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This paper introduces a new metric, to approximately lower-bound the error-variance in the estimation of an incident source's direction-of-arrival (DOA), for a sensor-array subject to random breakdown in its individual sensors. This new metric equals a weighted sum of Cramér-Rao bounds, each conditioned on a distinct event of sensors-breakdown. Those distinct events together describe the overall random phenomenon of the fallibility of the sensors that constitute the sensor-array. This new metric's tightness as an approximate lower bound is illustrated by Monte Carlo simulations of the maximum-likelihood estimator.