A Reliability Analysis Method and System for Safety-Critical Systems Based on Editable Petri Nets

Abstract

This invention discloses a reliability analysis method for safety-critical systems based on editable Petri nets. An editable Petri net model is established based on the dynamic fault characteristics of the safety-critical system. The editable Petri net model includes instantaneous transitions, random transitions, and editable transitions. The dimension of the dynamic fault characteristic space of the safety-critical system is determined based on the number of random transitions. Sampling is performed based on the dimension to obtain a sampling point sequence. The sampling point sequence is used as input to a Monte Carlo sampling algorithm, and transition occurrence times are generated through inverse transformation. Based on the generated transition occurrence times, the system failure probability is obtained using the Monte Carlo method. The system failure probability is obtained through multiple iterations, and the failure distribution is fitted to analyze the reliability of the safety-critical system. Editable transitions are added to the generalized random Petri net. These editable transitions can be defined as any fault logic, replacing the need for additional transitions and places, thus solving the problem of low efficiency in reliability analysis of safety-critical systems.

Description

Technical Field

[0001] This invention relates to reliability analysis of safety-critical systems, specifically to a method and system for reliability analysis of safety-critical systems based on editable Petri nets. Background Technology

[0002] With the increasing demands for system safety and reliability in modern society, the complexity and reliability requirements of safety-critical systems are also rising. The failure behaviors of safety-critical systems exhibit dynamic, temporal, and correlated characteristics. Modeling and simulating complex failure mechanisms is a major challenge for the safety and reliability analysis of safety-critical systems. Currently, dynamic fault trees, binary decision graphs, Markov chains, Bayesian networks, and Petri nets are the main methods used for reliability modeling. Thanks to their flexible network structures, Petri nets can describe the asynchronous concurrency, synchronization, mutual exclusion, nondeterminism, and hierarchical failure characteristics of safety-critical systems. However, handling the complex processes, interdependencies, and workflows of large systems requires large Petri nets, leading to an explosive increase in the number of places and transitions. This results in Petri net simulations consuming significant computational resources and reducing efficiency. Therefore, developing high-performance Petri net simulation algorithms is an urgent problem to be solved. Summary of the Invention

[0003] Purpose of the invention: To address the above-mentioned shortcomings, this invention provides a reliability analysis method and system for safety-critical systems based on editable Petri nets, which solves the problems of low efficiency and high computational resource consumption of existing Petri net-based reliability analysis and evaluation methods.

[0004] Technical Solution: To solve the above problems, this invention employs a reliability analysis method for safety-critical systems based on editable Petri nets, comprising the following steps:

[0005] (1) Analyze the dynamic fault characteristics of the safety-critical system and establish an editable Petri net model; the editable Petri net model includes instantaneous transitions, random transitions and editable transitions, and the editable transitions are connected to other transitions or places through relation arcs. The editable transitions are set according to the fault logic correspondence between places.

[0006] (2) Determine the spatial dimension of dynamic fault characteristics of safety-critical systems based on the number of random transitions;

[0007] (3) Sampling is performed based on the spatial dimension of dynamic fault features to obtain a sampling point sequence;

[0008] (4) The sampling point sequence is used as the input of the Monte Carlo sampling algorithm, and the transition time is generated by inverse transformation;

[0009] (5) Based on the generated transition occurrence time, obtain the system failure probability using the Monte Carlo method;

[0010] (6) Repeat step (5) until the specified number of iterations, then fit the failure distribution of the safety-critical system and analyze the reliability of the safety-critical system.

[0011] Furthermore, the settings for the editable transition include: the triggering conditions and constraints of the editable transition; the place where the editable transition generates tokens; the place where the editable transition removes tokens; and the number of times the editable transition can be ignited (EFT). When EFT equals 0, the editable transition is not allowed to be triggered.

[0012] Furthermore, the editable Petri net model is a six-tuple. ,in:

[0013] (1) A finite set representing places. Places are used to represent resources or conditions in a system.

[0014] (2) A finite set representing transitions. A transition represents an event or behavior in a system. In an editable Petri net, transitions include the following types:

[0015] 1) Immediate transitions: These transitions have higher priority than other types of transitions and are triggered immediately once enabled. Immediate transitions can have weights, representing the relative probability of triggering a particular immediate transition under competition among multiple immediate transitions.

[0016] 2) Weibull distribution transitions: These transitions have random delays, and the delay time follows a Weibull distribution.

