A multi-stage task system reliability comprehensive allocation method

Abstract

This invention designs a comprehensive reliability allocation technique for multi-stage task systems. Addressing the issue that existing technologies, by neglecting prior information about units and actual runtime, may lead to unreasonable allocation results, this invention integrates allocation weights obtained from the analytic hierarchy process (AHP) and prior unit failure rates using a logarithmic pooling method. Combined with the system reliability structure function, a linear equation system of failure rate indices is constructed. Solving this equation system yields the unit reliability allocation index. This invention comprehensively considers the actual runtime of units, prior information, and various engineering factors. The constructed linear equation system allocation model of failure rate indices improves the accuracy and computational efficiency of multi-stage task system reliability allocation models, and solves the problem that some results are overly conservative when general allocation methods are used for reliability allocation in multi-stage task systems. It provides support and decision-making for overall reliability design and has significant engineering application value.

Description

Technical Field

[0001] This invention relates to the field of system reliability design, and specifically to a method for comprehensive reliability allocation in a multi-stage task system. Background Technology

[0002] Currently, various system reliability allocation techniques have been developed, among which weight-based reliability allocation is the mainstream approach. Its core idea is to obtain a set of allocation weights through certain means and then allocate system reliability indicators according to these weights. However, research on reliability allocation for multi-stage task systems remains limited. A multi-stage task system refers to a system that executes a series of different tasks sequentially. Throughout the task execution process, subsystems and units dynamically join, persist, and exit as the task progresses, resulting in different unit combinations at different stages. The same unit may have different reliability levels at different stages, therefore, the actual runtime of each critical unit in the system is not necessarily the total task duration. In engineering, it is generally assumed that the reliability of a unit follows an exponential distribution relationship related to the unit failure rate and runtime. At the same reliability level, the longer the required runtime of a unit, the lower the required failure rate, which translates to a longer MTBF (Mean Time Between Failures), meaning a higher reliability requirement for the unit. Therefore, for multi-stage task systems, the actual runtime of units must be considered when allocating system reliability to assign more reasonable reliability indicators to each unit.

[0003] The commonly used reliability allocation method for multi-stage task systems in engineering is to assign indicators to the stage with the most deployed equipment based on the general reliability allocation method described above. This may lead to problems such as a coarse allocation model and overly conservative allocation results for some units, making it impossible for the system to achieve a reliability balance design, affecting overall reliability and even economy. Current multi-stage task system reliability indicator allocation techniques are mainly based on optimization methods. These allocation methods do not consider the different characteristics of the deployed units in different stages of some multi-stage task systems and require multiple iterations. Some researchers have considered the characteristics of multi-stage task systems with different units in different task stages. They first distribute the square root of the system reliability indicator equally to each stage, calculate the reliability of the deployed units in each stage using a modified scoring method, and then multiply and square root the reliability obtained from the different stages for each unit to obtain the final reliability indicator. However, the modified scoring method still requires multiple iterations to calculate the difference between the allocated reliability and the target reliability. Furthermore, this method does not consider the differences between stages, prior information of the equipment, and actual operating time when decomposing the system reliability indicator, which may also lead to unreasonable allocation results. Therefore, it is necessary to propose a new comprehensive reliability allocation method for multi-stage task systems that considers prior information of the equipment and actual operating time and does not require iterative solutions to meet the design requirements of practical engineering. Summary of the Invention

[0004] This invention proposes a comprehensive reliability allocation method for multi-stage task systems, which solves the problem that existing reliability allocation methods do not consider prior equipment information and actual runtime.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention proposes a comprehensive reliability allocation method for multi-stage task systems, which solves the problem that existing reliability allocation methods do not consider prior equipment information and actual runtime.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention proposes a method for comprehensive reliability allocation in a multi-stage task system, the method comprising: Step 1: Calculate the prior failure rate and total running time for each unit to be assigned reliability metrics. The prior failure rate is denoted as... The total running time is recorded as ; Step 2: Calculate the failure rate index for the entire system task cycle. λ s; Step 3: Establish system failure rate metric λs and total task time. Equations between; Step 4: Assign the unit failure efficiency vector for each reliability metric to be assigned. Transform into an allocation coefficient vector that takes prior information into account. ; Step 5: Determine based on project requirements Y Based on the allocation criteria, an analytic hierarchy process (AHP) model is established to calculate the AHP allocation coefficient vector of the playlist. ; Step Six: Assign coefficient vectors based on prior information from each unit. Calculate the unit fusion allocation coefficient vector ; Step 7: Combine unit fusion and allocation coefficient vector Establish pairwise relationships between unit failure rate indices and construct a system of linear equations; Step 8: Solve the system of linear equations from Step 7 to obtain the final failure rate index for each device. It can be converted into a severe mean time between failures (MTBF) indicator. .

