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We present a model of data retention for phase change memory devices in which the active medium is a thin layer of chalcogenide glass. Data retention capability is compromised when a crystalline path is spontaneously formed in the glassy host, essentially shunting the device. We determine the probability and statistics of device failure for systems in which the crystalline volume fraction is below the critical volume fraction of percolation theory. In that regime, we show that rectilinear crystalline path formation is favored and we determine the criteria for when such paths dominate over the typical percolation cluster scenario. Our analytical approach, based on modeling the formation of such paths in terms of a half-space random walk, leads to closed form expressions that relate data retention characteristics to device parameters. The model is used to examine the effects of device geometry, temperature, and external fields. The temporal statistics of device reliability are also considered for several failure mechanisms. A computer simulation is employed that supports our derived relationships between failure probability and device parameters.