A new construction method of system reliability was proposed in this paper based on network and relevant failure. Taking the component units as the nodes and the interaction relationships between the nodes as the side lines, a new directional network reliability model with certain network topology characteristics was constructed. It can indicate the complex topology relationship, interaction mechanism, and the transmission mechanism of failure affect between mechanical integration and electrical integration of system components. Compared with the traditional research methods, the relevant failure was considered during this process. Through the application of the fault data in the bogie system of high-speed train, it was shown that a new network reliability model which considered the relevant failure can be constructed by the method proposed in this paper and the result can be more accurate, especially for the complex mechanical and electrical integration systems.
Reliability study initially was developed from the reliability analysis of electronic components during World War II. From the beginning of the 1960s, reliability study was gradually expanded from a single reliability analysis of electronic component to the reliability of the general system [
The mechanism of high-speed train system is quite complex, and the coupling feature between components is strong. The relationship roles between components include mechanical effects, electrical effects, and information effects. Besides, the sensitivity between system elements is of a high degree. Any small change could cause the safe behavior of the entire system to rapidly deteriorate. However, the traditional analytical methods of its reliability, such as fault tree analysis [
One single component failure in high-speed train system may lead to another or more system components failure, which may be caused by space, environment, design, or human factors, which can be called as relevant failure. It can be divided into two types, one is caused by the outside factors, such as lightning which lead to electronic equipment failure, and the other is caused by a single shared component failure, which is mainly researched in this paper and always called as common cause failure (CCF).
A new construction method of system reliability was proposed in this paper based on common cause failure network. It can indicate the complex topology relationship, interaction mechanism, and the transmission mechanism of failure affect between mechanical integration and electrical integration of system components. It also provided a common cause failure reliability model as the research basis for the complex system safety assessment and analysis.
The common cause failure (CCF) event in high-speed train system is the result of simultaneous failure of two or more individual components failure due to a single shared cause. For example, carriage wheel failure may lead to other components failure of the high-speed trains.
The alpha factor model estimates the CCF frequencies from a set of ratios of failures and the total component failure rate. The parameters of the model are as follows:
The CCF basic event equation for any
Define
This study involved the following assumptions: the topology of the system is always unchanged; exclude the impact from nonsystem components; components failure rate is exponentially distributed; subsystems or systems failures are immediately repaired and the distribution of lifetime after repair is the same as the original; there are two states for the components, subsystems, or systems: normal and failure and the failure are unrepeatable elements.
In complex mechatronic systems, the topological relationships between the components and the interaction mechanism can be revealed by the connection types and impact direction between the components. In this way, the formalized expression of relevant attributes for the key components of system corresponding to the network and a clear expression of the topology of the network can be formed and embed the components properties.
According to the connection types and the impact direction between components, the formal expression of system’s connections can be shown in Table
The formal expression of system’s connections.
Connection types between components | Graphical representation | Description |
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Mechanical connection |
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Mechanical connection between components is unidirectional |
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Mechanical connection between components is bidirectional | |
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Electrical connection |
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Electrical connection between components is unidirectional |
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Electrical connection between components is bidirectional | |
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Information link |
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Information link between components is unidirectional |
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Information link between components is bidirectional |
System reliability model.
The bogie system of high-speed train was taken as the engineering background, which is a typical high-tech integrated system. As shown in Table
The components of high-speed train bogie system.
