冷备系统剩余寿命近似计算方法

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

Abstract

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

CLC Number:

TP20

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.

Figures/Tables 10

Table 1

Fig.1

Table 2

Table 3

Table 4

Fig.2

Table 5

Fig.3

Fig.4

Fig.5

References 32

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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]

Approximate calculation method for residual life of cold standby system

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