任意分布的冷备表决系统可靠度求解

k/n: M(G)冷备表决系统包含n个工作部件, M个冷储备件, 至少有k个部件工作时系统工作。然而, 现有对于k/n: M(G)冷备表决系统的研究集中在同型指数分布的情况, 缺乏针对其工作部件非同型且服从任意分布的情况的研究。本文研究了k/n: M(G)冷备表决系统的可靠度, 系统部件服从任意分布, 冷备件服从同一分布。对k=n的情况, 给出了M取任意值时部件同型和非同型情况下的系统可靠度解析式。对于k＜n的情况, 考虑了两种不同的冷备件替换策略, 给出了部件同型情况和非同型M取特定值情况下的系统可靠度解析式。蒙特卡罗仿真实验证明了所提方法的准确性。

Solution of reliability of cold standby voting system with arbitrary distribution

The k/n: M(G) cold standby voting system contains n work units, M cold reserve units, and at least k units work when the system is working. However, the existing research on the k/n: M(G) cold standby voting system focuses on the case of the same type of subsystems with an exponential distribution, without the consideration of a case where subsystems vary in types and obey an arbitrary distribution. In this paper, the reliability of the k/n: M(G) cold standby voting system is studied. The system units obey arbitrary distribution, and the cold standby units obey the same distribution. For the case of k=n, when M takes an arbitrary value, the system reliability formulas for the homotypic and non-homotypic units are given. For the case of k < n, two different cold standby unit replacement strategies are considered, and the system reliability formulas are given for the case of the homotypic unit and the case of non-homotypic units M taking a specific value. Monte Carlo simulation experiment proves the accuracy of the proposed method.