The effect of random noise in the spectra of astronomical objects can be
simulated by introducing in each pixel Gaussian noise computed as:
where 
is the variance in the pixel [j], and r1 and r2
two random numbers in the range 
. After the creation of
synthetic spectra, index errors can be derived as the
unbiased standard deviation of the measurements of each index
(typically we employed 
).
For illustration, we show the results of numerical simulations using a high S/N ratio spectrum of the bright star HR 3428 as a template. We have assumed this spectrum to be noiseless, i.e. the nominal values of the measured line-strength indices in this spectrum were considered as error free reference values. By dividing this template spectrum by different constant factors, we built a set of synthetic error spectra which were used to derive index errors as a function of the mean (S/N-ratio)/Å for different atomic and molecular indices (Fig. 1 (click here)). In a logarithmic scale, there is a clear linear correlation between the estimated relative error and the (S/N-ratio)/Å. In addition, and as it should be expected, at a fixed (S/N-ratio)/Å relative errors for atomic indices (with narrow bandpasses) are larger than for molecular indices.
Figure 1: Relative errors from numerical simulations in the
measurement of 21 line-strength indices in the bright star HR 3428, as a
function of the mean S/N-ratio per Å