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Combination of Errors

  1. Mar 18, 2013 #1
    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
     
  2. jcsd
  3. Mar 18, 2013 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    That last appears to be the "mean square error" rather than the "error".
     
  4. Mar 18, 2013 #3
    Would you suggest that my working to compute the standard error is correct?
     
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