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

Abstract

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

CLC Number:

TB114.3

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.

Figures/Tables 11

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References 31

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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

Solution of reliability of cold standby voting system with arbitrary distribution

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部件	分布	参数1	参数2
工作件1	指数	1/λ=1 000	—
工作件2	指数	1/λ=1 200	—
工作件3	指数	1/λ=1 500	—
工作件4	指数	1/λ=1 500	—
工作件5	正态	μ=1 000	σ=100
工作件6	正态	μ=1 500	σ=200
工作件7	威布尔	θ=1 500	γ=3
工作件8	威布尔	θ=2 000	γ=3
工作件9	瑞利	θ=1 414	—
冷备件	指数	1/λ=1 000	—

t/h	Ⅰ类			Ⅱ类
t/h	解算	仿真	误差/%	解算	仿真	误差/%
500	0.778 3	0.777 9	0.05	0.817 7	0.817 5	0.02
700	0.572 4	0.571 5	0.16	0.630 4	0.628 8	0.25
800	0.458 3	0.46	0.37	0.519 9	0.520 9	0.19
1 000	0.169 5	0.168 9	0.36	0.213 1	0.213 3	0.09