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This paper considers wireless sensor networks (WSNs) deployed to provide surveillance against intruders that wish to cross a given area. Due to limited resources, low manufacturing cost, and operation in harsh environments, nodes in such networks are subject to random failure in the field. Hence, there is a need to develop suitable reliability assessment mechanisms to quantify a WSN's ability to perform successfully. Here, we consider one such measure, called the breach path detection reliability (BPDREL), that applies to networks where any intruder crossing a line segment between some adjacent operating pairs of sensor nodes can be detected, and the network perimeter is made of a polygon of such line segments. Each breach path across the network is associated with a pair of entry-exit sides on the perimeter. Our measure takes into account intrusion events associated with any user-specified set of such entry-exit sides. Computing the exact BPDREL can be shown to be #P-hard. We extend existing results on the BPDREL by developing an approach for deriving lower bounds on the problem for arbitrary WSNs where the sink node is located on the network's perimeter. The resulting algorithm is used to analyze the impact of varying various network parameters on the overall network reliability.