[0007] In some embodiments, the failure rate index in step two The calculation is as shown in formula (1): (1) in, It serves as a reliability indicator for the entire system mission lifecycle. For the first n The duration of each task profile N This represents the total number of task profiles. .

[0008] In some embodiments, the equation constructed in step three is as shown in formula (2): (2) in, For the first i The failure rate index of each unit. for i Total runtime of each unit i =1,2,…, K , As a system reliability indicator, Total system task duration; In some embodiments, step four involves assigning the cell prior failure rate vector of each reliability metric to be assigned. Transform into an allocation coefficient vector that takes prior information into account. The specific conversion method is shown in formula (3): (3) in, For the first i Allocation coefficients for each unit, taking into account prior information. For the first i The prior failure rate of each unit can be obtained from historical data of similar products.

[0009] In some embodiments, step five specifically includes: Step 5.1: Assign the importance of the allocation criteria to the system reliability index using a 1-9 scale to construct a "criteria-system reliability index" judgment matrix A. r-o The importance of each unit relative to each allocation criterion is scored using a scale of 1 to 9, constructing a "unit-criterion" judgment matrix A. cx-r1 A cx-r2 ,...,A cx-rY ; Step 5.2: Solve for the judgment matrix A r-o and A cx-ry The eigenvectors and the largest eigenvalue, y =1,2,…, Y ; Step 5.3: For the judgment matrix A r-o and A cx-ry Perform a consistency check. y =1,2,…, Y ; Step 5.4: If the consistency check fails, return to Step 6 for rescoring; if it passes, calculate the global combined weight vector for each unit to be assigned a reliability index. ; Step 5.5: Calculate the analytic hierarchy process (AHP) allocation coefficients for each unit. ; In some embodiments, the solution formula in step 5.2 is as shown in formula (4): (4) Where A is the judgment matrix, that is, the judgment matrix A r-o and A cx-ry , Let E be the largest eigenvalue, E be the eigenvector, and A be the largest eigenvalue. r-o The eigenvectors obtained by solving are E r-o A cx-ry The eigenvectors obtained by solving are E cx-ry , y =1,2,…, Y .

[0010] In some embodiments, step 5.3 involves judging matrix A. r-o and A cx-ry The consistency check specifically involves calculating whether the consistency ratio C·R is less than 0.1. The formulas for calculating the consistency ratio C·R are shown in formulas (5) and (6): (5) (6) Wherein, C•I is the consistency index of the pairwise judgment matrices. m Let m be the order of the matrix, and R·I be the random consistency index. Table 2 shows the relationship between R·I and m.

[0011] In some embodiments, step 5.4 calculates the global combined weight vector of each unit for which a reliability metric to be assigned. The specific calculation formulas are as follows: (7) and (8): (7) (8) in, for E r-o The normalized vector obtained by formula (8) for E cx-ry The normalized vector obtained by formula (8) Y For the number of criteria, K The number of units; This represents the normalized vector, i.e. and , This represents the eigenvector, which is... E r-o and E cx-ry , y =1,2,..., Y .

[0012] In some embodiments, the specific calculation formula for the analytic hierarchy process (AHP) coefficient vector allocation in step 5.5 is as shown in formula (9): (9) in, For the first i The analytic hierarchy process (AHP) assigns coefficient vectors to each unit. For the first i The global combined weight vector of each unit.

[0013] In some embodiments, step six involves fusing the assigned coefficient vector. The specific calculation formula is formula (10): (10) in, V 1 represents the prior information allocation coefficient vector obtained from equation (3). V 2 is the analytic hierarchy process (AHP) coefficient vector obtained from equation (9). These are the normalization coefficients; the specific linear equation system in step seven is shown in formula (11): (11) in, This is a system failure rate indicator. Total task time. For the first i Total runtime of each unit For the first i The unit fusion allocation coefficient vector of each unit. For the first i The failure rate index of each unit. i =1,2,…, K Step Thirteen: Serious Time Without Failure (SLF) Indicator The specific calculation method is shown in formula (12): (12) in, For the first i The final failure rate index assigned to each device. For the first iThe critical time-to-failure (MTBF) index ultimately assigned to each device. i =1,2,…, K .

