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

Let's consider the following:

A ± ΔA

B ± ΔB

where A and B are the mean values while ΔA and ΔB are the respective standard errors.

The common combination of errors formulas are as follows:

y = A + B then, Δy = √(ΔA2+ΔB2)

y = k. A then, Δy = k.ΔA

Now my equation is,

y = k2 . [ A + k1 . ( A + B + C ) ]

May I know if my following working is correct?

( A + B + C )

= √(ΔA2+ΔB2 + ΔC2)

k1 . ( A + B + C )

= k1 . √(ΔA2+ΔB2 + ΔC2)

A + k1 . ( A + B + C )

= √[ΔA2 + (k1 . √(ΔA2+ΔB2 + ΔC2))2]

= √[ΔA2 + k12 . (ΔA2+ΔB2 + ΔC2)]

k2 . [ A + k1 . ( A + B + C ) ]

= k2 . √[ΔA2 + k12 . (ΔA2+ΔB2 + ΔC2)]

I am confused because I was suggested that it should be,

k2 . [ A + k1 . ( A + B + C ) ]

= k2 . √ [k1. ΔA2 + k12 . (ΔA2+ΔB2 + ΔC2)]

Your input in highly appreciated.

Charles