A reliability index allocation method considering multiple dimensions

Abstract

This invention relates to a reliability index allocation method considering multiple dimensions, comprising: determining an attribute matrix and the number of levels; the attribute matrix includes a factor matrix A and a scale matrix B, wherein factor matrix A has a cross-influence relationship with scale matrix B; determining the evaluation scale between factors; determining an indirect judgment matrix; determining a weight judgment matrix; determining the relative importance of each factor, thereby determining factor matrix A; performing consistency verification of factor matrix A according to a consistency index; obtaining an evaluation scale set, thereby determining scale matrix B; determining the comprehensive weight W; and allocating reliability indices. This invention is applicable to complex systems containing multiple components, each with relatively independent functions, and is suitable for reliability index allocation in complex systems, used to simultaneously consider the allocation of reliability indices across multiple dimensions and factors.

Description

Technical Field

[0001] This invention relates to a reliability index allocation method that considers multiple dimensions and factors. It is applicable to complex systems that contain multiple components and whose functions are relatively independent. It is suitable for the allocation of reliability indexes in complex systems and is used to simultaneously consider the allocation of reliability indexes based on multiple dimensions and factors. Background Technology

[0002] Reliability index allocation is a method of distributing system reliability indicators from top to bottom and from the whole to the parts to specified product levels. It can provide a basis for reliability design and to propose quantitative reliability requirements for downstream products. The scoring allocation method is one of the commonly used reliability allocation methods. Specifically, it uses expert scoring to score the system components and allocates reliability based on the scoring results.

[0003] As the functionality, performance, and reliability of aerospace systems continue to improve, system composition is becoming increasingly larger, and mission scenarios and failure modes are becoming more complex. Experts need to consider more and more factors during evaluation, and the requirements for refined design are becoming increasingly stringent. Faced with complex systems with high reliability requirements and limited margins, traditional methods of roughly evaluating only a few factors are no longer sufficient to meet engineering needs. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a reliability index allocation method that considers multiple dimensions for complex aerospace systems, so as to allocate reliability indexes more accurately for each component of the complex aerospace system.

[0005] The technical solution of this invention is:

[0006] A reliability index allocation method that considers multiple dimensions includes:

[0007] (1) Determine the attribute matrix and the number of levels; the attribute matrix includes factor matrix A and scale matrix B, and factor matrix A has a cross-influence relationship with scale matrix B;

[0008] (2) Determine the evaluation criteria among factors;

[0009] (3) Determine the indirect judgment matrix;

[0010] (4) Determine the weight judgment matrix;

[0011] (5) Determine the relative importance of each factor, thereby determining factor matrix A;

[0012] (6) Perform consistency verification of factor matrix A based on consistency index;

[0013] (7) Obtain the evaluation scale set, and thus determine the scaling matrix B;

[0014] (8) Determine the overall weight W;

[0015] (9) Assign reliability indicators.

[0016] Furthermore, based on the characteristics of complex aerospace systems and their constituent units, appropriate reliability indicators are selected, influencing factors are allocated, and a factor matrix is ​​constructed.

[0017] Factors influencing the allocation of reliability metrics include:

[0018] a) The simpler the unit, the higher the reliability index assigned to it;

[0019] b) The more mature the unit technology, the higher the reliability index assigned to it;

[0020] c) The shorter the unit's working time, the higher the reliability index assigned to it;

[0021] d) The more severe the consequences of the failure, the higher the reliability index assigned to it;

[0022] e) The more favorable the unit's operating conditions, the higher the reliability index assigned to it;

[0023] f) The worse the unit reachability, the higher the reliability index assigned to it;

[0024] g) The higher the economic value of a unit, the higher the reliability index assigned to it;

[0025] h) The better the manufacturability of a unit, the higher the reliability index assigned to it.

