  We investigate bipartite entanglement in random quantum $XY$ models at
equilibrium. Depending on the intrinsic time scales associated with
equilibration of the random parameters and measurements associated with
observation of the system, we consider two distinct kinds of disorder, namely
annealed and quenched disorders. We conduct a comparative study of the effects
of disorder on nearest-neighbor entanglement, when the nature of randomness
changes from being annealed to quenched. We find that entanglement properties
of the annealed and quenched disordered systems are drastically different from
each other. This is realized by identifying the regions of parameter space in
which the nearest-neighbor state is entangled, and the regions where a
disorder-induced enhancement of entanglement $-$ order-from-disorder $-$ is
obtained. We also analyze the response of the quantum phase transition point of
the ordered system with the infusion of disorder.
