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Designing reliable MEMS structures presents numerous challenges. Polycrystalline silicon fractures in a brittle manner with considerable variability in measured strength. Furthermore, it is not clear how to use measured tensile strength data to predict the strength of a complex MEMS structure. To address such issues, two recently developed high-throughput MEMS tensile test techniques have been used to estimate strength distribution tails by testing approximately 1500 tensile bars. There is strong evidence that the micromachined polycrystalline silicon that was tested in this paper has a lower bound to its tensile strength (i.e., a strength threshold). Process-induced sidewall flaws appear to be the main source of the variability in tensile strength. Variations in as-fabricated dimensions, stress inhomogeneity within a polycrystal, and variations in the apparent fracture toughness do not appear to be dominant contributors to tensile strength variability. The existence of a strength threshold implies that there is maximum flaw size, which consequently enables a linear elastic fracture mechanics flaw-tolerance analysis. This approach was used to estimate a lower bound for the strength of a double edge-notched specimen that compared favorably with our measured values.