Reliability evaluation of safety-critical equipment under imperfect maintenance strategy

doi:10.11949/0438-1157.20201144

Abstract

Abstract:

To realize the reliability evaluation of safety-critical equipment under incomplete maintenance conditions, the traditional reliability evaluation model does not consider the data difference between multiple fault samples and the complex problem of solving model parameters. This paper proposes a hybrid Kijima Ⅰ Virtual service age model. Firstly, the cumulative failure intensity function is used to describe the failure trend of the system on the time diagram. The appropriate reliability evaluation model is selected based on the AIC and BIC information criteria, and the non-linear constraint programming method is used to transform the estimated value of the distributed parameter under imperfect repair. Then, for the multi-category sample failure data caused by different reasons, the hybrid Kijima Ⅰ model is established by considering the difference between failure data. The case analysis of the ship unloading system of an LNG receiving station shows that this model is more effective than the commonly used mixed sample distribution model in actual reliability evaluation. At the same time this helps to achieve a balance between differentiated maintenance and high equipment availability.

Key words: imperfect repair, safety, Monte Carlo simulation, instrumentation, parameter estimation

摘要：

为实现不完全维修条件下的安全关键设备可靠性评估，针对传统可靠性评估模型未考虑多个故障样本间存在的数据差异问题，以及模型参数求解复杂的问题，提出了一种混合Kijima Ⅰ虚拟役龄模型。首先通过累积故障强度函数对时间图描述系统的故障趋势，根据AIC、BIC信息准则选取合适的可靠性评估模型，利用非线性约束规划法转换得到不完全维修下的分布参数估计值。随后针对不同故障原因造成的多类别样本故障数据，考虑故障数据间的差异性，建立了混合Kijima Ⅰ模型。将该模型应用到某LNG接收站卸船系统中，实例分析表明，该模型在实际可靠性评估中比常用的混合样本分布模型更加有效，有助于实现差异化维修和设备高可用性之间的平衡。

关键词: 不完全维修, 安全, Monte Carlo模拟, 仪器仪表, 参数估计

CLC Number:

X 937

QU Chi, WANG Haiqing, JIANG Weiwei, SUN Hao, ZHANG Jingkang. Reliability evaluation of safety-critical equipment under imperfect maintenance strategy[J]. CIESC Journal, 2021, 72(4): 2328-2336.

屈持, 王海清, 姜巍巍, 孙浩, 张景康. 不完全维修策略下的安全关键设备可靠性评估[J]. 化工学报, 2021, 72(4): 2328-2336.

Figures/Tables 12

Fig.1 Relationship between equipment operating time and virtual service age

Table 1 1—9 scale scoring criteria

序号	重要度关系	C_x,y
1	x,y两元素同等重要	1
2	x元素比y元素稍微重要	3
3	x元素比y元素明显重要	5
4	x元素比y元素强烈重要	7
5	x元素比y元素极度重要	9
6	x元素比y元素稍不重要	1/3
7	x元素比y元素明显不重要	1/5
8	x元素比y元素强烈不重要	1/7
9	x元素比y元素极度不重要	1/9

Fig.2 Flow chart of reliability assessment

Fig.3 Process flow chart of LNG receiving station

Fig.4 Partial flowchart of LNG unloading process

Table 2 Simulated fault data and preprocessing

序号	故障间隔时间/h	$d k, j$	$1 / d k, j$	$S (t k, j)$
1	14285	3	1/3	1/3
2	19282	3	1/3	2/3
3	23244	3	1/3	1
4	28204	3	1/3	4/3
5	35052	3	1/3	5/3
6	42876	3	1/3	2
7	52422	3	1/3	7/3
8	64010	3	1/3	8/3
9	77821	3	1/3	3
10	91611	3	1/3	10/3
11	106806	3	1/3	11/3
12	122879	3	1/3	4
13	138238	3	1/3	13/3
14	140000+	2

