运筹学学报 >
2025 , Vol. 29 >Issue 1: 55 - 62
DOI: https://doi.org/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
收稿日期: 2021-05-26
网络出版日期: 2025-03-08
基金资助
山西省高等学校哲学社会科学研究项目(2019W020)
版权
The inspection and preventive maintenance policy for a δ-shock model which has two types of failures
Received date: 2021-05-26
Online published: 2025-03-08
Copyright
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。
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, 2025 , 29(1) : 55 -62 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.01.005
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
| 1 | Esary J D , Marshall A W , Proschan F . Shock models and wear process[J]. Journal of Applied Probablity, 1973, 1, 627- 649. |
| 2 | Barlow R E , Proschan F . Statistical Theory of Reliability and Life Testing[M]. New York: Holt, Rinehart and Winston, Inc, 1975. |
| 3 | 李玲, 成国庆, 唐应辉. 带预防性维修的冲击模型最优检测更换策略[J]. 山东大学学报(理学版), 2011, 46 (9): 122- 126. |
| 4 | 李玲, 成国庆. 考虑不完全检测的冲击模型最优维修策略[J]. 运筹学学报, 2013, 17 (4): 33- 42. |
| 5 | 张斌, 张岚. 基于退化和随机冲击的非周期不完全预防维修模型[J]. 统计与决策, 2016, 14, 77- 80. |
| 6 | 张权, 李艳君, 王希彬. 连续有效冲击模型的可靠性[J]. 数学的实践与认识, 2018, 48 (19): 194- 198. |
| 7 | Zhao X , Sun L P , Wang M Y , et al. A shock model for multi-component system considering the cumulative effect of severely damaged components[J]. Computers & Industrial Engineering, 2019, 137, 1- 12. |
| 8 | Wang G J , Zhang Y L . δ-shock model and its optimal replacement policy[J]. Journal of Southeast University, 2001, 31, 121- 124. |
| 9 | Lam Y , Zhang Y L . A shock model for the maintenance of a repairable system[J]. Computer and Operations Research, 2004, 31, 1807- 1820. |
| 10 | Lam Y , Zhang Y L . A geometric-process maintenance model for a deteriorating system under a random environment[J]. IEEE Transactions on Reliability, 2003, 52 (1): 83- 90. |
| 11 | 成国庆, 李玲. 串联系统的δ-冲击模型及其维修策略优化[J]. 计算机集成制造系统, 2019, 25, 1- 12. |
| 12 | 岳德权, 高俏俏. 具有两种失效状态的δ-冲击模型的最优维修策略[J]. 系统工程理论与实践, 2015, 35 (8): 2113- 2119. |
| 13 | Wang G J , Zhang Y L . Geometric process model for a system with inspections and preventive repair[J]. Computers & Industrial Engineering, 2014, 75, 13- 19. |
| 14 | Yang L , Ma X B , Peng R , et al. A preventive maintenance policy based on dependent twostage deterioration and external shocks[J]. Reliability Engineering & System Safety, 2017, 160, 201- 211. |
| 15 | Zheng Z B , Zhou W H , Zheng Y F , et al. Optimal maintenance policy for a system with preventive repair and two types of failures[J]. Computers & Industrial Engineering, 2016, 98, 102- 112. |
| 16 | Li Y , Sheng Z , Lee C G , et al. A two-phase preventive maintenance policy considering imperfect repair and postponed replacement[J]. European Journal of Operational Research, 2019, 274 (3): 966- 977. |
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