有两种故障状态的δ-冲击模型的检测及预防维修策略研究

doi:10.15960/j.cnki.issn.1007-6093.2025.01.005

运筹学学报（中英文） ›› 2025, Vol. 29 ›› Issue (1): 55-62.doi: 10.15960/j.cnki.issn.1007-6093.2025.01.005

有两种故障状态的δ-冲击模型的检测及预防维修策略研究

高俏俏¹^,*(), 岳德权²

1. 山西大学经济与管理学院, 山西太原 030006
2. 燕山大学理学院, 河北秦皇岛 066004

收稿日期:2021-05-26 出版日期:2025-03-15 发布日期:2025-03-08
通讯作者: 高俏俏 E-mail:gaoqiaoqiao@sxu.edu.cn
基金资助:
山西省高等学校哲学社会科学研究项目(2019W020)

The inspection and preventive maintenance policy for a δ-shock model which has two types of failures

Qiaoqiao GAO¹^,*(), Dequan YUE²

1. School of Economics and Management, Shanxi University, Taiyuan 030006, Shanxi, China
2. School of Science, Yanshan University, Qinhuangdao 066004, Hebei, China

Received:2021-05-26 Online:2025-03-15 Published:2025-03-08
Contact: Qiaoqiao GAO E-mail:gaoqiaoqiao@sxu.edu.cn

摘要/Abstract

摘要：

本文研究了一类有两种故障状态的δ-冲击模型的预防维修策略, 系统是几何过程退化的, 并且在运行过程中系统故障可能有两种原因: 一种是由于自身寿命终止, 另一种是由于连续两次冲击的间隔小于某一固定值。系统的故障只有检测才可以发现, 当系统的工作时间达到某一值T时进行检测, 如未发生故障则进行预防维修, 预防维修使系统恢复到上一次故障维修后的状态, 如发生故障则进行故障维修, 且当系统的故障次数达到N时对其进行更换。以系统检测及预防维修的间隔和更换前的故障次数组成的二维策略(T, N)为策略, 利用更新过程和几何过程理论求出了系统长期运行单位时间内期望费用的表达式, 并进行了数值分析。

关键词: 冲击, 检测, 预防维修, 几何过程, 期望费用

Abstract:

In this paper, the preventive maintenance policy for a δ-shock model is studied. The system is a geometric process degradation system. The failure of the system on the one hand is because of the lifetime of the system, on the other hand is because of the interval of two consecutive shocks less than a fixed value. The fault of the system can only be found by inspection. When the working time of the system reaches a certain value, the inspect will be carried out, and preventive maintenance will be carried out if there is no fault. Preventive maintenance will restore the system to the state after the last fault maintenance, and if the system fault, a fault repair will be carried out. Based on the two-dimensional policy composed of the interval of system detection and the failure times before replacement, the expression of the expected cost per unit time of system is obtained by using the renewal process and geometric process theory. Finally, numerical examples are given.

Key words: shock, inspection, preventive maintenance, geometric process, expected cost

中图分类号:

高俏俏, 岳德权. 有两种故障状态的δ-冲击模型的检测及预防维修策略研究[J]. 运筹学学报（中英文）, 2025, 29(1): 55-62.

Qiaoqiao GAO, Dequan YUE. The inspection and preventive maintenance policy for a δ-shock model which has two types of failures[J]. Operations Research Transactions, 2025, 29(1): 55-62.

图/表 4

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参考文献 16

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	3	4	5	6	7	8	9
6	$ - $50.994 2	$ - $51.668 7	$ - $51.975 0	$ - $52.088 0	$ - $52.086 1	$ - $52.009 4	$ - $51.880 6
7	$ - $52.687 5	$ - $53.419 4	$ - $53.670 2	$ - $53.749 1	$ - $53.722 8	$ - $53.626 6	$ - $53.480 6
8	$ - $53.679 5	$ - $54.450 9	$ - $54.804 9	$ - $54.941 4	$ - $54.889 4	$ - $54.772 0	$ - $54.607 2
9	$ - $54.422 2	$ - $55.208 3	$ - $55.569 4	$ - $55.707 6	$ - $55.712 9	$ - $55.631 3	$ - $55.488 9
10	$ - $54.888 9	$ - $55.726 0	$ - $56.110 9	$ - $56.244 2	$ - $56.242 6	$ - $56.152 4	$ - $55.999 8
11	$ - $55.183 6	$ - $56.042 3	$ - $56.435 8	$ - $56.585 8	$ - $56.590 5	$ - $56.488 6	$ - $56.323 3
12	$ - $55.344 6	$ - $56.224 2	$ - $56.621 0	$ - $56.768 7	$ - $56.767 5	$ - $56.668 8	$ - $56.501 5
13	$ - $55.388 1	$ - $56.282 0	$ - $56.686 1	${\bf - 56.833 3}$	$ - $56.824 1	$ - $56.715 1	$ - $56.535 9
14	$ - $55.341 3	$ - $56.246 5	$ - $56.651 2	$ - $56.793 6	$ - $56.779 2	$ - $56.658 8	$ - $56.466 6
15	$ - $55.217 4	$ - $56.130 4	$ - $56.534 7	$ - $56.670 8	$ - $56.647 1	$ - $56.518 2	$ - $56.315 1
16	$ - $55.029 8	$ - $55.947 8	$ - $56.349 1	$ - $56.478 5	$ - $56.444 2	$ - $56.302 9	$ - $56.085 9
17	$ - $54.787 7	$ - $55.708 4	$ - $56.105 1	$ - $56.225 8	$ - $56.181 0	$ - $56.027 1	$ - $55.795 6

$ \theta $	$ (T^{}, N^{}) $	$ C(T^{}, N^{}) $	$ \delta $	$ (T^{}, N^{}) $	$ C(T^{}, N^{}) $
0.01	(17, 5)	$ - $65.921 5	1	(15, 6)	$ - $61.034 8
0.02	(17, 5)	$ - $64.537 8	2	(13, 6)	$ - $56.833 3
0.03	(15, 6)	$ - $62.427 9	3	(12, 6)	$ - $53.231 2
0.04	(14, 6)	$ - $59.813 6	4	(11, 7)	$ - $49.548 9
0.05	(13, 6)	$ - $56.833 3	5	(13, 6)	$ - $46.239 1
0.06	(12, 7)	$ - $53.665 2	6	(15, 5)	$ - $42.343 1
0.07	(11, 7)	$ - $50.415 3	7	(10, 8)	$ - $40.299 0
0.08	(10, 7)	$ - $47.103 8	8	(11, 7)	$ - $38.217 2
0.09	(9, 8)	$ - $43.865 0	9	(11, 5)	$ - $36.010 1
0.10	(9, 8)	$ - $40.688 8	10	(13, 6)	$ - $33.995 0

[1]	刘亚锋. 无线通信系统设计中的两个优化问题和相关优化方法[J]. 运筹学学报, 2019, 23(3): 47-62.
[2]	高俏俏, 岳德权, 赵冰. 有延迟修理的两部件串联系统的预防维修策略[J]. 运筹学学报, 2018, 22(4): 69-78.
[3]	程晓绚, 岳德权, 赵冰. 工作时间受限的单部件可修系统的维修策略[J]. 运筹学学报, 2017, 21(1): 78-86.
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有两种故障状态的δ-冲击模型的检测及预防维修策略研究

The inspection and preventive maintenance policy for a δ-shock model which has two types of failures

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