Table 2 Simulated fault data and preprocessing

序号	故障间隔时间/h	$d k, j$	$1 / d k, j$	$S (t k, j)$
1	14285	3	1/3	1/3
2	19282	3	1/3	2/3
3	23244	3	1/3	1
4	28204	3	1/3	4/3
5	35052	3	1/3	5/3
6	42876	3	1/3	2
7	52422	3	1/3	7/3
8	64010	3	1/3	8/3
9	77821	3	1/3	3
10	91611	3	1/3	10/3
11	106806	3	1/3	11/3
12	122879	3	1/3	4
13	138238	3	1/3	13/3
14	140000+	2

Fig.5 Cumulative failure intensity function versus time

Table 3 Model comparison results

模型分类		参数估计值			-lnL	AIC	BIC
修复如新	(Weibull)	形状参数=1.3198	尺度参数=64638	位置参数=8742	-167.2168	340.4336	342.3507
修复如旧	(NHPP)	形状参数=0.5754	强度参数=0.0051	—	-168.182	340.364	341.6421
不完全维修	(Kijima Ⅰ)	形状参数=0.7622	尺度参数=50527	—	-158.3391	320.6782	321.9563

Table 4 Comparison of evaluation results of different samples

样本大小	评估指标
样本大小	$α ?$	$θ ?$	相对误差
50	0.9919	0.00001	0.301
100	0.9411	0.00001	0.234
200	0.8393	0.00007	0.101
500	0.8126	0.00010	0.066
800	0.7906	0.00017	0.037
1000	0.7893	0.00016	0.035
2000	0.7639	0.00025	0.002

Table 4 Comparison of evaluation results of different samples

样本大小	评估指标
样本大小	$α ?$	$θ ?$	相对误差
50	0.9919	0.00001	0.301
100	0.9411	0.00001	0.234
200	0.8393	0.00007	0.101
500	0.8126	0.00010	0.066
800	0.7906	0.00017	0.037
1000	0.7893	0.00016	0.035
2000	0.7639	0.00025	0.002

Table 5 Pressure transmitter sample data

故障原因分类	故障间隔时间/h
输出不稳定	10240、15480、20089、26918、33572、42103、53751、65895、73163、79789、87050
输出偏差大	19399、24042、37841、46281、57214、66390、75448、85317
恶意网络攻击	62231、87600+

Table 6 Distribution parameters of mixed virtual service age model

样本	$α ?$	$θ ?$	w_l
样本1	1.0068	0.00002	0.627
样本2	1.0583	0.00001	0.2923
样本3	1.1698	0.000001	0.0807
混合样本	0.8641	0.0001	—

Table 6 Distribution parameters of mixed virtual service age model

样本	$α ?$	$θ ?$	w_l
样本1	1.0068	0.00002	0.627
样本2	1.0583	0.00001	0.2923
样本3	1.1698	0.000001	0.0807
混合样本	0.8641	0.0001	—

