Task reliability evaluation method for multi-stage repairable complex system

Abstract

The invention discloses a multi-stage repairable complex system task reliability evaluation method, and relates to the technical field of system reliability analysis, and the method comprises the steps: constructing a structure model of a complex system; constructing a fault tree of the complex system, and calculating the occurrence probability of each bottom event and each middle event in the fault tree; a state transition matrix is constructed, and the state transition probability in the state transition matrix is adjusted through the occurrence probability of each bottom event and the occurrence probability of each middle event; performing secondary adjustment on the state transition probability in the state transition matrix according to the state transition result of the maintained component; and determining the starting time and the ending time of the task and a plurality of stages contained in the task, updating a state probability vector by using the adjusted state transition matrix for each stage in a task time interval, taking the position of a normal state in the state probability vector of each stage as a normal state index, and calculating the task reliability of the complex system. And accurate evaluation of the reliability of the system task is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of system reliability analysis, and in particular to a reliability assessment method for a multi-stage repairable complex system task. Background Art

[0002] In modern industry and engineering, reliability assessment of complex systems is a key link to ensure safe and efficient operation of the systems. With the advancement of technology and the increase in system complexity, traditional reliability assessment methods have been unable to meet the needs of accurate assessment of multi-stage repairable complex systems. Such systems are usually composed of multiple components with complex logical relationships and functional dependencies. The systems go through multiple stages throughout their life cycle, including startup, stable operation, and shutdown maintenance. The operating status and failure modes of the systems may be different at each stage.

[0003] Traditional reliability assessment methods, such as failure mode and effects analysis (FMEA) and fault tree analysis (FTA), can identify potential failures and weak links in the system to a certain extent, but they have limitations when dealing with multi-stage, repairable complex systems. These methods often ignore the state transition characteristics of the system at different operating stages and the impact of component maintenance on system reliability, resulting in inaccurate and incomplete assessment results.

[0004] In addition, most of the existing reliability assessment methods are based on static data analysis and lack consideration of the dynamic operation process of the system. In practical applications, the operating status of complex systems changes over time, and component failures and maintenance activities can also cause the system status to shift. Therefore, it is difficult to accurately reflect the true reliability level of the system by relying solely on static data. Summary of the invention

[0005] 1. Technical issues to be resolved In view of the shortcomings of the prior art, the present invention provides a task reliability assessment method for a multi-stage repairable complex system. The method can comprehensively consider the system's structure, function, logical relationships between components, and state transition characteristics of components at different stages, while also needing to consider the impact of maintenance activities on system reliability. By constructing a system structural model, fault tree, and state transition matrix, and adjusting the state transition probability in combination with historical fault data and maintenance data, an accurate assessment of the system's task reliability can be achieved.

[0006] (II) Technical solution To achieve the above objectives, the present invention is implemented by the following technical scheme: a multi-stage repairable complex system task reliability assessment method, comprising the following steps: Construct a structural model of a complex system, including the structure, function and logical relationship between components of the complex system, divide the operation process of the complex system into multiple stages, and define the status of each component at different stages; Through the logical relationship and component functions between components in the structural model of the complex system, the fault tree of the complex system is constructed, including the failure mode of each component and the fault propagation path. Based on the historical fault data, the probability of occurrence of each bottom event and intermediate event in the fault tree is calculated; Define a state set for each component, calculate the probability of each component transferring from one state to another at different stages, construct a state transfer matrix for each stage, and adjust the state transfer probability in the state transfer matrix by the occurrence probability of each bottom event and intermediate event; Collect historical maintenance data of each component, including events, maintenance results, and state transition results of the component after maintenance, calculate the maintenance success rate of each component for different events, and make secondary adjustments to the state transition probability in the state transition matrix based on the state transition results of the component after maintenance; Determine the task start and end time, as well as the multiple stages included in the task. For each stage within the task time interval, use the adjusted state transfer matrix to update the state probability vector, use the position of the normal state in the state probability vector of each stage as the normal state index, and calculate the task reliability of the complex system.

