  We present a general prediction scheme of failure times based on updating
continuously with time the probability for failure of the global system,
conditioned on the information revealed on the pre-existing idiosyncratic
realization of the system by the damage that has occurred until the present
time. Its implementation on a simple prototype system of interacting elements
with unknown random lifetimes undergoing irreversible damage until a global
rupture occurs shows that the most probable predicted failure time (mode) may
evolve non-monotonically with time as information is incorporated in the
prediction scheme. In addition, both the mode, its standard deviation and, in
fact, the full distribution of predicted failure times exhibit sensitive
dependence on the realization of the system, similarly to ``chaos'' in
spinglasses, providing a multi-dimensional dynamical explanation for the broad
distribution of failure times observed in many empirical situations.