[0014] The following beneficial effects can be obtained by implementing the present invention: 1. This invention designs a comprehensive reliability allocation method for multi-stage task systems. Addressing the problem that existing multi-stage task system reliability allocation techniques fail to consider prior information of units and actual runtime, potentially leading to unreasonable allocation results, this invention integrates allocation weights obtained from the analytic hierarchy process (AHP) and prior unit failure rate data using a logarithmic pooling method. Combined with the system reliability relation, a system of linear equations for unit failure rate and system failure rate is constructed. Solving this system yields a unit failure rate allocation index that considers prior unit information, actual runtime, and various engineering factors. This enables the reasonable allocation of reliability indicators for key units in multi-stage task systems and a balanced design for system reliability.

[0015] 2. This invention designs a comprehensive reliability allocation method for multi-stage task systems. This invention can handle the reliability allocation problem of multi-stage task systems. The allocation comprehensively considers the actual runtime of units, prior reliability data, and various engineering factors. The linear equation system allocation model for failure rate indices constructed based on this model can improve the accuracy and computational efficiency of the reliability allocation model for multi-stage task systems, and solves the problem that some results are too conservative when general allocation methods are used for reliability allocation in multi-stage task systems. This technology can improve the system reliability allocation method, realize the reasonable allocation of reliability indices for multi-stage task systems, provide support and decision-making for overall reliability design, and has good engineering application value. Attached Figure Description

[0016] Figure 1 This is a flowchart of a multi-stage task system reliability comprehensive allocation method proposed in an embodiment of the present invention; Figure 2 This is a schematic diagram of the system hierarchy analysis model of a multi-stage task system reliability comprehensive allocation method proposed in an embodiment of the present invention. Detailed Implementation

[0017] This invention designs a comprehensive reliability allocation method for multi-stage task systems. Addressing the problem that existing multi-stage task system reliability allocation techniques fail to consider prior information of units and actual runtime, potentially leading to unreasonable allocation results, this invention integrates allocation weights obtained from the analytic hierarchy process (AHP) and prior failure rate data of units using a logarithmic pooling method. Combined with the system reliability relation, a system of linear equations for multi-stage task system failure rate indices is constructed, comprehensively considering prior information of units, actual runtime, and various engineering factors. Solving this system of equations achieves a reasonable allocation of system reliability indices. First, the prior failure rate and total runtime of each unit to be allocated are statistically analyzed, and the system reliability indices are converted into failure rate indices. A linear relationship between unit failure rate indices, actual runtime, system failure rate indices, and total task time can be established based on the system reliability structure function. Then, based on the prior failure rate of each unit, the prior information allocation coefficient vector is determined by taking the reciprocal and normalizing. V 1. Then, use the Analytic Hierarchy Process (AHP) to obtain the AHP allocation coefficient vector considering other engineering factors. V 2. Next, the two coefficient vectors are processed using logarithmic pooling to obtain the unit fusion allocation coefficient vector. V This leads to the establishment of pairwise failure rate ratios for individual units as supplementary equations. These equations, combined with the relationships between unit failure rate indices and system failure rate indices, form a system of K linear equations (K being the number of units) representing unit failure rates. Finally, solving this system of linear equations yields the unit failure rate indices, which are then converted into severe mean time between failures (MTBF) indices, etc.

[0018] This invention proposes a method for comprehensive reliability allocation in a multi-stage task system, the method comprising: Step 1: Calculate the prior failure rate and total running time of each unit to be assigned reliability metrics, and record them as follows: and Where C1, C2, ..., CK are the units for each reliability index to be assigned.

[0019] Step 2: Based on the system's full-task-cycle reliability index The success rate index was calculated. The specific calculation is as shown in formula (1): (1) in, It serves as a reliability indicator for the entire system mission lifecycle. For the first n The duration of each task profile N Total number of task profiles Step 3: Establish system failure rate indicators and the failure rate index to be solved for each unit The equation is given by formula (2): (2) in, Total system task time. The total runtime of each unit. i =1,2,…, K。

[0020] Step 4: Assign the unit failure efficiency vector for each reliability metric to be assigned. Transform into an allocation coefficient vector that takes prior information into account. The conversion method is as shown in formula (3): (3) in, Let be the allocation coefficient for the i-th unit, taking into account prior information. For the first i The prior failure rate of each unit can be obtained from historical data of similar products.

[0021] Step 5: Determine allocation criteria based on project requirements, such as work environment, technical level, and importance, and establish a system for allocation. Figure 2 The Analytic Hierarchy Process (AHP) model is shown. It is determined based on engineering requirements. Y Based on the allocation criteria, an analytic hierarchy process (AHP) model is established to calculate the AHP allocation coefficient vector of the playlist. .

