Structural system reliability analysis is of important significance for evaluating the safety of structures with many components. Since a structural system can be acted by static or dynamic load, a unified and efficient method is required to assess the system reliability of static or dynamic load induced structures. In this study, the direct probability integral method (DPIM) is proposed to uniformly attack system reliability problems of static and dynamic structures. Firstly, the static and first-passage dynamic reliability formulas of the series, parallel and mixed systems are established by the joint probability density function (PDF) of multiple performance functions. Based on the probability density integral equation (PDIE) of performance functions, the DPIM is proposed along the two approaches, i.e., DPIM-S and DPIM-H. The former computes the system reliability using the PDF of extreme value mapping of performance functions, which is obtained by smoothing Dirac delta function. In the latter, the system reliability formulas with Heaviside function are analytically derived by the PDIE of multiple performance functions. Specially, the role of smoothing of Dirac delta function in DPIM for stochastic response and reliability analyses is revealed. Finally, five typical examples, including two mathematical examples and three static and dynamic structural systems, demonstrate high efficiency and accuracy of the DPIM for system reliability computation. Because of omitting the smoothing of Dirac delta function, the DPIM-H takes less CPU time for solving system reliabilities of static and dynamic structures than DPIM-S, while the DPIM-S has a significant advantage of obtaining the PDF of performance function.

结构系统可靠性分析对于评价多构件结构的安全性具有重要意义。由于结构系统可以承受静载荷或动载荷，因此需要一种统一有效的方法来评估静载荷或动载荷引起的结构的系统可靠性。在这项研究中，直接概率积分法（DPIM）被提出来统一解决静态和动态结构的系统可靠性问题。首先，通过多个性能函数的联合概率密度函数(PDF)，建立了串联、并联和混合系统的静态和首过动态可靠性公式。基于性能函数的概率密度积分方程(PDIE)，提出了DPIM-S和DPIM-H两种方法的DPIM。前者使用性能函数极值映射的 PDF 计算系统可靠性，后者是通过平滑 Dirac delta 函数获得的。后者通过多性能函数的PDIE解析导出了带Heaviside函数的系统可靠性公式。特别地，揭示了 DPIM 中 Dirac delta 函数的平滑在随机响应和可靠性分析中的作用。最后，五个典型实例，包括两个数学实例和三个静态和动态结构系统，证明了DPIM在系统可靠性计算中的高效性和准确性。由于省略了 Dirac delta 函数的平滑，DPIM-H 比 DPIM-S 需要更少的 CPU 时间来解决静态和动态结构的系统可靠性，