  The spectrum and event rate of supernova relic neutrinos are calculated
taking into account the dependence on the time it takes for the shock wave in
supernova cores to revive. The shock revival time should depend on the still
unknown explosion mechanism of collapse-driven supernovae. The contribution of
black-hole-forming failed supernovae is also considered. The total event rate
is higher for models with a longer shock revival time and/or a failed-supernova
contribution. The hardness of the spectrum does not strongly depend on the
shock revival time, but the spectrum becomes hard owing to the failed
supernovae. Therefore, the shock-revival-time dependence of supernova relic
neutrinos has different systematics from the fractions of failed supernovae.