Fig.6 Reliability curve of mixed Kijima Ⅰ model and each sample

References 2

2	Wang Z M, Yang J G. Bayesian reliability analysis for NC machine tools with minimal repair[J]. Computer Integrated Manufacturing Systems, 2014, 20(9): 2215-2220.
3	王慧, 赵国超, 宋宇宁, 等. 基于改进的威布尔分布的液压支架可靠性评估方法[J]. 中国安全科学学报, 2018, 28(5): 99-104.
	Wang H, Zhao G C, Song Y N, et al. Reliability evaluation method of hydraulic support based on improved Weibull distribution[J]. China Safety Science Journal, 2018, 28(5): 99-104.
4	彭新凯, 王海清, 刘建利, 等. 石化安全设备寿命参数极大似然估计[J]. 中国安全科学学报, 2019, 29(2): 94-99.
	Peng X K, Wang H Q, Liu J L, et al. Maximum likelihood estimation of petrochemical safety equipment lifetime parameters[J]. China Safety Science Journal, 2019, 29(2): 94-99.
5	汪航, 王海清, 刘芳. 基于贝叶斯方法的石化设备失效数据推断技术研究[J]. 安全与环境学报, 2014, 14(6): 5-7.
	Wang H, Wang H Q, Liu F. Research on inference and forecasting technology for petrochemical equipment failure based on Bayesian method[J]. Journal of Safety and Environment, 2014, 14(6): 5-7.
6	王智明, 杨建国. 数控机床可靠性评估中的边界强度过程[J]. 上海交通大学学报, 2012, 46(10): 1622-1626, 1631.
	Wang Z M, Yang J G. Bounded intensity process and its applications in reliability assessment of NC machine tools[J]. Journal of Shanghai Jiao Tong University, 2012, 46(10): 1622-1626, 1631.
7	Tanwar M, Rai R N, Bolia N. Imperfect repair modeling using Kijima type generalized renewal process[J]. Reliability Engineering & System Safety, 2014, 124: 24-31.
8	任丽娜, 芮执元, 王智明. 可修系统不完全维修连续比例强度模型及应用[J]. 中南大学学报(自然科学版), 2015, 46(7): 2467-2473.
	Ren L N, Rui Z Y, Wang Z M. Imperfect repair continuous proportional intensity model for repairable systems and its application[J]. Journal of Central South University (Science and Technology), 2015, 46(7): 2467-2473.
9	Wang L, Hu H J, Wang Y Q, et al. The availability model and parameters estimation method for the delay time model with imperfect maintenance at inspection[J]. Applied Mathematical Modelling, 2011, 35(6): 2855-2863.
10	Geng J, Zhou D, Lv C, et al. A modeling approach for maintenance safety evaluation in a virtual maintenance environment[J]. Computer-Aided Design, 2013, 45(5): 937-949.
11	Kim J, Jeong H Y. Evaluation of the adequacy of maintenance tasks using the failure consequences of railroad vehicles[J]. Reliability Engineering & System Safety, 2013, 117: 30-39.
12	Nguyen D T, Dijoux Y, Fouladirad M. Analytical properties of an imperfect repair model and application in preventive maintenance scheduling[J]. European Journal of Operational Research, 2017, 256(2): 439-453.
13	Kijima M, Sumita U. A useful generalization of renewal theory: counting processes governed by non-negative Markovian increments[J]. Journal of Applied Probability, 1986, 23(1): 71-88.
1	任丽娜, 芮执元, 刘军, 等. 数控机床最小维修的全寿命周期可靠性评估[J]. 上海交通大学学报, 2015, 49(1): 19-23.
	Ren L N, Rui Z Y, Liu J, et al. Whole lifecycle reliability assessment of multiple NC machine tools with minimal repair[J]. Journal of Shanghai Jiao Tong University, 2015, 49(1): 19-23.
14	Cox D R. The Statistical Analysis of Dependencies in Point Process, Stochastic Point Processes[M]. Lewis P A W. New York: John Wiley, 1972: 55-66.
15	Syamsundar A, Naikan V N A. Imperfect repair proportional intensity models for maintained systems[J]. IEEE Transactions on Reliability, 2011, 60(4): 782-787.
16	张根保, 刘杰, 高琦樑, 等. 多台数控机床不完全维修的可靠性评估[J]. 重庆大学学报, 2014, 37(2): 1-6.
	Zhang G B, Liu J, Gao Q L, et al. Reliability assessment of multiple NC machine tools with imperfect repair[J]. Journal of Chongqing University, 2014, 37(2): 1-6.
17	Wang Z M, Yu X. Log-linear process modeling for repairable systems with time trends and its applications in reliability assessment of numerically controlled machine tools[J]. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2013, 227(1): 55-65.
18	Gasmi S. Estimating parameters of a log-linear intensity for a repairable system[J]. Applied Mathematical Modelling, 2013, 37(6): 4325-4336.
