基于向量通用生成函数的多性能参数多态系统可靠性分析

Reliability Analysis of Multi-state System with Multiple Performance Parameters Based on Vector-universal Generating Function

通用生成函数在多态系统可靠性分析中发挥着重要作用,但变量通用生成函数不能分析多性能参数多态系统。针对具有多种性能参数的多态系统可靠性分析的需要,提出了向量通用生成函数的定义和对应的运算符。根据多态串-并联系统的结构特点,提出了利用向量通用生成函数估算系统可靠度的步骤。最后利用算例进行了验证,并且与传统可靠性分析方法和Monte Carlo仿真方法所得到的结果进行了对比分析。算例的结果显示,向量通用生成函数能够准确快速地估算多性能参数多态系统可靠度,在多态系统可靠性分析和优化中具有应用前景。

The universal generating function plays an important role in reliability analysi s of multi-state system, but the universal generating function of a single vari able can’t analyze the reliability of multi-state system with multiple perform ance parameters. The vector-universal generating function is defined and the op erators are given to analyze the reliability of multi-state system with multipl e performance parameters. According to the structure characteristic of multi-st ate series-parallel system, the procedure of reliability analysis based on the vector-universal generating function is proposed. A numerical example illustrates the proposed method, and the results are compared with that obtained by traditional reliability method and Monte Carlo simulation. The resu lts show that the vector-universal generating function can estimate the reliabi lity of multi-state system with multiple performance parameters precisely and q uickly, and that the vector-universal generating function can be used for relia bility analysis and optimization of multi-state system in the future.