[0007] Furthermore, design drawings and technical documents of complex systems are collected, and a structural model of the complex system is constructed using system engineering modeling language tools. The structural model contains the connection and logical relationships between components, including physical connections, signal transmission, and functional dependencies; the functions of the complex system are decomposed into several sub-functions, each of which is implemented by a component or a combination of components, and the interaction relationships between the sub-functions are defined, including input, output, and control signals.

[0008] Furthermore, the failure of the complex system is taken as the top event and the starting point of the fault tree; the intermediate events and bottom events that lead to the top event are determined through the logical relationship and component functions between the components in the structural model of the complex system; according to the logical relationship between different events, the top event, the intermediate event and the bottom event are connected using logic gates to form a fault logic chain, and all events and logic gates are drawn into an inverted tree diagram, namely the fault tree.

[0009] Furthermore, based on the historical fault data, the occurrence probability of each bottom event and intermediate event in the fault tree is calculated. The bottom event probability is: P (bottom event) = N (bottom event) / total duration of the time range, where N (bottom event) is the number of bottom events within the time range, and the time range is the time period for statistical historical fault data; Intermediate event probability: calculated based on the type of logic gate connected to the intermediate event and the bottom event probability. For the AND gate: P (Intermediate Event) = P (Bottom Event 1)× P (Bottom event 2)×...× P (Bottom Event m ),in, P represents the probability, m Indicates the number of bottom events; for the OR gate: P (intermediate event) = 1-[1- P (bottom event 1)]×[1- P (Bottom event 2)]×...×[1- P (Bottom Event m )].

[0010] Furthermore, a state set is defined for each component. ,in, Represents the i-th state, and calculates the probability of each component transferring from one state to another at different stages, that is, the state transition probability. The state transition probability calculation formula is: ,in, Indicates that the component is Stage from state Transfer to state The probability of Indicates that the component is Stage from state Transfer to state The number of times , represents the i-th and j-th states, and S represents the number of states.

[0011] Furthermore, for each stage, the state transfer matrix is ​​constructed: ,in, Indicates Stage state transfer matrix; Get the occurrence probability of each bottom event and intermediate event, and adjust the state transition probability in the state transition matrix: ,in, Indicates that when some events occur, from the state Transfer to state The adjusted probability, represents the probability of the nth partial event occurring, adj After adjustment, event Represents an event. Some events include bottom events and intermediate events.

[0012] Furthermore, the repair success rate of each component for each event in some events is calculated: ,in, represents the repair success rate after some event e occurs, It indicates the number of times the component is restored to the state before the partial event e occurs after maintenance. Represents the total number of times some event e occurs.

[0013] Furthermore, the state transition probability in the state transition matrix is ​​adjusted according to the state transition result of the component after maintenance: ,in, Indicates that when some event e occurs, the maintenance of the component changes from state Transfer to state The probability of the impact, represents the probability of some event e occurring, Indicates that at stage k, the component changes from state The probability of reaching maintenance state r, Indicates that at stage k, the component changes from maintenance state r to state probability.

[0014] Furthermore, the state probability vector of the complex system is initialized. For each stage within the task time interval, the state probability vector is updated using the adjusted state transfer matrix. The calculation formula is: ,in, represents the state probability vector of the kth stage, Indicates The state probability vector of the stage, represents matrix multiplication, Represents the state transfer matrix after adjustment in the kth stage.

[0015] Furthermore, the position of the normal state in the state probability vector of each stage is used as the normal state index, and the task reliability of each stage is determined by the normal state index, and the task reliability of the complex system is calculated. The calculation formula is: , where R represents task reliability, represents the probability of being in the normal state at the kth stage, and x represents the normal state index.

[0016] (III) Beneficial effects The present invention provides a multi-stage repairable complex system task reliability assessment method, which has the following beneficial effects: (1) The constructed structural model can accurately reflect the physical structure of the system and the connection relationship between components, which is helpful for the subsequent analysis of the interaction between components and the fault propagation path. The operation process of the complex system is divided into multiple stages, each with a clear configuration and status, which helps to analyze the behavioral characteristics of the system at different stages.

