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	$\overset{?}{α}$	$\overset{?}{θ}$	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	$\overset{?}{α}$	$\overset{?}{θ}$	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	$\overset{?}{α}$	$\overset{?}{θ}$	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	$\overset{?}{α}$	$\overset{?}{θ}$	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

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