任意分布的冷备表决系统可靠度求解

doi:10.12305/j.issn.1001-506X.2022.07.33

摘要/Abstract

摘要：

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。

关键词: 可靠性, 表决系统, 冷储备, 非同型单元, 任意分布

Abstract:

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.

Key words: reliability, voting system, cold standby, non-homotypic units, arbitrary distribution

中图分类号:

TB114.3

胡听春, 孙宇锋, 李肖肖, 赵广燕. 任意分布的冷备表决系统可靠度求解[J]. 系统工程与电子技术, 2022, 44(7): 2357-2363.

Tingchun HU, Yufeng SUN, Xiaoxiao LI, Guangyan ZHAO. Solution of reliability of cold standby voting system with arbitrary distribution[J]. Systems Engineering and Electronics, 2022, 44(7): 2357-2363.

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t/h	仿真	同型公式		非同型公式
t/h	仿真	解算	误差/%	解算	误差/%
20	0.978 2	0.976 9	0.13	0.975 8	0.24
40	0.878 6	0.879 5	0.10	0.876 9	0.19
60	0.730 4	0.730 6	0.03	0.727 1	0.45

部件	分布	参数1	参数2
工作件1	正态	μ=100	σ=10
工作件2	指数	1/λ=150	—
工作件3	指数	1/λ=100	—
冷备件	威布尔	θ=20	γ=3

t/h	仿真	解算	误差/%
20	0.990 2	0.989 2	0.10
40	0.865 2	0.859 2	0.69
60	0.636 0	0.631 0	0.78

t/h	Ⅰ类			Ⅱ类
t/h	解算	仿真	误差/%	解算	仿真	误差/%
50	0.991 8	0.993 6	0.18	0.998 3	0.998 7	0.04
100	0.836 1	0.839 2	0.37	0.946 6	0.944 6	0.21
150	0.502 0	0.503 0	0.20	0.763 9	0.762 0	0.25
200	0.223 0	0.225 2	0.98	0.506 3	0.506 5	0.04

t/h	Ⅰ类			Ⅱ类
t/h	解算	仿真	误差/%	解算	仿真	误差/%
50	0.987 8	0.987 8	0	0.995 2	0.994 6	0.06
100	0.904 9	0.904 5	0.04	0.955 6	0.955 5	0.01
150	0.753 4	0.753 9	0.07	0.867 3	0.867 6	0.03
200	0.582 1	0.582 0	0.02	0.745 4	0.744 9	0.07