Availability Analysis for Equipment with Normal Life Distribution

doi:10.12382/bgxb.2022.0606

Abstract

Abstract:

Analytical calculation method for the analysis of equipment availability has the advantage of direct deduction process and accurate prediction of results, but it has been rarely reported due to the complexity of modeling process. Current availability analysis is mostly based on stochastic process or simulation methods. Considering preventive maintenance and condition-based maintenance, an analytical calculation method is proposed to calculate the operational availability and instantaneous availability of equipment, of which life is assumed to follow normal distribution. A simulation method is also constructed to determine the operational availability and instantaneous availability by simulating the working and maintenance process of the equipment. The analytical and simulation methods agree well with each other by comparing the availabilities of equipment with several set of different life distribution parameters. The proposed analytical method could provide support for the evaluation and optimization of preventive maintenance and condition-based maintenance schemes for equipment with normal life distribution.

Key words: equipment, operational availability, instantaneous availability, preventive maintenance, condition-based maintenance

CLC Number:

TJ07

CHEN Xu, ZHANG Shufeng, LI Yue, CHEN Xun, WANG Yashun. Availability Analysis for Equipment with Normal Life Distribution[J]. Acta Armamentarii, 2024, 45(3): 986-996.

Figures/Tables 15

Fig.1 Lifetime prediction model

Fig.2 Simulation process of preventative maintenance strategy

Fig.3 Analytical results of probability of maintenance before failure

Fig.4 Analytical results of operational availability

Fig.5 Operational availabilities of equipment after preventive maintenance and condition-based maintenance

Fig.6 Analytical results of instantaneous availability

Table 1 Simulated results of repeated experiment

组别及均值	i	j	R'_p	TBR	A'_p
1	1166	984	0.8439	91519	0.9152
2	1168	976	0.8356	91399	0.9140
3	1167	973	0.8338	91332	0.9133
4	1164	990	0.8505	91512	0.9151
5	1164	979	0.8411	91359	0.9136
6	1164	982	0.8436	91418	0.9142
7	1167	990	0.8483	91411	0.9141
8	1167	968	0.8295	91213	0.9121
9	1168	990	0.8476	91396	0.914
10	1165	984	0.8446	91387	0.9139
均值	1166	982	0.8418	91395	0.9139

Fig.7 Comparison between repeated simulated results and analytical results

Table 2 Simulated values with different working hours

指标仿真值	T_W/h
指标仿真值	10³	10⁴	10⁵	10⁶	10⁷	10⁸
R'_p	0.8334	0.8402	0.8423	0.8421	0.8412	0.8412
A'_p	0.9154	0.9139	0.9135	0.9135	0.9134	0.9134

Fig.8 Comparison between simulated results with different working hours and analytical results

Fig.9 Comparison between simulated results and analytical results of probability of maintenance before failure

Fig.10 Comparison between simulated results and analytical results of operational availability

Fig.11 Comparison between simulation fitted value and analytical results

Table 3 Maximum difference between the simulation fitted value and the theoretical solution

δ/h	ΔR_p/%	ΔA_p/%	ΔR_c/%	ΔA_c/%
5	1.767	0.149	1.588	0.165
15	0.502	0.098	0.591	0.078
25	0.891	0.033	0.831	0.113

Fig.12 Comparison between simulated results and analytical results of instantaneous availability

