  The distribution of the magnitudes of damage avalanches during a failure
process typically follows a power law. When these avalanches are recorded close
to the point at which the system fails catastrophically, we find that the power
law has an exponent which differs from the one characterizing the size
distribution of all avalanches. We demonstrate this analytically for bundles of
many fibers with statistically distributed breakdown thresholds for the
individual fibers. In this case the magnitude distribution $D(\Delta)$ for the
avalanche size $\Delta$ follows a power law $\Delta^{-\xi}$ with $\xi=3/2$ near
complete failure, and $\xi=5/2$ elsewhere. We also study a network of electric
fuses, and find numerically an exponent 2.0 near breakdown, and 3.0 elsewhere.
We propose that this crossover in the size distribution may be used as a signal
for imminent system failure.