19	Lim J H, Qu J, Zuo M J. Age replacement policy based on imperfect repair with random probability[J]. Reliability Engineering & System Safety, 2016, 149: 24-33.
20	Almalki S J, Nadarajah S. Modifications of the Weibull distribution: a review[J]. Reliability Engineering & System Safety, 2014, 124: 32-55.
21	Wang Z M, Yang J G. Numerical method for Weibull generalized renewal process and its applications in reliability analysis of NC machine tools[J]. Computers & Industrial Engineering, 2012, 63(4): 1128-1134.
22	Caroni C. “Failure limited” data and TTT-based trend tests in multiple repairable systems[J]. Reliability Engineering & System Safety, 2010, 95(6): 704-706.
23	Kvaløy J T, Lindqvist B H. TTT-based tests for trend in repairable systems data[J]. Reliability Engineering & System Safety, 1998, 60(1): 13-28.
24	Chen X M. Using akaike information criterion for selecting the field distribution in a reverberation chamber[J]. IEEE Transactions on Electromagnetic Compatibility, 2013, 55(4): 664-670.
25	张根保, 李冬英, 刘杰, 等. 面向不完全维修的数控机床可靠性评估[J]. 机械工程学报, 2013, 49(23): 136-141.
	Zhang G B, Li D Y, Liu J, et al. Reliability assessment for multiple NC machine tools oriented to general repair[J]. Journal of Mechanical Engineering, 2013, 49(23): 136-141.
26	王智明, 杨建国, 王国强, 等. 多台数控机床的时间截尾可靠性评估[J]. 哈尔滨工业大学学报, 2011, 43(3): 85-89.
	Wang Z M, Yang J G, Wang G Q, et al. Reliability evaluation of multiple NC machine tools with time truncation[J]. Journal of Harbin Institute of Technology, 2011, 43(3): 85-89.
27	Ghosh A, Majumdar S K. Modeling failure types and failure times of turning and boring machine systems[J]. International Journal of Quality & Reliability Management, 2010, 27(7): 815-831.
28	王海清, 陈韬婕, 刘祥妹. 数字化液化天然气接收站综合实验平台开发[J]. 实验室研究与探索, 2017, 36(6): 249-254.
	Wang H Q, Chen T J, Liu X M. Development of comprehensive experimental platform for LNG receiving terminal demanded by safety engineering international education[J]. Research and Exploration in Laboratory, 2017, 36(6): 249-254.
29	王海清, 徐慧敏, 田英帅, 等. 基于ALOHA软件探索LNG接收站仿真实验室的优化设计[J]. 实验技术与管理, 2020, 37(3): 230-234.
	Wang H Q, Xu H M, Tian Y S, et al. Exploration on optimization design of simulation laboratory for LNG receiving station based on ALOHA software[J]. Experimental Technology and Management, 2020, 37(3): 230-234.
30	朱建鲁, 李玉星, 王武昌, 等. LNG接收终端工艺流程动态仿真[J]. 化工学报, 2013, 64(3): 1000-1007.
	Zhu J L, Li Y X, Wang W C, et al. Dynamic simulation of LNG import terminal process[J]. CIESC Journal, 2013, 64(3): 1000-1007.
31	鲁毅, Yap E, 刘昳蓉, 等. 可靠性、可用性与可维修性分析在LNG接收站产能预测中的应用 [J]. 化工学报, 2015, 66: 430-438.
	Lu Y, Yap E, Liu Y R, et al. Reliability, availability and maintainability(RAM)modeling to predict production performance of LNG storage terminal[J]. CIESC Journal, 2015, 66: 430-438.
32	. Petroleum, petrochemical and natural gas industries — collection and exchange of reliability and maintenance data for equipment[S]. Switzerland: ISO, 2016.
33	SINTEF, NTNU. Offshore Reliability Data Handbook[M]. 6th ed. Norway: Det Norske Veritas (DNV), 2015.
34	屈持, 王海清, 刘建利, 等. 基于最小维修的石化安全设备区间截尾寿命数据分析[J]. 化工进展, 2020, 39(11): 4384-4390.
	Qu C, Wang H Q, Liu J L, et al. Interval censored life data of petrochemical safety equipment based on minimal maintenance[J]. Chemical Industry and Engineering Progress, 2020, 39(11): 4384-4390.
35	徐子军, 王海清, 陈韬婕, 等. 基于蒙特卡罗的石化设备寿命均值估计优化与应用[J]. 中国安全科学学报, 2016, 26(5): 70-75.
	Xu Z J, Wang H Q, Chen T J, et al. Optimization of petrochemical equipment MTTF estimation based on Monte Carlo and its application[J]. China Safety Science Journal, 2016, 26(5): 70-75.
36	Preacher K J, Selig J P. Advantages of Monte Carlo confidence intervals for indirect effects[J]. Communication Methods and Measures, 2012, 6(2): 77-98.
2	王智明, 杨建国. 数控机床最小维修的贝叶斯可靠性分析[J]. 计算机集成制造系统, 2014, 20(9): 2215-2220.