References 22

[1]	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.
	YANG Y. The discrete-time modeling, analysis and application for instantaneous availability of the systems under general probability distribution[D]. Nanjing: Nanjing University of Science & Technology, 2008. (in Chinese)
[2]	康锐. 可靠性、维修性、保障性要求论证[M]. 北京: 国防工业出版社, 2011.
	KANG R. Demonstration of reliability maintainability and supportability requirements[M]. Beijing: National Defense Industry Press, 2011. (in Chinese)
[3]	WANG N C, HU J W, MA L, et al. Availability analysis and preventive maintenance planning for systems with general time distributions[J]. Reliability Engineering & System Safety, 2020, 201:106993. doi: 10.1016/j.ress.2020.106993 URL
[4]	DE JONE B. Condition-based maintenance optimization based on matrix algebra[J]. Operations Research Letters, 2021, 49(5):741-747. doi: 10.1016/j.orl.2021.08.005 URL
[5]	BEHBAHANINIA A, BANIFATEME M, AZMAYESH M H, et al. Markov and monte carlo simulation of waste-to-energy power plants considering variable fuel analysis and failure rates[J]. Journal of Energy Resources Technology, Transactions of the ASME, 2022, 144(6):062101. doi: 10.1115/1.4051760 URL
[6]	许飞雪, 刘勤明, 叶春明, 等. 基于服务性能合同模式下单部件系统视情维修策略研究[J]. 计算机应用研究, 2021, 38(2):460-464.
	XU F X, LIU Q M, YE C M, et al. Research on condition-based maintenance for single-unit systems under performance-based contracting[J]. Application Research of Computers, 2021, 38(2):460-464. (in Chinese)
[7]	李景奎, 蔺瑞管, 段飞飞, 等. 考虑可靠度和可用度的民机维修间隔优化研究[J]. 机械设计与制造, 2021(1):282-285.
	LI J K, LIN R G, DUAN F F, et al. Research on optimization of civil aircraft maintenance interval considering reliability and availabilitys[J]. Machinery Design & Manufacture, 2021 (1):282-285. (in Chinese)
[8]	都业宏, 郁浩, 赵静, 等. 武器系统预防性维修间隔期的多目标决策研究[J]. 兵工学报, 2015, 36(6): 1089-1095. doi: 10.3969/j.issn.1000-1093.2015.06.018
	DU Y H, YU H, ZHAO J, et al. Multi-objective decision of preventive maintenance intervals of wapon systems[J]. Acta Armamentarii, 2015, 36(6): 1089-1095. (in Chinese)
[9]	LI J L, CHEN Y L, ZHANG Y, et al. Availability modeling for periodically inspection system with different lifetime and repair-time distribution[J]. Chinese Journal of Aeronautics, 2019, 32(7):1667-1672. doi: 10.1016/j.cja.2019.03.025 URL
[10]	徐波, 韩学山, 孙宏斌, 等. 状态部分可观测条件下电力设备状态检修决策模型[J]. 中国电机工程学报, 2018, 38(14):4107-4116, 4316.
	XU B, HAN X S, SUN H B, et al. Condition-based maintenance optimization model for partially observable power equipment[J]. Proceedings of the CSEE, 2018, 38(14):4107-4116, 4316. (in Chinese)
[11]	黄傲林, 李庆民, 张光宇. 基于仿真的劣化装备瞬时可用度估计[J]. 计算机仿真, 2014(4):9-13.
	HUANG A L, LI Q M, ZHANG G Y. Instantaneous availability evaluation of deteriorating equipment based on simulation[J]. Computer Simulation, 2014(4):9-13. (in Chinese)
[12]	李军亮, 滕克难, 杨春周, 等. 任务准备期内的军用飞机瞬时可用度[J]. 北京航空航天大学学报, 2017, 43(4):754-760.
	LI J L, TENG K N, YANG C Z, et al. Instantaneous availability of military aircraft during mission preparation period[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(4): 754-760. (in Chinese)
[13]	曹晋华, 程侃. 可靠性数学引论[M]. 北京: 高等教育出版社, 2006.
	CAO J H, CHENG K. Introduction to mathematical reliability[M]. Beijing: Higher Education Press, 2006. (in Chinese)
[14]	任思超. 单部件可修系统瞬时可用度的波动分析[D]. 南京: 南京理工大学, 2017.
	REN S C. Fluctuation analysis of the instantaneous availability for a one-unit repairable system[D]. Nanjing: Nanjing University of Science & Technology, 2017. (in Chinese)
[15]	YANG Y, LI Q B, CHEN X F, et al. Fluctuation analysis of instantaneous availability for the parallel repairable systems[J]. IEEE ACCESS, 2019, 7:53358-53364. doi: 10.1109/Access.6287639 URL
[16]	徐宗昌. 装备保障性工程与管理[M]. 北京: 国防工业出版社, 2010.
	XU Z C. Supportability engineering and management for equipment[M]. Beijing: National Defense Industry Press, 2010. (in Chinese)
[17]	石慧, 曾建潮. 基于寿命预测的预防性维护维修策略[J]. 计算机集成制造系统, 2014, 20(5):1133-1140. doi: 10.13196/j.cims.2014.05.shihui.1133.8.20140516
	SHI H, ZENG J C. Preventive maintenance strategy based on life prediction[J]. Computer Integrated Manufacturing Systems, 2014, 20(5):1133-1140. (in Chinese)
[18]	兰成明, 任登路, 徐阳, 等. 平行钢丝斜拉索疲劳性能评定Ⅱ:斜拉索疲劳寿命模型[J]. 土木工程学报, 2017, 50(7):69-77.
	LAN C M, REN D L, XU Y, et al. Fatigue property assessment of parallel wire stay cableⅡ:fatigue life model for stay cable[J]. China Civil Engineering Journal, 2017, 50(7):69-77. (in Chinese)
[19]	杜晓明, 古平, 高鲁, 等. 基于仿真的装备保障效能评估[M]. 北京: 国防工业出版社, 2017:122-123.
	DU X M, GU P, GAO L, et al. Effectiveness evaluation of equipment support based on simulation[M]. Beijing: National Defense Industry Press, 2017:122-123. (in Chinese)
[20]	林名驰, 唐政, 宁明强, 等. 基于Wiener过程的动态性能检测视情维修策略[J]. 兵器装备工程学报, 2021, 42(7):40-45.
	LIN M C, TANG Z, NING M Q, et al. Condition-based maintenance strategy for dynamic performance detection based on Wiener process[J]. Journal of Ordnance Equipment Engineering, 2021, 42(7):40-45. (in Chinese)
[21]	刘颖. 基于不确定寿命的可靠性理论[M]. 北京: 国防工业出版社, 2018:26.
	LIU Y. Reliability theory based on uncertain lifetimes[M]Beijing: National Defense Industry Press, 2018:26. (in Chinese)
[22]	陈循. 机电系统可靠性工程[M]. 北京: 科学出版社, 2010:7-8, 53.
	CHEN X. Reliability engineering of mechatronics system[M]. Beijing: Science Press, 2010:7-8,53. (in Chinese)