common derivations
time dependent from time independent variable
\[\forall t: x(t,:) = x(:)\]total uncertainty from random and systematic uncertainty
symbol
description
unit
variable name
\(\mu_{x}\)
total uncertainty for a variable x
same as that of \(x\)
<variable>_uncertainty {:}
\(\mu^{r}_{x}\)
uncertainty due to random effects for a variable x
same as that of \(x\)
<variable>_uncertainty_random {:}
\(\mu^{s}_{x}\)
uncertainty due to systematic effects for a variable x
same as that of \(x\)
<variable>_uncertainty_systematic {:}
The pattern : for the first dimensions can represent any combination of dimensions for which x {:} exists.
\[\mu_{x} = \sqrt{{\mu^{r}_{x}}^2 + {\mu^{s}_{x}}^2}\]total uncertainty from vertical covariance
symbol
description
unit
variable name
\(S_{x}(i,j)\)
covariance for a variable x
square of that of \(x\)
<variable>_covariance {:,vertical,vertical}
\(\mu_{x}(i)\)
total uncertainty for a variable x
same as that of \(x\)
<variable>_uncertainty {:,vertical}
The pattern : for the dimensions can represent any combination of dimensions for which x {:,vertical} exists.
\[\forall i: \mu_{x}(i) = \sqrt{S(i,i)}\]