[0026] Furthermore, the scaling matrix B is the evaluation scale b for all factors. ij The set of evaluation scales b ij The scale value of the j-th unit on the i-th factor is assigned as the scale value. The higher the reliability index, the lower the scale value.

[0027] Furthermore, the evaluation criteria among the determining factors are specifically as follows:

[0028] The degree of influence on system reliability indicators is factor weight a. i The weights of all factors form a factor matrix A. The evaluation scale is defined based on the importance of each reliability index to the reliability contribution of the influencing factors. The evaluation scale is a relatively symmetrical discrete interval.

[0029] Furthermore, the determination of the indirect judgment matrix specifically involves:

[0030] The indirect judgment matrix A* of factor matrix A is obtained by comparing each pair of the determined evaluation criteria:

[0031]

[0032] In the formula, a* ix The metric is used to evaluate the reliability of the i-th factor in comparison with the x-th factor.

[0033] Furthermore, the determination of the weight judgment matrix specifically involves:

[0034] Define r i Ranking index of the relative importance of each factor:

[0035]

[0036] In the formula, I represents the total number of selected factors.

[0037] Then the weights of each factor a' ix for:

[0038]

[0039] In the formula:

[0040] r max The maximum sorting index;

[0041] r min The minimum sorting index;

[0042] x m This represents the relative importance score, taking the median value of the ranking index.

[0043] Furthermore, determining the relative importance of each factor specifically involves:

[0044] The relative weight a' is calculated using the root method. i :

[0045]

[0046] For a' ix After normalization, the relative importance weights 'a' of each element can be obtained. i :

[0047]

[0048] Then we can obtain matrix A = [a1, a2, ..., a...]. i ].

[0049] Furthermore, consistency verification is performed based on consistency metrics, specifically as follows:

[0050] If the consistency index CI ≤ 0.10, then the consistency of factor matrix A is considered to be good, that is, the relative importance of each factor is acceptable.

[0051]

[0052] In the formula, λ max For matrix [a' ix The largest eigenvalue of ].

[0053] Furthermore, the acquisition of the evaluation scale set specifically includes:

[0054] Define evaluation scale b ij Let represent the scale value of the j-th unit on the i-th factor. The rating scale is selected within a certain positive integer range. When a higher reliability index is assigned to the j-th unit based on the i-th factor, the rating scale of the i-th factor for that unit is lower. This scaling evaluation is performed K times in a loop. Each component of the system is evaluated for different factors, resulting in the initial rating scale set and the set of initial scaling matrices. The initial scaling matrices are as follows:

[0055]

[0056] Adding the initial scaling matrices together yields the final scaling matrix B:

[0057]

[0058] Furthermore, the determination of the comprehensive weight W specifically involves:

[0059] The initial comprehensive matrix W* is obtained by following the formula W* = A × B. Each value in matrix W* represents the initial comprehensive weight. Normalizing these initial comprehensive weights yields the comprehensive matrix and its comprehensive weights W = [W1, W2, ..., W...]. j ] or W = [W1, W2, ..., W j ] T .

[0060] Furthermore, reliability metrics are allocated in the following manner:

[0061]

[0062] In the formula: W j R represents the overall weight of the j-th unit; j The reliability assigned to the j-th unit;

[0063] R S This is a reliability indicator for the system.

[0064] The advantages of this invention compared to the prior art are:

[0065] This invention is applicable to complex systems that contain multiple components and whose functions are relatively independent. It is suitable for the allocation of reliability indicators for complex systems and is used to consider the allocation of reliability indicators from multiple dimensions and factors at the same time. Attached Figure Description

[0066] Figure 1 This is a schematic diagram illustrating the relationship between the attribute matrices and weights of each layer.

[0067] Figure 2 This is a flowchart illustrating the implementation of the present invention; Detailed Implementation

[0068] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0069] Suppose a system M consists of m units, each labeled as unit j (j = 1, 2, ..., m), and reliability indexes are assigned to it based on the comprehensive matrix method.