[0017] 3) Editable transitions: These transitions can be edited into any logic, including but not limited to priority, voting, or function-related logic.

[0018] All transitions are triggered according to the following rules:

[0019] 1) A change It can be triggered if and only if each input library it is connected to... The number of tokens satisfies Furthermore, the input library for the suppression arc does not contain a token.

[0020] 2) When a change When triggered, it consumes tokens from the input database and generates tokens in the output database. Specifically, for each input database... The number of tokens has decreased. And for each output library The number of tokens increased .

[0021] (3) : An input function that defines the input arc between places and transitions. Indicates from the warehouse To change The weight of the arc represents the triggering transition. The amount of resources or conditions required.

[0022] (4) : An output function that defines the output arc between transitions and places. Indicates change to the warehouse The weight of the arc represents the triggering transition. The number of resources or conditions generated subsequently.

[0023] (5) A suppression function that defines the suppression arc between places and transitions. If a token exists in P, even if the transition... Even if the triggering conditions are met, it cannot be triggered.

[0024] (6) : An initial token function that represents the token for each place in the initial state of the system. The token represents the quantity of resources in the system or the degree to which conditions are met.

[0025] Furthermore, in step (3), based on the dynamic fault feature space dimension, a sampling point sequence is generated through Latin hypercube sampling (LHS), and p samples are extracted from n dimensions. The LHS sampling process is as follows:

[0026] (1) Divide each dimension. For the first dimension... One dimension, , representing each dimension The boundaries of each interval are as follows:

[0027]

[0028] in It is the first Minimum value of each dimension It is the width of each interval. It is the first The maximum value of each dimension;

[0029] (2) Randomly select a point within each interval of each dimension. Let Indicates the first The first dimension A uniformly random number within a certain interval, with values ​​ranging from 1 to 2. For each interval in each dimension, the randomly selected points are calculated as follows:

[0030]

[0031] (3) Randomly pair sample points for each dimension. Generate a sample point for each dimension. Random arrangement of length Then, for each dimension and sample points The final Latin hypercube sampling points are calculated as follows:

[0032]

[0033] In Monte Carlo sampling of editable Petri nets All are 0. All are 1.

[0034] Furthermore, in step (4), the optimal Latin hypercube sample space sampling point sequence is used as the input to the Monte Carlo sampling algorithm, and the inverse transformation formula is:

[0035]

[0036] in, Let be the delay time corresponding to the time delay transition when the i-th component is sampled for the j-th time. is the scaling parameter of the Weibull distribution, and k is the shape parameter of the Weibull distribution.

[0037] Furthermore, the specific steps for obtaining the system failure time based on the Monte Carlo method in step (5) are as follows:

[0038] (5.1) Abstract the expression of the editable Petri net model and obtain the forward matrix of the editable Petri net. Backward matrix Suppression matrix , tag matrix transition delay matrix ;

[0039] (5.2) Set the number of iterations For each iteration, perform the following operations:

[0040] (5.2.1) Obtain the probability value of the optimal Latin hypercube sample space sampling point sequence and the transition delay matrix. The failure rate is obtained through step (4) to determine the time delay. Store it in a time-delay set middle;

[0041] (5.2.2) For each time Traverse all transitions and perform the following operations:

[0042] 1) Traverse all time delay transitions and update the token position according to the tag matrix and transition occurrence rules.

[0043] 2) Traverse the instant transitions and update the current label matrix if the conditions are met. .

[0044] 3) Check the location indicating system failure ( Does the device have a token? If so, set the current time. Save to the "system failure time" set and reinitialize the tag matrix. ).

[0045] (5.3) For each time ,calculate Less than or equal to in the set The number of elements ,pass Calculation time The probability of internal system failure.

[0046] This invention also employs a reliability analysis device for safety-critical systems, including a model building module for analyzing the dynamic fault characteristics of safety-critical systems and building an editable Petri net model; the editable Petri net model includes instantaneous transitions, random transitions, and editable transitions, and the editable transitions are connected to other transitions or places through relation arcs, and the editable transitions are set according to the fault logic correspondence between places;

[0047] The calculation module is used to determine the dynamic fault feature space dimension of the safety-critical system based on the number of random transitions; to perform sampling based on the dynamic fault feature space dimension to obtain a sampling point sequence; and to use the sampling point sequence as input to the Monte Carlo sampling algorithm to generate the transition occurrence time through inverse transformation.