[0022] Step 5.1: Assign the importance of the allocation criteria to the system reliability index using a 1-9 scale to construct a "criteria-system reliability index" judgment matrix A. r-o The importance of each unit relative to each allocation criterion is scored using a scale of 1 to 9, constructing a "unit-criterion" judgment matrix A. cx-ry ,in, y =1,2,…, Y The meanings of each scale are shown in Table 1. a ij Represents the first in the judgment matrix i Line number j Elements in the column; Table 1.1-9 Definition Table of Scale Method Step 5.2: Solve for the judgment matrix A r-o and A cx-ry The eigenvectors and the largest eigenvalue are calculated using formula (4): (4) Where A is the judgment matrix, that is, the judgment matrix Ar-o and A cx-ry , Let E be the largest eigenvalue, E be the eigenvector, and A be the largest eigenvalue. r-o The eigenvectors obtained by solving are E r-o A cx-ry The eigenvectors obtained by solving are E cx-ry , y =1,2,…, Y .

[0023] Step 5.3: For the judgment matrix A r-o and A cx-ry Perform a consistency test to determine whether the consistency ratio C·R is less than 0.1. The formulas for calculating the consistency ratio C·R are shown in formulas (5) and (6): (5) (6) Wherein, C•I is the consistency index of the pairwise judgment matrices. m Let m be the order of the matrix, and R·I be the random consistency index. Table 2 shows the relationship between R·I and m. Table 2 Random Consistency Index R·I Step 5.4: If the consistency check fails, return to Step 6 for rescoring; if it passes, calculate the global combined weight vector for each unit to be assigned a reliability index. The specific calculation formulas are as follows: (7) and (8): (7) (8) in, for E r-o The normalized vector obtained by formula (8) for E cx-ry The normalized vector obtained by formula (8) Y For the number of criteria, K The number of units; This represents the normalized vector, i.e. and , This represents the eigenvector, which is... E r-o and E cx-ry , y =1,2,..., Y .

[0024] Step 5.5: Calculate the analytic hierarchy process (AHP) allocation coefficients for each unit. The specific calculation formula is shown in formula (9): (9) in, For the first i The analytic hierarchy process (AHP) assigns coefficient vectors to each unit. For the first i The global combined weight vector of each unit.

[0025] Step 6: Calculate the unit fusion allocation coefficient vector The specific calculation formula is formula (10): (10) in, V 1 represents the prior information allocation coefficient vector obtained from equation (3). V 2 is the analytic hierarchy process (AHP) coefficient vector obtained from equation (9). This is the normalization coefficient.

[0026] Step 7: Combine unit fusion and allocation coefficient vector Establish pairwise relationships for unit failure rate indices and construct a system of linear equations, as shown in formula (11): (11) in, This is a system failure rate indicator. Total system task time. For the first i Total runtime of each unit For the first i The unit fusion allocation coefficient vector of each unit. For the first i The failure rate index of each unit. i =1,2,…, K .

[0027] Step 8: Solve the system of linear equations from Step 7 to obtain the final failure rate index for each device. And convert it into a severe mean time between failures (MTBF) metric. The specific calculation method is shown in formula (12): (12) in, For the first i The final failure rate index assigned to each device. For the first i The critical time-to-failure (MTBF) index ultimately assigned to each device.i =1,2,…, K .

[0028] The above description is a further detailed explanation of the present invention in conjunction with specific preferred embodiments. It should not be considered that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of patent protection determined by the submitted claims.

Claims

1. A method for comprehensive reliability allocation in a multi-stage task system, characterized in that, The method includes: Step 1: Calculate the prior failure rate and total running time for each unit to be assigned reliability metrics. The prior failure rate is denoted as... The total running time is denoted as ; Step 2: Calculate the failure rate index for the entire system task cycle. ; Step 3: Establish unit failure rate indicators Total unit runtime System failure rate indicators and total task time Equations between them i =1,2,…, K ; Step 4: Assign the unit failure efficiency vector for each reliability metric to be assigned. Transform into an allocation coefficient vector that takes prior information into account. ; Step 5: Determine based on project requirements Y Based on the allocation criteria, an analytic hierarchy process (AHP) model is established to calculate the AHP allocation coefficient vector of the playlist. ; Step Six: Assign coefficient vectors based on prior information from each unit. Calculate the unit fusion allocation coefficient vector ; Step 7: Combine the unit fusion and allocation coefficient vector Establish pairwise relationships between unit failure rate indices and construct a system of linear equations; Step 8: Solve the system of linear equations from Step 7 to obtain the final failure rate index for each device. It can be converted into a severe mean time between failures (MTBF) indicator. .