[0070] (a) Determine the attribute matrix and the number of levels.

[0071] 1.1 Method for Determining the Attribute Matrix

[0072] The attribute matrix used for assigning system reliability indicators can be determined by comprehensively considering various influencing factors and their relationships, based on the system design and usage characteristics. The attribute matrix is ​​determined using the following principles:

[0073] a) Principle of completeness: The allocation of reliability indicators for complex systems involves multiple influencing factors. It should include environmental applicability and economic factors as much as possible, as well as resource utilization and resource consumption factors. The attribute matrix must be able to fully reflect the overall situation of the system to be allocated in order to ensure the comprehensiveness and reliability of the allocation.

[0074] b) Exclusivity principle: Under the premise of ensuring the integrity of the attribute matrix, the attribute matrix should be applicable, comprehensive and representative, and avoid the recurrence of the same or similar attribute matrices (influencing factors), and ensure that the correlation between the weights of each attribute in the same matrix is ​​as small as possible;

[0075] c) Hierarchical principle: A hierarchical structure model is formed by classifying and categorizing the various influencing factors. The factors should be identified and classified according to their logical relationships and importance, so that they are placed at different levels to ensure that the allocation is reasonable and scientific.

[0076] d) Operability principle: The connotation and extension of the set attribute matrix should be clear, objectively and truthfully reflecting the reliability attributes of each stage in the system life cycle, avoiding ambiguity in the definition and extension of each attribute matrix, unclear boundaries between elements, and semantic overlap.

[0077] e) Combining dynamic and static elements: Taking into account both dynamic and static elements, the attribute matrix is ​​determined. The dynamic attribute matrix can reflect the evolution of the system and unit states and the changes in technical states, while the static attribute matrix can reflect the relative stability of the reliability level of a certain characteristic of the system during its life cycle (such as the usage stage).

[0078] f) Combining qualitative and quantitative approaches: Different attribute matrices contain different elements, which can be either quantitative or qualitative. Qualitative elements should be quantified using quantitative levels, while quantitative elements with continuous data distribution should be discretized using intervals.

[0079] When determining the specific values ​​of each attribute matrix, if the elements in the attribute matrix have a cross-influence relationship with the next level attribute elements ( Figure 1 (The relationship between the dashed arrows) can be used to determine the weights of each element in the matrix using the square root method; if each element in the attribute matrix has a one-to-one influence relationship with the next level attribute element ( Figure 1 (The relationship between the solid arrows in the matrix) can be used to determine the weights of each element in the matrix using the scaling evaluation method.

[0080] A and B are attribute matrices, with hierarchical distinctions. The comprehensive matrix W is obtained by multiplying the attribute matrices at each level sequentially. Weights can be assigned to the factors in each level of the attribute matrix using methods such as scoring or scaling. Figure 1 As shown.

[0081] W*=A×B (1)

[0082] The most commonly used attribute matrices are factor matrices and scaling matrices. For ease of description, the factor matrix is ​​defined as matrix A, and the scaling matrix as matrix B. Matrix A has a cross-influence relationship with matrix B; therefore, the square root method is used to determine the relative weights of each element in matrix A. Matrix B is not further stratified, and is equivalent to a one-to-one influence relationship; the scaling evaluation method is used to determine the weights of each element in the matrix.

[0083] 1.2 Factor Matrix

[0084] First, based on the characteristics of the system and its constituent units, appropriate reliability indicators are selected to allocate influencing factors and construct a factor matrix. For complex aerospace systems, the following factors are generally considered. When using the allocation method of this invention, the complete set of the following factors can be used, or factors can be reduced or added as appropriate according to the characteristics of the system and units. In this invention, the determined factor labels are i (i = 1, 2…I).