[0048] The analysis module is used to obtain the system failure probability based on the transition occurrence time generated by the calculation module using the Monte Carlo method, and after multiple iterations, fit the failure distribution of the safety-critical system to analyze the reliability of the safety-critical system.

[0049] Beneficial effects: Compared with existing technologies, the significant advantage of this invention is the addition of editable transitions to the generalized random Petri net. These editable transitions can be defined as any fault logic as needed, replacing the addition of extra transitions and places, thus solving the problem of low efficiency in reliability analysis of safety-critical systems based on generalized random Petri nets. Furthermore, the improved Latin hypercube sampling solves the problem of low sample space filling rate in random sampling, making it suitable for large-scale safety-critical systems. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating the reliability analysis method in this invention.

[0051] Figure 2 In the diagram, (a) represents the editable Petri net model with priority AND gates. Figure 2 (b) in the model is a generalized stochastic Petri net model.

[0052] Figure 3 This is a schematic diagram of a dynamic fault tree for a cardiac assist system.

[0053] Figure 4 This is a schematic diagram of a generalized stochastic Petri net model for a cardiac assist system.

[0054] Figure 5 This is a schematic diagram of an editable Petri net model for a cardiac assist system.

[0055] Figure 6 This diagram illustrates the convergence of unreliability in Latin hypercube sampling and random sampling. Detailed Implementation

[0056] like Figure 1 As shown in this embodiment, a reliability analysis method for a safety-critical system based on an editable Petri net includes the following steps:

[0057] Step 1: Analyze the dynamic fault characteristics of safety-critical systems and establish an editable Petri net model;

[0058] An editable Petri net is a six-tuple ,in:

[0059] A finite set representing places. Places are used to represent resources or conditions in a system.

[0060] A finite set representing a transition. A transition represents an event or behavior in the system.

[0061] : An input function that defines the input arc between places and transitions. Indicates from the warehouse To change The weight of the arc represents the triggering transition. The amount of resources or conditions required.

[0062] : An output function that defines the output arc between transitions and places. Indicates change to the warehouse The weight of the arc represents the triggering transition. The number of resources or conditions generated subsequently.

[0063] A suppression function that defines the suppression arc between places and transitions. If a token exists in P, even if the transition... Even if the triggering conditions are met, it cannot be triggered.

[0064] : An initial token function that represents the token for each place in the initial state of the system. The token represents the quantity of resources in the system or the degree to which conditions are met.

[0065] An editable Petri net includes the following transitions:

[0066] Immediate transitions: These transitions have higher priority than other types of transitions and are triggered immediately once enabled. Immediate transitions can have weights, representing the relative probability of triggering a particular immediate transition under competition among multiple immediate transitions.

[0067] Weibull distribution transitions: These transitions have random delays, and the delay time follows a Weibull distribution.

[0068] Editable transitions: These transitions can be edited into any logic, including but not limited to priority, voting, or function-related logic.

[0069] All transitions are triggered according to the following rules:

[0070] A change It can be triggered if and only if each input library it is connected to... The number of tokens satisfies Furthermore, the input library for the suppression arc does not contain a token.

[0071] When a change When triggered, it consumes tokens from the input database and generates tokens in the output database. Specifically, for each input database... The number of tokens has decreased. And for each output library The number of tokens increased .

[0072] An editable Petri net contains an editable transition, which can be configured with any logic, such as a priority AND gate, represented by a black diamond. Editable Petri nets introduce relation arcs, specifically designed to connect editable transitions to other transitions or places, represented by dashed lines.

[0073] Editable transitions consist of the following four parts:

[0074] (1) Triggering conditions and constraints for editable transitions.

[0075] (2) A library of editable transitions that generate tokens.

[0076] (3) Editable migration of tokens in the library.

[0077] (4) The number of times an editable transition can be fired (EFT). When EFT equals 0, an editable transition is not allowed to be fired.

[0078] Figure 2 (b) in the figure shows a generalized stochastic Petri net model of the PAND gate. This fault logic needs to reflect the sequence of events, so additional transitions and places are required to build the generalized stochastic Petri net model. Figure 2 (a) shows an editable Petri net model of the priority AND gate, which replaces the PAND logic with an editable transition T2.

[0079] Step 2: Abstract the representation of the editable Petri net;

[0080] Obtain the forward matrix of an editable Petri net Backward matrix Suppression matrix , tag matrix transition delay matrix .

[0081] Step 3: Determine the dimension of the sample space based on the number of random transitions;

[0082] Determine the number of random transitions in an editable Petri net. If there are n random transitions, then the dimension of the sample space is n.

