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1. 南京理工大学 理学院, 南京 210094;
2. 北京航空航天大学 可靠性与系统工程学院, 北京 100083

Fluctuation analysis of instantaneous availability under minor repair
REN Sichao1, YANG Yi2, CHEN Yang2, KANG Rui2
1. School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China;
2. School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-03-11; Accepted: 2016-04-15; Published online: 2016-04-26
Foundation item: National Natural Science Foundation of China (61104132, 61573041, 61573043)
Corresponding author. YANG Yi, E-mail:yang_cissy@163.com
Abstract: The renewal model of one-unit repairable system with three states (up, minor repair, repair) is put forward on the basis of the renewal model with three states (up, delay-repair, repair). The steady availability is improved in the new model. The renewal equation in the model is transformed into the ordinary differential equation to obtain the analytical expression of instantaneous availability. A novel set of fluctuation theory including the basic definition and decision lemma of fluctuation function is used to analyze the fluctuation of instantaneous availability, which gives conditions for fluctuation existence of instantaneous availability. Combined with the practical background, conditions are used to show the influence of different rates on fluctuation when fault rate is fixed, which provides the method of fluctuation suppression. The method is that mean to repair time is controlled to be less than a quarter of mean to failure time. Simulation results are in agreement with theoretical results.
Key words: instantaneous availability     renewal model     fluctuation theory     minor repair     fluctuation suppression

1 预备知识

1.1 模型引入

 (1)
 (2)

 图 1 单部件三状态的更新模型 Fig. 1 A renewal process for one unit with three states
1.2 模型变化

1) 部件发生永久性故障之前，有且仅有一次暂时性故障。

2) 故障小修所用时间不计。

3) 故障小修后部件恢复，但故障率不发生改变。

4) 永久性故障修理后，部件如新。

 (3)
 (4)

 (5)

ΔX的分布函数为

 图 2 带有故障小修的单部件三状态更新过程 Fig. 2 A renewal process for one unit with three states under minor repair
1.3 模型性质

 (6)

 (7)

 (8)

 (9)

 (10)
 (11)
 (12)
 (13)

2 波动分析

1) 若Δ≥0，则A(t) 没有波动性。

2) 若Δ < 0，则A(t) 有波动性。

1) Δ=0

 (14)

2) Δ>0

 (15)

3) Δ < 0

 (16)

 图 3 3种情形下瞬时可用度曲线 Fig. 3 Curves of instantaneous availability in three cases
3 波动抑制

 图 4 修复率对瞬时可用度波动的影响 Fig. 4 Influence of repair rate on fluctuation of instantaneous availability