[0017] Through fault tree analysis, the intermediate events and bottom events that lead to system failures, as well as the logical relationship between them, are clearly identified, and the propagation path of system failures is intuitively displayed, which helps to understand the root cause and propagation mechanism of system failures. The occurrence probability of bottom events and intermediate events is calculated based on historical failure data, providing accurate data support for reliability assessment.

[0018] (2) By defining a state set for each component and calculating the state transition probability, a state transition matrix of the complex system is constructed. This can accurately describe the dynamic behavior of the complex system at different stages and provide a basis for reliability assessment. By adjusting the state transition probability in the state transition matrix based on the probability of occurrence of each basic event and intermediate event, the impact of system failures on the reliability of the complex system can be more accurately reflected, thereby improving the accuracy of the assessment.

[0019] (3) By collecting the historical maintenance data of each component, we can have a more comprehensive understanding of the maintenance status and performance changes of the components. Maintenance activities are one of the important factors affecting the reliability of complex systems. By considering the state transition results of the components after maintenance, the state transition probability in the state transition matrix is ​​adjusted, thereby realizing the consideration of the dynamic performance of the complex system.

[0020] (4) At each stage within the mission time interval, the state probability vector is updated using the adjusted state transfer matrix, which can dynamically reflect the changes in the state of the complex system over time and comprehensively consider dynamic factors such as multi-stage characteristics and maintenance strategies, thereby more comprehensively evaluating the mission reliability of the complex system. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 A schematic diagram of the steps of the multi-stage repairable complex system task reliability assessment method of the present invention; Figure 2 It is a flow chart of the multi-stage repairable complex system task reliability assessment method of the present invention. DETAILED DESCRIPTION

[0022] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0023] See also Figure 1-Figure 2 The present invention provides a multi-stage repairable complex system task reliability assessment method, comprising the following steps: Step 1: Build a structural model of the complex system, including the structure, function and logical relationship between components of the complex system, divide the operation process of the complex system into multiple stages, and define the status of each component at different stages; The step 1 includes the following contents: Step 101: Collect design drawings of complex systems, including system architecture diagrams, component connection diagrams, etc., obtain technical documents, including system operation manuals, maintenance manuals, component manuals, etc., and collect historical fault data, including fault records, maintenance records, fault analysis reports, etc.; Step 102: Use CAD (computer-aided design) software or SysML (system engineering modeling language) and other tools to build a structural model of the complex system based on design drawings and technical documents. The structural model contains the connection relationship and logical relationship between components, including physical connection, signal transmission, functional dependency, etc. Step 103: Decompose the functions of the complex system into several sub-functions, each of which is implemented by a component or a combination of components, and define the interaction relationship between the sub-functions, including input, output, control signals, etc.; Step 104: Divide the operation process of the complex system into multiple stages, such as the startup stage, the stable operation stage, the shutdown maintenance stage, etc., define the status of each component in different stages, such as normal, faulty, maintenance, etc., and determine the state transition rules, that is, the conditions for the component to switch between different states; Specifically, the division of phases should be based on the system's usage scenarios and task requirements, ensuring that each phase can reflect the different characteristics of the system under different circumstances. For example, the startup phase may involve the system's initialization process, the stable operation phase reflects the system's performance under normal working conditions, and the downtime and maintenance phase focuses on the system's repair and maintenance activities. Each phase should have a clear configuration and state to reflect the different characteristics of the system at different stages. For example, a complex system includes a startup phase, a stable operation phase, a downtime and maintenance phase, etc. Specifically, when defining the status of a component, it is necessary to ensure the comprehensiveness and accuracy of the status. For example, the normal status indicates that the component is working normally, the faulty status indicates that the component is faulty, and the maintenance status indicates that the component is undergoing maintenance. The state transition rules should clearly describe the conditions for the component to transition between different states. These rules should be based on the actual operation of the complex system and historical data. The constructed structural model can accurately reflect the physical structure of the system and the connection relationship between components, which is helpful for the subsequent analysis of the interaction between components and the fault propagation path. The operation process of the complex system is divided into multiple stages, each with a clear configuration and status, which helps to analyze the behavioral characteristics of the system at different stages.