[0083] Step 4: Based on the sample space dimension, generate a sequence of sample space sampling points using the Latin Hypercube Sampling Algorithm (LHS).

[0084] The LHS sampling process involves drawing p samples from n dimensions as follows:

[0085] (1) Divide each dimension. For the first dimension... One dimension, , representing each dimension The boundaries of each interval are as follows:

[0086]

[0087] in It is the first Minimum value of each dimension It is the width of each interval. It is the first The maximum value of each dimension;

[0088] (2) Randomly select a point within each interval of each dimension. Let Indicates the first The first dimension A uniformly random number within a certain interval, with values ​​ranging from 1 to 2. For each interval in each dimension, the randomly selected points are calculated as follows:

[0089]

[0090] (3) Randomly pair sample points for each dimension. Generate a sample point for each dimension. Random arrangement of length Then, for each dimension and sample points The final Latin hypercube sampling points are calculated as follows:

[0091]

[0092] In Monte Carlo sampling of editable Petri nets All are 0. All are 1.

[0093] Step 5: Calculate the Euclidean distance between sampling points to obtain the minimum sampling point spacing of the sampling point sequence in the sample space. Based on the number of iterations, maximize the minimum sampling point spacing to obtain the optimal Latin hypercube sampling point sequence.

[0094] Given two sample points and ( and ), the Euclidean distance between them It can be calculated using the following formula:

[0095]

[0096] The minimum Euclidean distance between all sample points is expressed by the following formula. :

[0097]

[0098] Based on the number of iterations, find the case where d is maximized. ;

[0099] Step 6: Use the optimal Latin hypercube sample space sampling point sequence calculated in Step 5 as input to the Monte Carlo sampling algorithm, and generate the transition time through inverse transformation;

[0100] In reliability analysis, component failure distribution is generally an exponential distribution. The inverse transformation formula of the Weibull distribution is shown below:

[0101]

[0102] in, Let be the delay time corresponding to the time delay transition when the i-th component is sampled for the j-th time. is the scaling parameter of the Weibull distribution, and k is the shape parameter of the Weibull distribution.

[0103] Step 7: Using the transition time calculated in Step 6 as input, the system failure probability is obtained based on the Monte Carlo method using the editable Petri net abstraction method from Step 2.

[0104] The Monte Carlo method is as follows:

[0105] (1) Abstract the expression of the editable Petri net model and obtain the forward matrix of the editable Petri net. Backward matrix Suppression matrix , tag matrix transition delay matrix ;

[0106] (2) Set the number of iterations For each iteration, perform the following operations:

[0107] (2.1) Obtain the probability value of the optimal Latin hypercube sample space sampling point sequence and the transition delay matrix. The failure rate is obtained through step (4) to determine the time delay. Store it in a time-delay set middle;

[0108] (2.2) For each time Traverse all transitions and perform the following operations:

[0109] 1) Traverse all time delay transitions and update the token position according to the tag matrix and transition occurrence rules.

[0110] 2) Traverse the instant transitions and update the current label matrix if the conditions are met. .

[0111] 3) Check the location indicating system failure ( Does the device have a token? If so, set the current time. Save to the "system failure time" set and reinitialize the tag matrix. ).

[0112] (3) For each time ,calculate Less than or equal to in the set The number of elements ,pass Calculation time The probability of internal system failure.

[0113] Step 8: Repeat step 7 until the specified number of iterations, fit the system fault distribution, and analyze the reliability of the safety-critical system.

[0114] This example uses a cardiac assist system as the test object. The system consists of four modules: triggers, a CPU unit, a motor section, and a pump, which are used as a repository for an editable Petri net. The triggers consist of a crossbar switch (CS) and a system monitor (SS). A failure of either CS or SS triggers a failure of both CPUs. The CPU unit is a warm-switch unit with a primary P and a backup B, and a sleep rate of 0.54. For the motor section (MOTORSECT) to function properly, either MOTOR or MOTORC needs to be operational. The pump unit consists of two cold-switch units, each with a primary pump (PUMP_1 and PUMP_2) and sharing a backup pump (Backup_PUMP). For the pump unit to fail, all three pumps must fail, and CSP_1 must fail before (or simultaneously with) CSP_2. All components of the cardiac assist system have an exponentially distributed reliability function.

