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The optimum allocation of a fixed stock of unreliable units to a random number of demands is discussed. The demands occur at Poisson times; several types of criteria are described, but the most important optimum presented is of the probability that at least one allotted unit does not fail at every Poisson demand. Hence this concerns how unreliable elements can best be used to create a reliable system. The allocation problem arose in a military system analysis context. The results presented exemplify how system science concepts (Poisson models, recursive computation, and cost/ benefit comparisons) and current computing tools can be applied to practical problems.