[R] Calculating with tolerances (error propagation)

[David Winsemius]

On Sep 9, 2010, at 6:50 AM, Jan private wrote:

> Hello Bernardo,
>
> ---------
> If I understood  your problem this script solve your problem:
>
> q<-0.15 + c(-.1,0,.1)
> h<-10 + c(-.1,0,.1)
> 5*q*h
> [1]  2.475  7.500 12.625
> ---------
>
> OK, this solves the simple example.
> But what if the example is not that simple. E.g.
>
> P = 5 * q/h
>
> Here, to get the maximum tolerances for P, we need to divide the  
> maximum
> value for q by the minimum value for h, and vice versa. Is there any  
> way
> to do this automatically, without thinking about every single step?
>
> There is a thing called interval arithmetic (I saw it as an Octave
> package) which would do something like this.
>
> I would have thought that tracking how a (measuring) error propagates
> through a complex calculation would be a standard problem of
> statistics?? In other words, I am looking for a data type which is a
> number with a deviation +- somehow attached to it, with binary  
> operators
> that automatically knows how to handle the deviation.
>
> Thank you,	
> Jan
>
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David Winsemius, MD
West Hartford, CT