[0024] Step 2: Construct a fault tree of the complex system through the logical relationships and functions between components in the structural model of the complex system, including the failure modes of each component and the failure propagation path. Calculate the probability of occurrence of each bottom event and intermediate event in the fault tree based on historical failure data. The step 2 includes the following contents: Step 201: Taking the failure of the complex system as the top event and the starting point of the fault tree, the failure mode, cause of the failure and the impact of the failure on the function of the complex system of each component are identified through the failure and impact analysis method; Specifically, according to the functional requirements and mission objectives of the complex system, the top event of the fault tree is determined, that is, the situation where the system cannot complete the predetermined function or the task fails. The failure and effects analysis method (FMEA) is a systematic analysis method that conducts a detailed analysis of each component of the system, product or process to find possible failure modes and analyze the impact of these failure modes on the system or product function; Step 202: Determine the intermediate events and bottom events that lead to the top event through the logical relationships and functions of the components in the structural model of the complex system. The intermediate event is a fault or abnormal state between the top event and the bottom event. The bottom event is a basic event in the fault tree, such as a single component fault or an external influencing factor. Step 203: According to the logical relationship between different events (such as AND, OR, NOT, etc.), use logic gates (such as AND gates, OR gates, etc.) to connect the top event, the middle event, and the bottom event to form a fault logic chain. The logic gates represent the causal relationship between different events and the fault propagation path; For example, a simple system consisting of three components (A, B, C), where components A and B are connected in series and component C is connected in parallel with them, functions when both A and B are working properly and C is at least partially working; Component functions: A is responsible for signal input, B is responsible for signal processing, and C is responsible for signal output; Logical relationship: A and B are connected in series, and C and A / B are connected in parallel; Failure Mode and Effects Analysis: A Fault: No signal input, the simple system cannot operate; Fault B: Signal processing fails and the simple system cannot output the correct result; C Fault (partial or complete): signal output is blocked or distorted; Intermediate events: Intermediate event 1: A or B fails, resulting in interruption of the signal processing chain; Intermediate event 2: Part C fails, causing signal output distortion; Fault logic chain: Top event: Simple system does not work properly; Intermediate event 1 (AND gate): A is faulty and B is normal, or A is normal and B is faulty; Intermediate event 2 (OR gate): Part C fails; Bottom events: A failure, B failure, C partial failure.

[0025] Step 204: Draw all events and logic gates into an inverted tree diagram, i.e., a fault tree, where the root of the fault tree is the top event (e.g., a simple system cannot operate normally), the leaves are the bottom events (e.g., A fault, B fault, C partial fault), and the middle nodes are the middle events (e.g., A fault and B normal); Step 205: Calculate the occurrence probability of each bottom event and intermediate event in the fault tree according to the historical fault data, the bottom event probability: P (bottom event) = N (bottom event) / total duration of the time range, where N (bottom event) is the number of bottom events within the time range, and the time range is the time period for statistical historical fault data; Intermediate event probability: calculated based on the type of logic gate connected to the intermediate event and the probability of the bottom event. For the AND gate: all input events (bottom events) must occur at the same time before the output event (intermediate event) occurs. P (Intermediate Event) = P (Bottom Event 1)× P (Bottom Event 2)×...× P (Bottom Event m ),in, P represents the probability, m Indicates the number of bottom events; for an OR gate: if at least one input event (bottom event) occurs, the output event (intermediate event) will occur. P (Intermediate event) =1-[1- P (bottom event 1)]×[1- P (Bottom event 2)]×...× [1- P (Bottom Event m)] (assuming independence of events); Through fault tree analysis, the intermediate events and bottom events that lead to system failures, as well as the logical relationship between them, are clearly identified, and the propagation path of system failures is intuitively displayed, which helps to understand the root cause and propagation mechanism of system failures. The occurrence probability of bottom events and intermediate events is calculated based on historical failure data, providing accurate data support for reliability assessment.

