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A binary distributed detection system comprises a bank of local decision makers (LDM's) and a central information processor (the data fusion center, DFC). All LDM's survey a common volume for a binary {[H.sub.0], [H.sub.1]} phenomenon. Each LDM forms a binary decision: it either accepts [H.sub.1] ("target-present") or [H.sub.0] ("target-absent"). The LDM is fully characterized by its performance probabilities (probability of false alarm and probability of detection). The decisions are transmitted to the DFC through noiseless communication channels. The DFC then optimally combines the local decisions to obtain a global decision ("target-present" or "target-absent") which minimizes a Bayesian objective function. Along with the local decisions, the DFC in our architecture remembers and uses its most recent decision in synthesizing each new decision. When operating in a stationary environment, our architecture converges to a steady-state decision in finite time with probability one, and its detection performance during convergence and in steady state is strictly determined. Once convergence is proven, we apply the results to the detection of signals with random phase and amplitude. We further provide a geometric interpretation for the behavior of the system: the unit square of the current ([P.sub.f], [P.sub.d]) known to the DFC is partitioned into polygons, one of which defines a "stopping set" of values. If the current ([P.sub.f], [P.sub.d]) falls into this region, there is no way to leave it, and hence there is no reason to continue testing.