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Theoretical results of magnetic bubble device long-term reliability testing are reported. The bubble during propagation along Permalloy tracks is represented by a simple, one-dimensional stochastic model. An equation to describe fluctuation in cylindrical bubble radius is approximated in the Langevin type stochastic differential equation, in which a set of small effects, such as interaction among bubbles and crystal nonuniformity, are considered as a white noise forcing term. Estimating the average time to bubble annihilation or runout (bubble memory mean time to failure) is reduced to a level-crossing problem for a random process. Calculated bias field margin degradation shows a qualitative agreement with experimental results for an actual bubble device. Bubble material parameters for obtaining maximum operation time are suggested.