In this paper we present a new built-in test methodology for detecting and locating faults in digital systems. The technique is called roving emulation and consists of an off-line snap shot type emulation or simulation of operating components in a system. Its primary application is in testing systems in the field where real-time fault detection is not required. The primary performance measure of this test schema is taken to be the expected value of the error latency, i.e., the time required to detect a fault once it first occurs. The primary results of this paper deal with deriving equations for the error latency. We present both a probabilistic and service-waiting model to analyze the expected error latency in a system tested via roving emulation. The effects of various controllable and uncontrollable system parameters on error latency are studied. Finally, the technique is applied to a system consisting of combinational logic modules, and numerical results are presented.