Number | Subsystems | Number | Components |
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01 | Framework | 1 | Side beams |
2 | Crossbeam | ||
3 | Vertical support beams connecting beam air spring | ||
4 | Support beam of air spring | ||
5 | Brake bracket of roulette | ||
6 | Positioning arm seat | ||
7 | The mounting base of pressurized cylinder | ||
8 | Vertical stopper | ||
9 | The motor hanging brackets | ||
10 | Gear box hanging brackets | ||
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02 | Wheel pairs | 11 | The axles |
12 | The wheels | ||
13 | The brake disc | ||
14 | The device of gears | ||
15 | The bearing | ||
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03 | Axle boxes apparatus | 16 | Axis box |
17 | The front cover of axis | ||
18 | The back cover of axis | ||
19 | The positioning node of rubber elastic | ||
20 | Bearing units | ||
21 | Bearing temperature detectors | ||
22 | Speed sensors | ||
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04 | The first suspension apparatus | 23 | The spring device of axle box |
24 | The vertical damper of axle boxes | ||
25 | The positioning node of rubber elastic | ||
26 | The arrangements for lifting of wheels | ||
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05 | The secondary suspension apparatus | 27 | Lateral damper |
28 | Antisnake damper | ||
29 | Air spring device | ||
30 | The central traction drawbars seat | ||
31 | Height adjustment valve | ||
32 | Transverse backstop | ||
33 | Traction drawbars | ||
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06 | Traction drives | 34 | Couplings |
35 | The traction motor | ||
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07 | Braking device | 36 | Brake callipers |
37 | Piping systems | ||
38 | Brake booster cylinder | ||
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08 | Tread surface cleaning device | 39 | Air cylinder |
40 | Grinding |
Based on the modeling approach proposed in this paper, the reliability model of bogie system of high-speed train was constructed based on common cause failure network, as shown in Figure
High-speed train bogie system reliability model.
Statistics of common cause failure.
Failure | CCF |
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1 |
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2 |
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3 |
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10 |
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11 |
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12 |
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14 |
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16 |
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23 |
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24 |
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30 |
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Because the reliability degree of the components has the characters of exponential distribution in the bogie system of high-speed train, the reliability of components can be calculated according to the failure rate when the time is
The laboratory experiment of forty individual components can be finished when the working time is similar to the statistical example. Based on the above method, the reliability of individual components can be obtained and marked as
Similarly, when the components with the relationship of common cause failure were connected with each other in their group, the reliability of eleven groups in Table
In order to verify the practical outcome of the construction and its corresponding evaluation method, the practical reliability results
Comparison of reliability results.
Number | Reliability of individual components |
Reliability considering common cause failure |
Practical reliability |
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4 | 1 | 1 | 1 |
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9 | 0.9998 | 0.9937 | 0.9964 |
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15 | 0.9999 | 0.9999 | 0.9999 |
16 | 0.9998 | 0.9990 | 0.9988 |
17 | 1 | 0.9999 | 0.9998 |
18 | 1 | 0.9997 | 0.9999 |
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21 | 0.9988 | 0.9988 | 0.9988 |
22 | 0.9964 | 0.9964 | 0.9964 |
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29 | 0.9989 | 0.9923 | 0.9958 |
30 | 0.9999 | 0.9999 | 0.9999 |
31 | 0.9954 | 0.9954 | 0.9954 |
32 | 0.9947 | 0.9953 | 0.9948 |
33 | 0.9991 | 0.9969 | 0.9933 |
34 | 0.9992 | 0.9959 | 0.9943 |
35 | 0.9985 | 0.9985 | 0.9985 |
36 | 0.9963 | 0.9963 | 0.9963 |
37 | 0.9992 | 0.9992 | 0.9992 |
38 | 0.9993 | 0.9993 | 0.9993 |
39 | 0.9942 | 0.9942 | 0.9942 |
40 | 0.9905 | 0.9905 | 0.9905 |
As shown in Table
This paper presents a new method to build the reliability model of system based on common cause failure network, which showed obvious advantages compared with the reliability of individual components. The main conclusions include the following. Taking the component units as the nodes and the interaction relationships between the nodes as the side lines, a new directional network reliability model with certain network topology characteristics was constructed. It can indicate the complex topology relationship, interaction mechanism, and the transmission mechanism of failure affect between mechanical integration and electrical integration of system components. Taking the bogie system of high-speed train as the engineering background, the reliability model considering common cause failure was constructed based on the method proposed in this paper. After application and verification, it showed to be much more accurate to the practical condition and the effectiveness of the method proposed in this paper was verified. The common cause failure network reliability model of the whole high-speed train can also be built in the same way. The subsequent research can focus on the analysis and safety assessment based on these reliability models, providing a new way to research safety problem for the high-speed train system and other complex systems.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge the financial support of the Projects of National Science Support Plan of China (2011BAG01802), State Key Laboratory of Rail Traffic Control and Safety (RCS2014ZT23), and CRH3 High-Speed Train Fault Data Research (I11L00060).