  The collective strength of a system of fibers, each having a failure
threshold drawn randomly from a distribution, indicates the maximum load
carrying capacity of different disordered systems ranging from disordered
solids, power-grid networks, to traffic in a parallel system of roads. In many
of the cases where the redistribution of load following a local failure can be
controlled, it is a natural requirement to find the most efficient
redistribution scheme, i.e., following which system can carry the maximum load.
We address the question here and find that the answer depends on the mode of
loading. We analytically find the maximum strength and corresponding
redistribution schemes for sudden and quasi static loading. The associated
phase transition from partial to total failure by increasing the load has been
studied. The universality class is found to be dependent on the redistribution
mechanism.
