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This paper proposes a performance indicator to evaluate the capability of a maintainable stochastic-flow network (MSFN). This MSFN is required to preserve a minimal service level so that it can send d units of data or commodity from the source to the sink through multiple paths within time T. The proposed system reliability performance indicator quantifies the probability that a MSFN delivers a capacity level above the minimal service level with a budget no greater than B. Two procedures are integrated in the proposed algorithm: a procedure to estimate system reliability, and an adjusting procedure that utilizes the branch-and-bound approach for exact system reliability. The estimated system reliability with lower and upper bounds, and the exact system reliability, are then computed by applying the recursive sum of disjoint products (RSDP) algorithm.