目的 研究单自由度线性和非线性包装件位移响应首次穿越损坏的概率问题。方法 对于单自由度线性包装件，通过理论分析的方法将位移首次穿越问题转化为标准正态变量空间中的几何分析问题，建立确定设计点的分析方法，应用一次可靠度方法分析首次穿越损坏概率。分析系统设计点激励与镜像激励之间的关系，通过最优化方法分析应用镜像激励确定单自由度非线性包装件设计点的方法。结果 单自由度线性和非线性包装件的设计点激励均等于系统初始位移为阈值时的镜像激励。结论 在系统稳态响应阶段，可应用镜像激励准确分析出系统的设计点，并由此分析出包装件的位移首次穿越损坏概率。

The work aims to study the first-passage failure probability of single-degree-of-freedom (SDOF) linear and nonlinear package displacement response. For the linear SDOF package, the displacement first-passage problem was analyzed by the geometry in the space of standard normal random variables based on the theoretical analysis. The analytical method for determining the design points was established. The first-passage failure probability was analyzed by the first order reliability method. The relationship between design point excitation and mirror image excitation of the system was analyzed. The method used to determine the design points of nonlinear SDOF package with mirror image excitation was analyzed by the method of optimization. The design point excitations of linear and nonlinear SDOF packages were identical to the mirror image excitation when the system's initial displacement was the threshold. In the steady-state response phase of the system, the design points of the system can be accurately analyzed by mirror image excitation, based on which the displacement first-passage failure probability of the package is analyzed.