In this article, we examine the coverage and reliability of distributed sensor networks that are designed for surveillance applications. In particular, we examine a model of sensor network coverage based on Poisson processes, and illustrate how this model combines with standard reliability models to provide estimates of field degradation over time. The results of the article illustrate how the number of sensors required changes with respect to reliability criteria, and how to design and re-seed sensor fields to maintain a minimal level of surveillance coverage. The formulation in the article is presented analytically, and all results are compared to numerical simulations.