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Most methods of system reliability analysis assume that the precise probability distributions of the component lifetime to failure are available, and the system components are independent. However this assumption may be unreasonable in a wide scope of cases. Therefore, imprecise reliability modes of a bridge system structure are put forward in this paper, for cases when the above assumptions are violated. The analysis is based on only some partial information about the component lifetime distributions including points of unknown distributions, and probabilities on nested intervals. The effect of the component independence condition on the reliability of systems is studied. The formulas of the unreliability of the bridge system structure are obtained in the explicit form under different conditions.