex]C²)

k₁ . ( A + B + C )
= k₁ . √([itex]\Delta[/itex]A²+[itex]\Delta[/itex]B² + [itex]\Delta[/itex]C²)

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

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


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