[0115] Figure 4 and Figure 5 The generalized stochastic Petri net model and the editable Petri net model of the cardiac assist system are presented. Table 1 shows the definition of editable transitions in the editable Petri net model of the cardiac assist system, and Table 2 shows the comparison of simulation results. The simulation results demonstrate that the method proposed in this embodiment can reduce the simulation time of Petri nets and increase computational efficiency while ensuring computational accuracy. Figure 6This paper presents a comparison between improved Latin hypercube sampling and random sampling, where LHS represents the unreliability convergence curve of improved Latin hypercube sampling, and Random represents the unreliability convergence curve of random sampling. The x-axis represents sample size, and the y-axis represents the unreliability of the cardiac assist system. Figure 6 It can be seen that the improved Latin hypercube sampling converges faster than random sampling, proving the effectiveness of the method proposed in this invention.

[0116] Table 1. Definitions of editable transitions in the editable Petri net model of cardiac assist systems.

[0117] T1 Editable transition T1 Set EFT = 1 If EFT>0 if CS.dn or SS.dn>0: P.dn and B.dn gets a token EFT = 0 T2 Editable transition T2 Set EFT = 1 If EFT>0 if P.dn>0: if B.dn>0: Part1.dn gets a token EFT = 0 else B.work gets a token B.up removes a token T3 Editable transition T3 Set EFT = 1 If EFT>0 if MS.dn>0: if MA.dn>0: PAND.dn gets a token EFT = 0 T4 Editable transition T4 Set EFT = 1 If EFT>0 if MA.dn>0: if MB.dn>0: CSP1.dn gets a token EFT = 0 else MB.work gets a token MB.up removes a token T5 Editable transition T5 Set EFT = 1 If EFT>0 if PA.dn or PB.dn>0: if PS.dn>0: Part3.dn gets a token EFT = 0 else PS.work gets a token PS.up removes a token T6 Editable transition T6 Set EFT = 1 If EFT>0 if Part1.dn or Part2.dn or Part3.dn>0: TE gets a token EFT = 0

[0118] Table 2 Comparison of Generalized Random Petri Nets and Editable Petri Nets

[0119] Generalized Stochastic Petri Net 0.6593 1705 Editable Petri Net 0.6571 861

Claims

1. A reliability analysis method for safety-critical systems based on editable Petri nets, characterized in that, Includes the following steps: (1) Analyze the dynamic fault characteristics of safety-critical systems and establish an editable Petri net model; The editable Petri net model includes instantaneous transitions, random transitions, and editable transitions. Editable transitions connect other transitions or locations through relational arcs. The editable transitions are configured according to the fault logic correspondence between locations. The safety-critical systems include a heart support system, a flight control system, and a vehicle-to-ground communication system. (2) Determine the spatial dimension of dynamic fault characteristics of safety-critical systems based on the number of random transitions; (3) Based on the dynamic fault feature space dimension, perform Latin hypercube sampling (LHS) to obtain the sampling point sequence; (4) The sampling point sequence is used as the input of the Monte Carlo sampling algorithm, and the transition time is generated by inverse transformation; (5) Based on the generated transition occurrence time, obtain the system failure probability using the Monte Carlo method; (6) Repeat step (5) until the specified number of iterations, then fit the failure distribution of the safety-critical system and analyze the reliability of the safety-critical system; The settings for editable transitions include: triggering conditions and constraints for editable transitions; the location of tokens generated by editable transitions; the location of tokens removed by editable transitions; and the number of times an editable transition can be ignited (EFT). When EFT equals 0, triggering an editable transition is not allowed. The editable Petri net model is a six-tuple. ,in: (1) It is a finite set representing places, which are used to represent resources or conditions in the system; (2) It is a finite set representing transitions, where a transition represents an event or behavior in the system; All transitions are triggered according to the following rules: 1) A change The triggering occurs if and only if the transition... Each input library connected The number of tokens satisfies Furthermore, the input library for the suppression arc does not contain a token; 2) When a change When triggered, the transition The tokens consumed from the input database and the tokens generated in the output database are used to generate tokens for each input database. The number of tokens has decreased. And for each output library The number of tokens increased ; (3) It is an input function that defines the input arc between places and transitions; Indicates from the warehouse To change The weights of the input arcs represent the triggering transitions. The required quantity of resources or conditions; (4) It is an output function that defines the output arc between transitions and places; Indicates change to the warehouse The weight of the output arc represents the trigger transition. The number of resources or conditions generated subsequently; (5) It is a suppression function that defines the suppression arc between places and transitions; if a token exists in P, even if the transition... Even if the triggering conditions are met, it cannot be triggered. (6) It is an initial token function that represents the token of each place in the initial state of the system; the token represents the amount of resources in the system or the degree to which conditions are met.