4 结论

1) 用故障小修替代修理延迟得到的新模型仍然为更新模型。新模型适用更新模型的基本性质以及波动理论。

2) 故障小修模型具有简化瞬时可用度波动的存在条件，以及提升稳态可用度的优势。

3) 对于故障小修模型的波动抑制，可以采用调整修复率λ3或平均修理时间1/λ3的方法。

 [1] 康锐, 王自立. 可靠性系统工程的理论与技术框架[J]. 航空学报, 2005, 26 (5): 633–636. KANG R, WANG Z L. Framework of theory and technique on reliability system engineering[J]. Acta Aeronautica et Astronautica Sinica, 2005, 26 (5): 633–636. (in Chinese) [2] BESNARD F, FISCHER K, BERTLING L.Reliability-centred asset maintenance-A step towards enhanced reliability, availability, and profitability of wind power plants[C]//Proceedings of Innovative Smart Grid Technologies Conference Europe.Piscataway, NJ:IEEE Press, 2010:1-8. [3] JACKSON D S, KUNZINGER F F. Calculation of system availability using traffic statistics[J]. Bell Labs Technical Journal, 2003, 7 (3): 139–150. DOI:10.1002/bltj.10024 [4] DVORSKA J, PODIVIN L, LIPP A, et al.GBAS GAST D availability analysis for business aircraft[C]//Proceedings of IEEE Aerospace Conference.Piscataway, NJ:IEEE Press, 2013:1-15. [5] TU M H, XIAO L L, XU D X.Maximizing the availability of replicated services in widely distributed systems considering network availability[C]//Proceedings of 7th International Conference on Software Security and Reliability.Piscataway, NJ:IEEE Press, 2013:178-187. [6] AMIRI M, PRENOSIL V.General solution for MTTF and steady-state availability of NMR system[C]//Proceedings of 9th International Symposium on Reconfigurable and Communication-Centric Systems-on-Chip.Piscataway, NJ:IEEE Press, 2014:1-4. [7] SMITH D T.Calculating the system steady-state availability as a function of subsystem steady-state availability[C]//Proceedings of IEEE Southeastcon.Piscataway, NJ:IEEE Press, 2014:1-3. [8] PHAM H. Commentary:Steady-state series-system availability[J]. IEEE Transactions on Reliability, 2003, 52 (2): 146–147. DOI:10.1109/TR.2003.811164 [9] HUANG K, MI J. Properties and computation of interval availability of system[J]. Statistics and Probability Letters, 2013, 83 (5): 1388–1396. DOI:10.1016/j.spl.2013.01.018 [10] MACIEJEWSKI H, CABAN D. Estimation of repairable system availability within fixed time horizon[J]. Reliability Engineering and System Safety, 2008, 93 (1): 100–106. DOI:10.1016/j.ress.2006.10.016 [11] 杨懿. 一般概率分布下系统瞬时可用度离散时间建模分析与应用[D]. 南京: 南京理工大学, 2008: 20-47. YANG Y.The instantaneous availability of the systems under discrete time modeling analysis and application in general probability distribution[D].Nanjing:Nanjing University of Science and Technology, 2008:20-47(in Chinese). [12] 杨懿, 任思超, 于永利. 均匀分布下系统瞬时可用度理论分析[J]. 北京航空航天大学学报, 2016, 42 (1): 28–34. YANG Y, REN S C, YU Y L. Theory analysis of system instantaneous availability under uniform distribution[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42 (1): 28–34. (in Chinese) [13] 温艳清, 崔利荣, 刘宝亮. 修理工带休假的n部件冷贮备可修系统[J]. 北京航空航天大学学报, 2016, 42 (3): 569–575. WEN Y Q, CUI L R, LIU B L. Cold standby n-component repairable system with repairman vacation[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42 (3): 569–575. (in Chinese) [14] XUE A C, JING Q, LUO L, et al.Instantaneous availability for the protection devices based on non-homogeneous Markov model and a case study[C]//Proceedings of 33rd Chinese Control Conference.Piscataway, NJ:IEEE Press, 2014:6524-6527. [15] 林元烈. 应用随机过程[M]. 北京: 清华大学出版社, 2002: 58-71. LIN Y L. Applied stochastic processes[M]. Beijing: Tsinghua University Press, 2002: 58-71. (in Chinese) [16] NEIL M, MARQUEZ D. Availability modelling of repairable systems using Bayesian networks[J]. Engineering Applications of Artificial Intelligence, 2012, 25 (4): 698–704. DOI:10.1016/j.engappai.2010.06.003 [17] 张庆. 带有故障小修的单部件可修系统的预防维修策略[D]. 成都: 西南交通大学, 2012: 19-37. ZHANG Q.Preventive maintenance strategy of one-unit repairable system with minor repair[D].Chengdu:Southwest Jiaotong University, 2012:19-37(in Chinese). [18] YIN M L, ANGUS J E, TRIVEDI K S. Optimal preventive maintenance rate for best availability with hypo-exponential failure distribution[J]. IEEE Transactions on Reliability, 2013, 62 (2): 351–361. DOI:10.1109/TR.2013.2256672 [19] DERSIN P, PERONNE A, ARROUM C.Selecting test and maintenance strategies to achieve availability target with lowest life-cycle cost[C]//Proceedings of Reliability and Maintainability Symposium.Piscataway, NJ:IEEE Press, 2008:301-306. [20] 程志军, 郭波. 机会维修策略下的系统可用度分析[J]. 数学的实践与认识, 2006, 36 (10): 137–140. CHENG Z J, GUO B. Analysis of system availability under opportunity maintenance steategy[J]. Journal of Mathematics in Practice and Theory, 2006, 36 (10): 137–140. (in Chinese) [21] 徐文静. 不完全维修条件下的可用度与维修策略分析[D]. 长沙: 国防科学技术大学, 2008: 26-63. XU W J.Analysis of maintenance strategy and availability under imperfect repair[D].Changsha:National University of Defense Technology, 2008:26-63(in Chinese). [22] 曹晋华, 程侃. 可靠性数学引论[M]. 2版 北京: 高等教育出版社, 2012: 182-261. CAO J H, CHENG K. A mathematical introduction to reliability[M]. 2nd ed Beijing: Higher Education Press, 2012: 182-261. (in Chinese) [23] REN S C, YANG Y, XU H L.Fluctuation analysis of instantaneous availability under delay-repair[C]//Proceedings of the 35th Chinese Control Conference.Piscataway, NJ:IEEE Press, 2016:6746-6750.

#### 文章信息

REN Sichao, YANG Yi, CHEN Yang, KANG Rui

Fluctuation analysis of instantaneous availability under minor repair

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(3): 602-607
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0195