2. The multi-stage task system reliability comprehensive allocation method according to claim 1, characterized in that, Failure rate index in step two The calculation is as shown in formula (1): （1） in, It serves as a reliability indicator for the entire system task lifecycle. For the first n The duration of each task profile N This represents the total number of task profiles. .

3. The multi-stage task system reliability comprehensive allocation method according to claim 1, characterized in that, The equation constructed in step three is as shown in formula (2): （2） in, For the first i The failure rate index of each unit. for i Total runtime of each unit i =1,2,…, K , As a system reliability indicator, This represents the total system task duration.

4. The multi-stage task system reliability comprehensive allocation method according to claim 3, characterized in that, In step four, the prior failure rate vector of each reliability index to be assigned is... Transform into an allocation coefficient vector that takes prior information into account. The specific conversion method is shown in formula (3): （3） in, For the first i Allocation coefficients for each unit, taking into account prior information. For the first i The prior failure rate of each unit can be obtained from historical data of similar products.

5. The multi-stage task system reliability comprehensive allocation method according to claim 4, characterized in that, Step five specifically includes: Step 5.1: Assign the importance of the allocation criteria to the system reliability index using a 1-9 scale to construct a "criteria-system reliability index" judgment matrix A. r-o The importance of each unit relative to each allocation criterion is scored using a scale of 1 to 9, constructing a "unit-criterion" judgment matrix A. cx-r1 A cx-r2 ,...,A cx-rY ; Step 5.2: Solve for the judgment matrix A r-o and A cx-ry The eigenvectors and the largest eigenvalue, y =1,2,…, Y ; Step 5.3: For the judgment matrix A r-o and A cx-ry Perform a consistency check. y =1,2,…, Y ; Step 5.4: If the consistency check fails, return to Step 6 for rescoring; if it passes, calculate the global combined weight vector for each unit to be assigned a reliability index. ; Step 5.5: Calculate the analytic hierarchy process (AHP) allocation coefficients for each unit. .

6. The multi-stage task system reliability comprehensive allocation method according to claim 5, characterized in that, The solution formula in step 5.2 is as shown in formula (4): （4） Where A is the judgment matrix, that is, the judgment matrix A r-o and A cx-ry , Let E be the largest eigenvalue, E be the eigenvector, and A be the largest eigenvalue. r-o The eigenvectors obtained by solving are E r-o A cx-ry The eigenvectors obtained by solving are E cx-ry , y =1,2,…, Y .

7. The multi-stage task system reliability comprehensive allocation method according to claim 6, characterized in that, In step 5.3, the judgment matrix A is... r-o and A cx-ry The consistency check specifically involves calculating whether the consistency ratio C·R is less than 0.

1. The formulas for calculating the consistency ratio C·R are shown in formulas (5) and (6): （5） （6） Wherein, C•I is the consistency index of the pairwise judgment matrices. m Let m be the order of the matrix, and R·I be the random consistency index. Table 2 shows the relationship between R·I and m.

8. The multi-stage task system reliability comprehensive allocation method according to claim 7, characterized in that, In step 5.4, the global combined weight vector of each unit to be assigned a reliability index is calculated. The specific calculation formulas are as follows: (7) and (8): （7） （8） in, for E r-o The normalized vector obtained by formula (8) for E cx-ry The normalized vector obtained by formula (8) Y For the number of criteria, K The number of units; This represents the normalized vector, i.e. and , This represents the eigenvector, which is... E r-o and E cx-ry , y =1,2,..., Y .

9. The multi-stage task system reliability comprehensive allocation method according to claim 7, characterized in that, The specific calculation formula for the analytic hierarchy process (AHP) coefficient vector allocation in step 5.5 is shown in formula (9): （9） in, For the first i The analytic hierarchy process (AHP) assigns coefficient vectors to each unit. For the first i The global combined weight vector of each unit.

10. The multi-stage task system reliability comprehensive allocation method according to claim 9, characterized in that, Step six involves merging and allocating the coefficient vector. The specific calculation formula is formula (10): （10） in, V 1 represents the prior information allocation coefficient vector obtained from equation (3). V 2 is the analytic hierarchy process (AHP) coefficient vector obtained from equation (9). These are the normalization coefficients; the linear equation system in step twelve is specifically shown in formula (11): （11） in, This is a system failure rate indicator. Total task time. For the first i Total runtime of each unit For the first i The unit fusion allocation coefficient vector of each unit. For the first i The failure rate index of each unit. i =1,2,…, K The severe time-to-failure index in step thirteen. The specific calculation method is shown in formula (12): （12） in, For the first i The final failure rate index assigned to each device. For the first i The critical time-to-failure (MTBF) index ultimately assigned to each device. i =1,2,…, K .

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