失效信息已知时r/n(G)表决系统的剩余寿命预测

doi:10.12305/j.issn.1001-506X.2022.05.37

摘要/Abstract

摘要：

剩余寿命预测在可靠性工程中十分重要。而r/n(G)表决系统由于结构复杂, 对于其剩余寿命研究相对较少。本文假定部件寿命服从指数-威布尔分布, 在部件失效信息已知的情况下, 推导得到了表决系统剩余寿命期望的解析式, 也分别给出了失效信息未知和部件寿命服从威布尔分布这两种特殊情况下的解析式。仿真实验证明了所提方法的准确性和有效性, 也表明忽略部件失效信息对系统的剩余寿命进行预测, 所得结果偏差很大。

关键词: 剩余寿命, 失效信息, 指数-威布尔分布, r/n(G)表决系统

Abstract:

In reliability engineering, it is of great significance to predict the residual life of systems. However, research on residual life of r-out-of-n: G system is insufficient due to its complex structure. Assuming that the lifetime of components follows exponential-Weibull distribution, the closed-form of residual life for r-out-of-n: G system is derived when the component failure information is known. Specifically, the closed-forms are also presented when failure information is unknown and component lifetime follows Weibull distribution. The simulation results demonstrate the effectiveness and accuracy of the proposed method and further indicate that prediction results of residual life for systems deviate greatly by neglecting the failure information of the components.

Key words: residual life, failure information, exponential-Weibull distribution, r-out-of-n: G system

中图分类号:

TP114.3

刘鸿彬, 赵骞, 贾祥, 郭波. 失效信息已知时r/n(G)表决系统的剩余寿命预测[J]. 系统工程与电子技术, 2022, 44(5): 1738-1746.

Hongbin LIU, Qian ZHAO, Xiang JIA, Bo GUO. Residual life prediction of r-out-of-n: G systems with known failure information[J]. Systems Engineering and Electronics, 2022, 44(5): 1738-1746.

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表决系统	工作时间τ	数值计算	仿真结果	误差率
无失效信息3/4(G) (α=2, β=3.4 η=50)	τ₁=25	24.532 5	24.849 0	0.012 9
	τ₂=30	19.608 0	19.512 5	0.004 9
	τ₃=35	14.947 3	15.286 4	0.022 7
	τ₄=40	10.911 2	10.932 6	0.002 0
失效1个部件的3/4(G) (α=2, β=3.4, η=50)	τ₁=25	18.483 9	18.766 1	0.015 3
	τ₂=30	14.360 8	14.588 0	0.015 8
	τ₃=35	10.921 0	11.019 3	0.009 0
	τ₄=40	8.232 8	8.294 8	0.007 5
无失效信息3/5(G) (α=3.5, β=1.8, η=150)	τ₁=80	124.495 4	124.506 9	0.000 1
	τ₂=85	119.497 9	119.815 4	0.002 7
	τ₃=90	114.503 5	114.211 4	0.002 6
	τ₄=95	109.515 1	110.073 0	0.005 1
失效2个部件的3/5(G) (α=3.5, β=1.8, η=150)	τ₁=80	76.006 7	76.498 8	0.006 5
	τ₂=85	71.940 5	71.565 5	0.005 2
	τ₃=90	68.056 5	67.373 7	0.010 1
	τ₄=95	64.363 7	64.986 8	0.009 7

表决系统	工作时间τ	80%置信区间数值计算	80%置信区间仿真结果
无失效信息3/4(G) (α=2, β=3.4, η=50)	τ₁=25	[15.161 9, 33.840 2]	[15.080 5, 33.668 0]
	τ₂=30	[10.292 8, 28.855 1]	[10.246 5, 29.369 2]
	τ₃=35	[5.992 9, 23.937 2]	[6.044 6, 23.743 7]
	τ₄=40	[3.041 8, 19.249 7]	[3.049 2, 19.405 4]
失效1个部件的3/4(G) (α=2, β=3.4, η=50)	τ₁=25	[7.474 5, 29.332 7]	[7.605 8, 29.408 8]
	τ₂=30	[4.389 2, 24.590 3]	[4.096 4, 24.1438]
	τ₃=35	[2.512 4, 20.168 3]	[2.253 0, 20.259 6]
	τ₄=40	[1.496 1, 16.243 7]	[1.598 3, 16.536 4]
无失效信息3/5(G) (α=3.5, β=1.8, η=150)	τ₁=80	[78.934 5, 172.565 5]	[78.992 1, 169.881 4]
	τ₂=85	[73.937 2, 167.566 7]	[71.101 5, 169.722 6]
	τ₃=90	[68.944 5, 162.567 9]	[66.894 4, 162.867 8]
	τ₄=95	[63.962 6, 157.570 6]	[63.667 7, 156.289 6]
失效2个部件的3/5(G) (α=3.5, β=1.8, η=150)	τ₁=80	[25.650 8, 129.608 9]	[27.537 8, 126.931 8]
	τ₂=85	[22.563 9, 124.948 9]	[22.984 2, 127.434 6]
	τ₃=90	[19.823 5, 120.375 8]	[19.915 7, 118.450 3
	τ₄=95	[17.421 7, 115.901 9]	[15.599 4, 116.775 8]

卫星代号	动量轮个数	发射年份	截尾年份	截尾时间/月
S1	5	2000年	2004年	51.95
S2	5	2002年	2005年	38.14
S3	5	2005年	2007年	27.29

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