2. The reliability analysis method for safety-critical systems according to claim 1, characterized in that, In step (3), based on the dynamic fault feature space dimension, a sampling point sequence is generated by Latin hypercube sampling (LHS), and p samples are extracted from n dimensions. The LHS sampling process is as follows: (1) Divide each dimension into The interval, for the first interval One dimension, The first of each dimension The boundaries of each interval are as follows: ； in It is the first Minimum value of each dimension It is the width of each interval. It is the first The maximum value of each dimension; (2) Randomly select a point within each interval of each dimension, and let Indicates the first The first dimension A uniformly random number within a certain interval, with values ​​ranging from 1 to 2. For each interval in each dimension, the location of the randomly selected point is calculated as follows: ； (3) Randomly pair sample points for each dimension to generate a sample point for each dimension. Random arrangement of length Then, for each dimension No. The final Latin hypercube sampling points are calculated as follows: (The sample points are within a certain interval.) ； In Monte Carlo sampling of editable Petri nets All are 0. All are 1.

3. The reliability analysis method for safety-critical systems according to claim 2, characterized in that, Based on the sampling point sequence generated by Latin hypercube sampling (LHS), the Euclidean distance between the sampling points is calculated to obtain the minimum sampling point spacing in the sample space. Then, based on the number of iterations, the minimum sampling point spacing is maximized to obtain the optimal Latin hypercube sample space sampling point sequence. (Two sample points...) and ( and Euclidean distance between ) The calculation formula is: ； Minimum Euclidean distance between all sample points The calculation formula is: ； Based on the number of iterations, find the case where d is maximized. .

4. The reliability analysis method for safety-critical systems according to claim 3, characterized in that, In step (4), the optimal Latin hypercube sample space sampling point sequence is... As input to the Monte Carlo sampling algorithm, the inverse transform formula is: ； in, Let be the delay time corresponding to the time delay transition of the i-th component during the j-th sampling. is the scaling parameter of the Weibull distribution, and k is the shape parameter of the Weibull distribution.

5. The reliability analysis method for safety-critical systems according to claim 4, characterized in that, The specific steps for obtaining the system fault time based on the Monte Carlo method in step (5) are as follows: (5.1) Abstract the expression of the editable Petri net model and obtain the forward matrix of the editable Petri net. Backward matrix Suppression matrix , tag matrix transition delay matrix ; (5.2) Set the number of iterations For each iteration, perform the following operations: (5.2.1) Obtain the probability value of the optimal Latin hypercube sample space sampling point sequence and the transition delay matrix. The failure rate is obtained through step (4) to determine the time delay. Store it in a time-delay set middle; (5.2.2) For each time Traverse all transitions and perform the following operations: 1) Traverse all delay transitions and update the token position according to the tag matrix and transition occurrence rules; 2) Traverse the instant transitions and update the current label matrix if the conditions are met. ; 3) Check if there is a token at the location indicating system failure. If so, set the current time. Save to In the set, and reinitialize the tag matrix; (5.3) For each time ,calculate Less than or equal to in the set The number of elements ,pass Calculation time The probability of internal system failure.

6. The reliability analysis method for safety-critical systems according to claim 1, characterized in that, An editable Petri net model is established for the cardiac assist system, with places representing triggers, CPU units, motor parts and pumps, and transitions representing place failures.

7. An apparatus for a reliability analysis method for safety-critical systems according to claim 1, characterized in that, It includes a model building module for analyzing the dynamic fault characteristics of safety-critical systems and building an editable Petri net model; the editable Petri net model includes instantaneous transitions, random transitions and editable transitions, and the editable transitions are connected to other transitions or places through relation arcs, and the editable transitions are set according to the fault logic correspondence between places; The calculation module is used to determine the dynamic fault characteristic space dimension of a safety-critical system based on the number of random transitions. Sampling is performed based on the dynamic fault feature space dimension to obtain a sampling point sequence; the sampling point sequence is used as the input of the Monte Carlo sampling algorithm, and the transition occurrence time is generated through inverse transformation; The analysis module is used to obtain the system failure probability based on the transition occurrence time generated by the calculation module using the Monte Carlo method, and after multiple iterations, fit the failure distribution of the safety-critical system to analyze the reliability of the safety-critical system.

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