How to calculate the propagation error for a tricky Eq

[andresfirman]

Hello Please help me, my function is;

alpha = [ i1.g2 / (i2.g1) - 1 ] / ( t1-t2 )

I will have to measure i1, i2, g1, g2, t1 and t2 them
I made classical error porpagation, but I don't know if this is ok.

How is the proper way to calculate the propagation error for alpha?

 

[BvU]

Hello Please help me, my function is;

alpha = [ i1.g2 / (i2.g1) - 1 ] / ( t1-t2 )

I will have to measure i1, i2, g1, g2, t1 and t2 them
I made classical error porpagation, but I don't know if this is ok.

How is the proper way to calculate the propagation error for alpha?

Hello andresfirman,

PF culture encourages you to set up some attempt before assistance is given.
What is the general formula for error propagation that you are using ?

 

[andresfirman]

Hello andresfirman,

PF culture encourages you to set up some attempt before assistance is given.
What is the general formula for error propagation that you are using ?

Hi, I`m using

d(alpha)/d(i1)*Δi1 + d(alpha)/d(i2)*Δi2 + d(alpha)/d(g1)*Δg1 + d(alpha)/d(g2)*Δg2 + d(alpha)/d(t1)*Δt1 + d(alpha)/d(t2)*Δt2

Δi1 = 0.3 %
Δi2 = 0.3 %
Δg1 = 3.2 %
Δg2 = 3.2 %
Δt1 = 0.2 C
Δt2 = 0.2 C

Its values aprox are;
t1 and t2 is near 26 C
g1 and g2 is near 950
and i1 and i1 are near 7.5

it give me aprox 1000 % of error its too big I think, I don't know where is the problem. I don't think that the quantities errors are too big for the answer of 1000 %

 

[haruspex]

t1 and t2 is near 26 C

But how near are they to each other? When you take differences of numbers of similar size the error percentage can get hugely magnified.
Same issue arises with i1.g2-i2.g1.

 

[andresfirman]

But how near are they to each other? When you take differences of numbers of similar size the error percentage can get hugely magnified.
Same issue arises with i1.g2-i2.g1.

Hi!;
t1 = 27.6 C
t2 = 44.9 C
g1 = 993
g2 = 1000
i1 = 7.5
i2 = 7.6

so, alpha is a very low number
alpha = 0.0003766

 

[haruspex]

g1 = 993
g2 = 1000
i1 = 7.5
i2 = 7.6

There's a problem. The ratio of the products, as in your equation, differs from 1 by only 0.6%. That effectively amplifies the error percentage by 1/0.006= 167.