[0026] Step 3: Define a state set for each component , calculate the probability of each component transferring from one state to another at different stages, and for each stage, construct a state transfer matrix, and adjust the state transfer probability in the state transfer matrix by the occurrence probability of each bottom event and intermediate event; The step three includes the following contents: Step 301: Define a state set for each component ,in, represents the i-th state. For example, a component may have states such as “normal”, “faulty”, and “under maintenance”. The number of times each component transitions from one state to another at different stages is collected from historical data; Step 302: Calculate the probability of each component transferring from one state to another state at different stages, that is, the state transfer probability. The state transfer probability calculation formula is: ,in, Indicates that the component is Stage from state Transfer to state The probability of Indicates that the component is Stage from state Transfer to state The number of times , represents the i-th and j-th states, and S represents the number of states; Step 303: For each stage, construct a state transition matrix: ,in, represents the state transfer matrix of the kth stage; Step 304: Obtain the occurrence probability of each bottom event and intermediate event, and adjust the state transition probability in the state transition matrix: ,in, Indicates that when some events occur, from the state Transfer to state The adjusted probability, represents the probability of the nth partial event occurring, adj After adjustment, eventRepresents an event, and some events include bottom events and middle events; It should be noted that such direct adjustment may cause the state transfer matrix to no longer satisfy the property that the sum of rows is 1 (that is, the sum of the probabilities of all possible transitions from a certain state should be 1). Therefore, the adjusted probabilities need to be normalized.

[0027] By defining a state set for each component and calculating the state transition probability, a state transfer matrix of the complex system is constructed, which can accurately describe the dynamic behavior of the complex system at different stages and provide a basis for reliability assessment. By adjusting the state transition probability in the state transfer matrix based on the probability of occurrence of each basic event and intermediate event, the impact of system failures on the reliability of the complex system can be more accurately reflected, thereby improving the accuracy of the assessment.

[0028] Step 4: Collect the historical maintenance data of each component, including partial events, maintenance results, and state transition results of the component after maintenance, calculate the maintenance success rate of each component for each event in the partial events, and make a secondary adjustment to the state transition probability in the state transition matrix based on the state transition results of the component after maintenance; The step 4 includes the following contents: Step 401: Collect historical maintenance data of each component in detail from historical maintenance records, including but not limited to maintenance timestamp, partial events (including bottom events and intermediate events), maintenance duration, maintenance results (success / failure), and status transition results of the component after maintenance. For example, a maintenance record may transition a component from a "faulty" state to a "under maintenance" state, and then to a "normal" state after the maintenance is successful. Step 402: Based on the historical maintenance data, the maintenance success rate of each component for each event in the partial events (including the bottom event and the intermediate event) is calculated: ,in, represents the repair success rate after some event e occurs, It indicates the number of times the component is restored to the state before the partial event e occurs after maintenance. represents the total number of occurrences of some event e; Step 403: According to the state transition result of the repaired component, the state transition probability in the state transition matrix is ​​adjusted: ,in, Indicates that when some event e occurs, the maintenance of the component changes from state Transfer to state The probability of the impact, represents the probability of some event e occurring, Indicates that at stage k, the component changes from state The probability of reaching maintenance state r, Indicates that at stage k, the component changes from maintenance state r to state probability; By collecting the historical maintenance data of each component, we can have a more comprehensive understanding of the maintenance status and performance changes of the components. Maintenance activities are one of the important factors affecting the reliability of complex systems. By considering the state transition results of the components after maintenance, the state transition probability in the state transition matrix is ​​adjusted, thereby realizing the consideration of the dynamic performance of the complex system.

