  Core-Collapse Supernovae, failed supernovae and quark novae are expected to
release an energy of few $10^{53}$ ergs through MeV neutrinos and a network of
detectors is operative to look online for these events. However, when the
source distance increases and/or the average energy of emitted neutrinos
decreases, the signal statistics drops and the identification of these low
statistic astrophysical bursts could be challenging. In a standard search,
neutrino detectors characterise the observed clusters of events with a
parameter called multiplicity, i.e. the number of collected events in a fixed
time-window. We discuss a new parameter called $\xi$ (=multiplicity/duration of
the cluster) in order to add the information on the temporal behaviour of the
expected signal with respect to background. By adding this parameter to the
multiplicity we optimise the search of astrophysical bursts and we increase
their detection horizon. Moreover, the use of the $\xi$ can be easily
implemented in an online system and can apply also to a network of detectors
like SNEWS. For these reasons this work is relevant in the multi-messengers era
when fast alerts with high significance are mandatory.
