  Existing models for the analysis of concurrent processes tend to focus on
fail-stop failures, where processes are either working or permanently stopped,
and their state (working/stopped) is known. In fact, systems are often affected
by grey failures: failures that are latent, possibly transient, and may affect
the system in subtle ways that later lead to major issues (such as crashes,
limited availability, overload). We introduce a model of actor-based systems
with grey failures, based on two interlinked layers: an actor model, given as
an asynchronous process calculus with discrete time, and a failure model that
represents failure patterns to inject in the system. Our failure model captures
not only fail-stop node and link failures, but also grey failures (e.g.,
partial, transient). We give a behavioural equivalence relation based on weak
barbed bisimulation to compare systems on the basis of their ability to recover
from failures, and on this basis we define some desirable properties of
reliable systems. By doing so, we reduce the problem of checking reliability
properties of systems to the problem of checking bisimulation.