[0029] Step 5: Determine the task start and end time, as well as the multiple stages included in the task. For each stage within the task time interval, use the adjusted state transfer matrix to update the state probability vector, use the position of the normal state in the state probability vector of each stage as the normal state index, and calculate the task reliability of the complex system.

[0030] The step five includes the following contents: Step 501: Determine the task start time and end time, as well as the multiple stages included in the task (corresponding to the multiple stages in the operation process of the complex system). At the beginning of the task, initialize the state probability vector of the complex system according to the initial state of the complex system (usually starting from the "normal" state). For example, if the complex system is initially in the "normal" state, then (Assume that the first element of the state probability vector P_0 represents the "normal" state, and subsequent elements represent other states); It should be noted that the initialization of the state probability vector is based on the initial state of the complex system, setting the probability representing the initial state to 1 and the probability of all other states to 0. However, in practical applications, if the complex system is likely to be in an abnormal state at startup (for example, due to manufacturing defects or previously unrepaired faults), the initial state probability vector needs to be adjusted accordingly; Step 502: For each stage within the task time interval, the state probability vector is updated using the adjusted state transfer matrix, and the calculation formula is: ,in, represents the state probability vector of the kth stage, Indicates The state probability vector of the stage, represents matrix multiplication, represents the state transfer matrix after adjustment in the kth stage; It should be noted that the state probability vector is updated using the adjusted state transfer matrix. The "adjustment" here refers to the modification of the original state transfer matrix according to the partial event probabilities and maintenance success rates calculated in steps three and four. The state transfer matrix after the second adjustment; Step 503: The position of the normal state in the state probability vector of each stage is used as the normal state index, the task reliability of each stage is determined by the normal state index, and the task reliability of the complex system is calculated. The calculation formula is: , where R represents task reliability, represents the probability of being in the normal state at the kth stage, and x represents the normal state index; At each stage within the mission time interval, the state probability vector is updated using the adjusted state transfer matrix, which can dynamically reflect the changes in the state of the complex system over time, comprehensively consider dynamic factors such as multi-stage characteristics and maintenance strategies, and thus more comprehensively evaluate the mission reliability of the complex system.

[0031] In the application, the several formulas involved are all calculated by removing dimensions and taking their numerical values. The formula is a formula of the most recent real situation obtained by collecting a large amount of data and performing software simulation. The coefficients in the formula are set by technicians in this field according to actual conditions.

[0032] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination thereof. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product. A person of ordinary skill in the art may appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein may be implemented in combination with electronic hardware, computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution.

[0033] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, and may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0034] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application.

Claims

1. A multi-stage repairable complex system task reliability assessment method, characterized by: The following steps are involved: Construct a structural model of a complex system, including the structure, function and logical relationship between components of the complex system, divide the operation process of the complex system into multiple stages, and define the status of each component at different stages; Through the logical relationship and component functions between components in the structural model of the complex system, the fault tree of the complex system is constructed, including the failure mode of each component and the fault propagation path. Based on the historical fault data, the probability of occurrence of each bottom event and intermediate event in the fault tree is calculated; Define a state set for each component, calculate the probability of each component transferring from one state to another at different stages, construct a state transfer matrix for each stage, and adjust the state transfer probability in the state transfer matrix by the occurrence probability of each bottom event and intermediate event; Collect historical maintenance data of each component, including events, maintenance results, and state transition results of the component after maintenance, calculate the maintenance success rate of each component for different events, and make secondary adjustments to the state transition probability in the state transition matrix based on the state transition results of the component after maintenance; Determine the task start and end time, as well as the multiple stages included in the task. For each stage within the task time interval, use the adjusted state transfer matrix to update the state probability vector, use the position of the normal state in the state probability vector of each stage as the normal state index, and calculate the task reliability of the complex system.

2. The method for evaluating the reliability of a multi-stage repairable complex system task according to claim 1, characterized in that: Collect design drawings and technical documents of complex systems, use system engineering modeling language tools to build a structural model of the complex system. The structural model contains the connection and logical relationships between components, including physical connections, signal transmission, and functional dependencies; decompose the functions of the complex system into several sub-functions, each of which is implemented by a component or a combination of components, and define the interaction relationship between sub-functions, including input, output, and control signals.

