  A detection system, modeled in a graph, is composed of "detectors" positioned
at a subset of vertices in order to uniquely locate an ``intruder" at any
vertex. \emph{Identifying codes} use detectors that can sense the presence or
absence of an intruder within distance one. We introduce a fault-tolerant
identifying code called a \emph{redundant identifying code}, which allows at
most one detector to go offline or be removed without disrupting the detection
system. In real-world applications, this would be a necessary feature, as it
would allow for maintenance on individual components without disabling the
entire system. Specifically, we prove that the problem of determining the
lowest cardinality of an identifying code for an arbitrary graph is
NP-complete, we determine the bounds on the lowest cardinality for special
classes of graphs, including trees, cylinders, and cubic graphs.