[1]	Xianheng YI, Wu ZHOU, Xiaoshu CAI, Tianyi CAI. Measurable range of nanoparticle concentration using optical fiber backward dynamic light scattering [J]. CIESC Journal, 2023, 74(8): 3320-3328.
[2]	Xiaoyang LIU, Jianliang YU, Yujie HOU, Xingqing YAN, Zhenhua ZHANG, Xianshu LYU. Effect of spiral microchannel on detonation propagation of hydrogen-doped methane [J]. CIESC Journal, 2023, 74(7): 3139-3148.
[3]	Cheng YUN, Qianlin WANG, Feng CHEN, Xin ZHANG, Zhan DOU, Tingjun YAN. Deep-mining risk evolution path of chemical processes based on community structure [J]. CIESC Journal, 2023, 74(4): 1639-1650.
[4]	Zhongliang XIAO, Bilu YIN, Liubin SONG, Yinjie KUANG, Tingting ZHAO, Cheng LIU, Rongyao YUAN. Research progress of waste lithium-ion battery recycling process and its safety risk analysis [J]. CIESC Journal, 2023, 74(4): 1446-1456.
[5]	Yuanjing MAO, Zhi YANG, Songping MO, Hao GUO, Ying CHEN, Xianglong LUO, Jianyong CHEN, Yingzong LIANG. Estimation of SAFT-VR Mie equation of state parameters and thermodynamic properties of C₆—C₁₀ alcohols [J]. CIESC Journal, 2023, 74(3): 1033-1041.
[6]	Jianglong DU, Wenqi YANG, Kai HUANG, Cheng LIAN, Honglai LIU. Heat dissipation performance of the module combined CPCM with air cooling for lithium-ion batteries [J]. CIESC Journal, 2023, 74(2): 674-689.
[7]	Ke YANG, Chensheng WANG, Hong JI, Kai ZHENG, Zhixiang XING, Haipu BI, Juncheng JIANG. Experimental study on inhibition of methane explosion by polydopamine coated mixed powder [J]. CIESC Journal, 2022, 73(9): 4245-4254.
[8]	Shanshan LIAO, Shaogang ZHANG, Junjun TAO, Jiahao LIU, Jinhui WANG. Numerical simulation analysis of vertical jet fire impinging on the pipeline [J]. CIESC Journal, 2022, 73(9): 4226-4234.
[9]	Yan WANG, Jia HE, Jingjing YANG, Chendi LIN, Wentao JI. Inhibition of polyethylene dust explosion by oxalate and bicarbonate [J]. CIESC Journal, 2022, 73(9): 4207-4216.
[10]	Jing YANG, Zhenkang LIN, Jun TANG, Cheng FAN, Kening SUN. A review of fault characteristics, fault diagnosis and identification for lithium-ion battery systems [J]. CIESC Journal, 2022, 73(8): 3394-3405.
[11]	Jingwei ZHANG, Yiwei ZHOU, Zhuo CHEN, Jianhong XU. Advances in frontiers of organic synthesis in microreactor [J]. CIESC Journal, 2022, 73(8): 3472-3482.
[12]	Rongshan BI, Zhihui HAN, Shaohui TAO, Xiaoyan SUN, Shuguang XIANG. Recognizing historical operating conditions by determining the density peaks at kernel density estimation of heat diffusion [J]. CIESC Journal, 2022, 73(4): 1615-1622.
[13]	Mengya ZHOU, Kuibin ZHOU, Chao WANG, Mengyuan HUANG, Yifan WANG, Juncheng JIANG. Flame behavior of horizontal propane jet fire in a pit [J]. CIESC Journal, 2022, 73(2): 960-971.
[14]	Fengli ZHANG, Hui PAN, Jinjiang WANG. Multi-parameter correlation early warning method of heat exchanger based on multivariate state estimation [J]. CIESC Journal, 2022, 73(2): 814-826.
[15]	Cheng ZHANG, Lizhi PAN, Yuan LI. Fault detection and diagnosis method based on weighted statistical feature KICA [J]. CIESC Journal, 2022, 73(2): 827-837.