G-混合冗余策略下多状态可修系统的可靠性

doi:10.12305/j.issn.1001-506X.2024.07.20

系统工程与电子技术 ›› 2024, Vol. 46 ›› Issue (7): 2383-2392.doi: 10.12305/j.issn.1001-506X.2024.07.20

• 系统工程 • 上一篇

G-混合冗余策略下多状态可修系统的可靠性

温艳清¹, 刘宝亮¹^,*, 师海燕¹, 邱青安², 高采文¹

1. 山西大同大学数学与统计学院, 山西大同 037009
2. 北京理工大学管理与经济学院, 北京 100081

收稿日期:2023-03-16 出版日期:2024-06-28 发布日期:2024-07-02
通讯作者: 刘宝亮
作者简介:温艳清(1980—), 女, 副教授, 硕士研究生导师, 博士, 主要研究方向为系统可靠性理论及其应用、随机建模
刘宝亮(1982—), 男, 教授, 硕士研究生导师, 博士, 主要研究方向为系统可靠性理论及其应用、复杂系统建模及其优化
师海燕(1982—), 女, 副教授, 硕士, 主要研究方向为系统可靠性理论及其应用、排队论
邱青安(1991—), 男, 副教授, 博士研究生导师, 博士, 主要研究方向为系统可靠性理论及其应用、复杂系统建模及其优化
高采文(1978—), 女, 教授, 硕士, 主要研究方向为不确定理论及其应用、可靠性理论及其应用
基金资助:
国家自然科学基金(72371030);国家自然科学基金(71601101);国家自然科学基金(72001026);山西省基础研究计划(20210302124310);山西省高等学校科技创新计划(2022L415);山西省研究生教育创新计划(2023XJG004);山西师范大学人文社科基金(RWSK2307)

Reliability of multi-state repairable systems under G-mixed redundancy strategy

Yanqing WEN¹, Baoliang LIU¹^,*, Haiyan SHI¹, Qing'an QIU², Caiwen GAO¹

1. College of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China
2. School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China

Received:2023-03-16 Online:2024-06-28 Published:2024-07-02
Contact: Baoliang LIU

摘要/Abstract

摘要：

本文对G-混合冗余策略下可修系统的可靠性进行了研究, 该系统由4个部件和1个修理工组成, 修理工采用多重休假策略, 以使人力资源得到充分利用。模型中各类随机变量用PH(phase-type)分布来描述, 由此建立了通用性较好的系统可靠性模型, 并运用矩阵分析的方法推导出系统在瞬态和稳态情形下的一些可靠性指标。最后, 通过数值算例验证了模型的适用性, 并对G-混合冗余策略下系统的可靠性与K-混合冗余策略下系统的可靠性进行了比较。结果表明, 所提出的可靠性模型在G-混合冗余策略下的可靠性明显高于在K-混合冗余策略下的可靠性。

关键词: PH分布, 多重休假, G-混合冗余策略, 可修系统

Abstract:

In this paper, the reliability for a repairable system under G-mixed redundancy strategy is investigated. The system consists of four components and a repairman, in which the multiple vacation policy of the repairman is adopted so that the human resources can be fully utilized. The phase-type (PH) distribution is used to describe various random variables in the model. A system reliability model with better commonality is developed, and some reliability indexes of the system are obtained in both transient and stationary regimes by employing matrix-analytic method. Finally, the applicability of the model is verified by numerical examples, and the system reliability under G-mixed redundancy strategy is compared with that under K-mixed redundancy strategy. The results show that the proposed reliability model under G-mixed redundancy strategy is significantly higher than that under the K-mixed redundancy strategy.

Key words: phase-type (PH) distribution, multiple vacation, G-mixed redundancy strategy, repairable system

中图分类号:

F254.3
O213

温艳清, 刘宝亮, 师海燕, 邱青安, 高采文. G-混合冗余策略下多状态可修系统的可靠性[J]. 系统工程与电子技术, 2024, 46(7): 2383-2392.

Yanqing WEN, Baoliang LIU, Haiyan SHI, Qing'an QIU, Caiwen GAO. Reliability of multi-state repairable systems under G-mixed redundancy strategy[J]. Systems Engineering and Electronics, 2024, 46(7): 2383-2392.

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随机变量	分布参数
工作部件寿命	$\mathrm{PH}\left[\boldsymbol{\alpha}=(1, 0), \boldsymbol{W}=\left(\begin{array}{cc}-0.40 & 0.30 \\0.25 & -0.30\end{array}\right)\right]$ 平均寿命: 13.333 3
故障部件维修时间	$\mathrm{PH}\left[\boldsymbol{\gamma}=(1, 0), \boldsymbol{T}=\left(\begin{array}{cc}-1.30 & 0.90 \\0.90 & -1.30\end{array}\right)\right]$ 平均维修时间: 2.500 0
维修工休假时间	$\mathrm{PH}\left[\boldsymbol{\beta}=(1, 0), \boldsymbol{S}=\left(\begin{array}{cc}-1.65 & 0.95 \\0.95 & -1.65\end{array}\right)\right]$ 平均休假时间: 1.428 6

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G-混合冗余策略下多状态可修系统的可靠性

Reliability of multi-state repairable systems under G-mixed redundancy strategy

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冗余策略	n_A	n_s	n_G
主动	4	0	-
贮备	1	3	-
混合	3	1	-
K-混合	3	1	-
G-混合	3	1	2