On the reliability analysis of structural system, the narrow-bound method is often used to compute the system failure probability. But it is difficult to calculate two-dimensional joint failure probability p_(fij) accurately and conveniently. Based on geometry analysis, a new solution for p_(fij) is presented in this paper. The solution is pithy and precise; its precision can be adjusted through a parameter Δθ. The system failure probability can be estimated satisfactorily by applying the deduced solution to narrow-bound equation. An example testifies that the new narrow-bound method can narrow the width of bounds of structural system failure probability effectively.
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