冷备系统剩余寿命近似计算方法

doi:10.12305/j.issn.1001-506X.2023.03.33

摘要/Abstract

摘要：

冷备系统是提高系统可靠性的重要手段。然而, 由于结构复杂, 对于n中取k冷备系统剩余寿命的研究相对较少。为此, 提出了一种冷备系统剩余寿命近似计算方法。首先, 通过解析法、数值方法以及仿真方法获得冷备系统任意时刻的可靠度。在此基础上, 进一步利用组合辛普森公式, 得到冷备系统剩余寿命的点估计与区间估计近似值。算例分析部分首先研究了这种计算方式的偏差及影响近似计算精度的因素, 在此基础上通过实验验证了所提近似计算方法简单高效, 具有较高的准确性。通过与已有方法进行对比, 进一步说明了所提方法的适用性。

关键词: 冷备系统, 剩余寿命, 组合辛普森公式

Abstract:

Cold standby redundancy is an important approach to increase the reliability of a system. However, research on the residual life of k-out-of-n cold standby system is insufficient because of its structure's complexity. Thus, an approximate calculation method is proposed to fill this gap. Firstly, the analytical method, the numerical method and the simulation method are used and the reliability of this system at any certain time can be obtained. Then, based on the compound Simpson formula, the point estimation as well as the confidence interval of residual life of cold standby system can be calculated. The bias of this numerical method is discussed and factors affecting the calculation approximate precision of the proposed method are analyzed. The proposed method then proves to be quite simple, efficient and accurate. By comparing with the existing methods, the suitability of the proposed method is validated.

Key words: cold standby system, residual life estimation, compound Simpson formula

中图分类号:

TP20

赵骞, 谭尧, 吴波, 蒋平, 郭波. 冷备系统剩余寿命近似计算方法[J]. 系统工程与电子技术, 2023, 45(3): 913-920.

Qian ZHAO, Yao TAN, Bo WU, Ping JIANG, Bo GUO. Approximate calculation method for residual life of cold standby system[J]. Systems Engineering and Electronics, 2023, 45(3): 913-920.

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积分区间/h	寿命估计/h	相对误差/%
[0, 200]	160.926 6	-19.54
[0, 300]	160.926 6	-5.83
[0, 400]	197.025 6	-1.49
[0, 500]	199.317 5	-0.34
[0, 600]	199.855 0	-0.07
[0, 100 0]	199.999 8	0.000 2

w	寿命估计/h	相对误差/%
5	201.103 1	0.550
10	200.078 9	0.039
20	200.001 6	8×10^-4
30	200.000 0	7×10^-6

(n, k)	λ₀/h^-1	τ/h	理论值/h	近似值/h	相对误差/%
(5, 2)	0.01	20	180.14	180.39	0.14
		40	161.54	161.80	0.16
		60	145.39	145.64	0.69
	0.02	20	80.77	81.28	0.63
		40	65.98	66.52	0.82
		60	56.10	56.68	1.03
(5, 3)	0.01	20	82.02	82.15	0.16
		40	69.86	70.00	0.20
		60	61.99	62.14	0.24
	0.02	20	34.93	35.00	0.20
		40	28.34	28.43	0.32
		60	25.09	25.18	0.36
(5, 4)	0.01	20	38.89	38.90	0.03
		40	34.62	34.64	0.06
		60	32.35	32.38	0.09
	0.02	20	17.31	17.32	0.06
		40	15.48	15.49	0.06
		60	14.66	14.67	0.07

(n, k)	(η, β)	τ/h	仿真值/h	近似值/h	相对误差/%
(5, 2)	(100, 2)	20	172.85	173.44	0.34
		40	152.54	153.44	0.59
		60	133.72	133.53	-0.14
	(50, 2)	20	76.96	76.72	-0.31
		40	56.92	57.04	0.21
		60	39.60	39.93	0.83
	(100, 3)	20	176.71	177.33	0.35
		40	157.17	157.33	0.10
		60	137.42	137.34	0.06
(5, 3)	(100, 2)	20	90.24	90.10	0.16
		40	70.48	70.58	0.14
		60	53.35	53.36	0.02
	(50, 2)	20	35.33	35.29	0.11
		40	20.00	20.08	0.40
		60	12.14	12.34	1.65
	(100, 3)	20	92.00	91.90	-0.11
		40	72.30	71.92	-0.53
		60	52.10	52.46	0.69
(5, 4)	(100, 2)	20	49.56	50.13	1.15
		40	34.53	34.70	0.49
		60	24.85	24.77	-0.32
	(50, 2)	20	17.25	17.35	-0.58
		40	9.28	9.34	-5.17
		60	5.70	6.11	7.19
	(100, 3)	20	58.25	58.39	0.24
		40	39.52	39.36	0.40
		60	24.22	24.46	0.99

方法	点估计/h	区间估计/h
数值方法	172.85	[94.50, 263.50]
仿真方法	173.44	[95.13, 262.26]