  We study the interplay of disorder with pumping and decay in coupled
qubit-cavity arrays, the Jaynes-Cummings-Hubbard model. We find that relatively
weak disorder can wash out the bistability present in the clean pumped system,
and that moreover, the combination of disorder in on-site energies and decay
can lead to effective phase disorder. To explore these questions, we present a
non- equilibrium generalisation of Stochastic-Mean-Field theory, providing a
simple tool to address such questions. This technique is developed for rather
general forms of light-matter coupling, driving, dissipation, and on-site
disorder, making it applicable to a wide range of systems.
