  In this paper we deal with a novel survival function recently introduced by
Boczek et al. (2020). The concept is worth to study because of its possible
implementation in real life situations and mathematical theory, as well. The
main ingredient in the generalization is the conditional aggregation operator
related to a conditional set. The aim of this paper is the comparison of this
new notion with the standard survival function. We state sufficient conditions
under which the generalized survival function coincides, resp. is greater or
smaller than survival function. The main result is the characterization of the
family of conditional aggregation operators (on discrete settings) for which
the generalized survival function coincides with the standard survival
function.
