  The time to failure, $T$, of dynamical models of fracture for a hierarchical
load-transfer geometry is studied. Using a probabilistic strategy and
juxtaposing hierarchical structures of height $n$, we devise an exact method to
compute $T$, for structures of height $n+1$. Bounding $T$, for large $n$, we
are able to deduce that the time to failure tends to a non-zero value when $n$
tends to infinity. This numerical conclusion is deduced for both power law and
exponential breakdown rules.