3. The method for evaluating task reliability of a multi-stage repairable complex system according to claim 1, characterized in that: The failure of a complex system is taken as the top event and the starting point of the fault tree. The intermediate events and bottom events that lead to the top event are determined through the logical relationship and component functions between components in the structural model of the complex system. According to the logical relationship between different events, the top event, intermediate event and bottom event are connected using logic gates to form a fault logic chain. All events and logic gates are drawn into an inverted tree diagram, namely the fault tree.

4. The method for evaluating task reliability of a multi-stage repairable complex system according to claim 3 is characterized by: According to the historical fault data, the occurrence probability of each bottom event and intermediate event in the fault tree is calculated. The bottom event probability is: P (bottom event) = N (bottom event) / total duration of the time range, where N (bottom event) is the number of bottom events within the time range, and the time range is the time period for statistical historical fault data; Intermediate event probability: calculated based on the type of logic gate connected to the intermediate event and the bottom event probability. For the AND gate: P (Intermediate Event) = P (Bottom Event 1)× P (Bottom event 2)×...× P (Bottom Event m ),in, P represents the probability, m Indicates the number of bottom events; for the OR gate: P (intermediate event) = 1-[1- P (bottom event 1)]×[1- P (Bottom event 2)]×...× [1- P (Bottom Event m )].

5. The method for evaluating the reliability of a multi-stage repairable complex system task according to claim 1, characterized in that: Define a state set for each component ,in, Represents the i-th state, and calculates the probability of each component transferring from one state to another at different stages, that is, the state transition probability. The state transition probability calculation formula is: ,in, Indicates that the component is Stage from state Transfer to state The probability of Indicates that the component is Stage from state Transfer to state The number of times , represents the i-th and j-th states, and S represents the number of states.

6. The method for evaluating task reliability of a multi-stage repairable complex system according to claim 5, characterized in that: For each stage, construct the state transition matrix: ,in, Indicates Stage state transfer matrix; Get the occurrence probability of each bottom event and intermediate event, and adjust the state transition probability in the state transition matrix: ,in, Indicates that when some events occur, from the state Transfer to state The adjusted probability, represents the probability of the nth partial event occurring, adj After adjustment, event Represents an event. Some events include bottom events and intermediate events.

7. The method for evaluating task reliability of a multi-stage repairable complex system according to claim 1, characterized in that: Calculate the repair success rate of each component for each event in the partial events: ,in, represents the repair success rate after some event e occurs, It indicates the number of times the component is restored to the state before the partial event e occurs after maintenance. Represents the total number of times some event e occurs.

8. The method for evaluating the reliability of a multi-stage repairable complex system task according to claim 7 is characterized by: According to the state transition results of the repaired components, the state transition probability in the state transition matrix is ​​adjusted: ,in, Indicates that when some event e occurs, the maintenance of the component changes from state Transfer to state The probability of the impact, represents the probability of some event e occurring, Indicates that at stage k, the component changes from state The probability of reaching maintenance state r, Indicates that at stage k, the component changes from maintenance state r to state probability.

9. The method for evaluating task reliability of a multi-stage repairable complex system according to claim 1, characterized in that: Initialize the state probability vector of the complex system. For each stage within the task time interval, use the adjusted state transfer matrix to update the state probability vector. The calculation formula is: ,in, represents the state probability vector of the kth stage, Indicates The state probability vector of the stage, represents matrix multiplication, Represents the state transfer matrix after adjustment in the kth stage.

10. The method for evaluating task reliability of a multi-stage repairable complex system according to claim 9, characterized in that: The position of the normal state in the state probability vector of each stage is used as the normal state index. The task reliability of each stage is determined by the normal state index, and the task reliability of the complex system is calculated. The calculation formula is: , where R represents task reliability, represents the probability of being in the normal state at the kth stage, and x represents the normal state index.

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