[0085] a) The simpler the unit, the higher the reliability index should be assigned to it;

[0086] b) The more mature the unit technology, the higher the reliability index should be assigned to it;

[0087] c) The shorter the unit's operating time, the higher the reliability index should be assigned to it;

[0088] d) The more severe the consequences of a failure, the higher the reliability index should be assigned to it;

[0089] e) The more favorable the unit's operating conditions, the higher the reliability index should be assigned to it;

[0090] f) The worse the reachability of a unit, the higher the reliability index should be assigned to it;

[0091] g) The higher the economic value of a unit, the higher the reliability index should be assigned to it;

[0092] h) The better the manufacturability of a unit, the higher the reliability index should be assigned to it.

[0093] 1.3 Scale Matrix:

[0094] Scale matrix B is the evaluation scale b for all factors. ij The set of values ​​represents the second-level attribute matrix of the comprehensive weight matrix. Evaluation scale b ij The scale value of the j-th unit on the i-th factor is assigned as the scale value. The higher the reliability index, the lower the scale value.

[0095] (ii) Determining the rating scale among factors

[0096] The degree of influence of the above factors on the system reliability index is the factor weight a. i The weights of all factors form a factor matrix A. An evaluation scale is defined based on the importance of each factor's contribution to reliability. The evaluation scale is a relatively symmetrical discrete interval, such as [0, 1, 2] or [3, 2, 1, 1 / 3, 1 / 2]. For example, when the evaluation scale is [0, 1, 2]:

[0097] For reliability, Factor 1 and Factor 2 are equally important, and the evaluation criterion is 1.

[0098] For reliability, factor 1 is more important than factor 2, and the evaluation criterion is 2;

[0099] For reliability, factor 1 is less important than factor 2, and the evaluation criterion is 0.

[0100] (III) Determining the Indirect Judgment Matrix

[0101] The selected factors are compared pairwise using the evaluation criteria in (II) to obtain the indirect judgment matrix A of matrix A. * .

[0102]

[0103] In the formula a* ixThe metric is used to evaluate the reliability of the i-th factor in comparison with the x-th factor.

[0104] (iv) Determine the weight judgment matrix

[0105] Define ri as the ranking index of the relative importance of each factor, as shown in formula (3):

[0106]

[0107] In the formula, I represents the total number of selected factors.

[0108] The weights of each factor (ranked by relative importance in this invention) are calculated according to formula (4):

[0109]

[0110] In the formula:

[0111] r max The maximum sorting index;

[0112] r min The minimum sorting index;

[0113] x m The relative importance index is taken as the median value of the ranking index in this invention.

[0114] (v) Determine the relative importance of each factor

[0115] The relative weights are calculated using the square root method, as shown in formula (5):

[0116]

[0117] For a' ix After normalization, the relative importance weights of each element can be obtained, as shown in formula (6):

[0118]

[0119] Then we can obtain matrix A = [a1, a2, ..., a...]. i ].

[0120] (vi) Consistency verification

[0121] Based on the analytic hierarchy process (AHP) theory, if the consistency index (CI) ≤ 0.10, the judgment matrix can be considered to have good consistency, meaning that the relative importance of each factor is acceptable. The verification formula is shown in formula (7).

[0122]

[0123] In the formula, λ max For matrix [a' ixThe largest eigenvalue of ].

[0124] (vii) Obtaining the evaluation scale set

[0125] After determining the relevant information of the factor matrix, the scaling matrix B can be further determined.

[0126]

[0127] The evaluation scale (b) is defined here. ij The scale value of the j-th unit on the ith factor is given by the following criteria: The scale should be selected within a positive integer range, such as [1, 2, 3, 4, 5] or [1, 2, 3, 4, 5, 6, 7, 8, 9]. When a higher reliability index is assigned to the j-th unit based on the ith factor, the scale of the ith factor for that unit should be lower. K iterations of scale evaluation can be performed to evaluate each component of the system for different factors, resulting in a set of initial scale matrices. Each initial scale matrix is ​​as follows:

[0128]

[0129] (viii) Determine the scaling matrix

[0130] Adding the initial scaling matrices together yields the final scaling matrix:

[0131]

[0132] (ix) Determining the overall weight

[0133] According to formula (1) W*=A×B of this invention, the initial comprehensive matrix can be obtained, and each value in the matrix is ​​the initial comprehensive weight. The initial comprehensive weights in this initial comprehensive matrix are then normalized according to formula (6) to obtain the comprehensive matrix and its comprehensive weights. or

[0134] (x) Reliability Allocation

[0135] The reliability index of the system is allocated according to formula (11):

[0136]

[0137] In the formula:

[0138] W j —The overall weight of the j-th unit;

[0139] R j —The reliability assigned to the j-th unit;

[0140] R S —System reliability metrics.

[0141] (xi) Verification of allocation results

[0142] After the allocation is completed, the reliability index is verified according to formula (12).

[0143]

[0144] If the formula holds true, the current reliability index allocation is complete; if it does not, the allocation elements and evaluation criteria should be readjusted.

[0145] Example:

[0146] The specific implementation method is described using the reliability allocation process of a certain system as an example.

[0147] Assuming a system consists of 7 (J=7) devices, reliability allocation for this system involves 4 (K=4) scaling assessments to assign reliability indicators. The system's reliability requirement is R≥0.9. The implementation process is as follows: Figure 2 The specific steps are as follows:

[0148] (a) Determine the attribute matrix and the number of levels.

[0149] Based on practical engineering experience and the experience of this system, the matrix used for allocation was determined to be a factor matrix, and the scaling matrix can be further subdivided into the next level of the factor matrix.

[0150] By comprehensively weighing the expected use of the system and the functional differences of each part, six factors (I=6) were identified as elements in the factor matrix: unit complexity, technology maturity, consequences of unit failure, working conditions, accessibility, and unit economic value. Each element was rated on a 5-level scale, and the subsequent scaling assessment yielded a scale level of 1 to 5 for each factor.

[0151] (ii) Determining the rating scale among factors

[0152] In this case, the assessment criteria are tentatively set at 3, and the above 6 factors are compared in pairs.

[0153] a) For reliability, Factor 1 and Factor 2 are equally important, and the rating scale = 1;

[0154] b) For reliability, factor 1 is more important than factor 2, and the evaluation scale = 2;

[0155] c) For reliability, factor 1 is less important than factor 2, and the evaluation criterion is 0.

[0156] (III) Determining the Indirect Judgment Matrix

[0157] Using three judgment scales of 1, 2, and 0, indirect judgment matrices are given for the six influencing factors. Then, the relative importance ranking index r of each factor is obtained by applying formula (3). i As shown in Table 1.

[0158] Table 1 Indirect Judgment Matrix

[0159]

[0160] (iv) Determine the weight judgment matrix

[0161] The indirect judgment matrix is ​​converted into a judgment matrix by applying formula (4). The judgment matrix is ​​shown in Table 2.

[0162] Table 2 Judgment Matrix

[0163]

[0164]

[0165] (v) Determine the relative importance of each factor

[0166] The relative importance a' of each factor is calculated using formula (5). i .

[0167] The relative importance is normalized using formula (6) to obtain the factor weight a. i Specific data is shown in Table 3.

[0168] Table 3. Relative Importance of Each Factor

[0169]

[0170] (vi) Consistency verification

[0171] Using formula (7), the consistency index of this case is calculated.

[0172] The consistency check passed.

[0173] (vii) Obtaining the rating scale matrix set

[0174] Each of the six factors mentioned above was rated on a scale of 1 to 5. The scale sets given for each rating are shown in Table 4.

[0175] Table 4. Evaluation scale set for each factor

[0176]

[0177]

[0178] (viii) Determine the scaling matrix

[0179] Table 5 shows the scaling matrix for the reliability allocation of this system, determined according to formula (10).

[0180] Table 5 Scaling Matrix for Each Product

[0181]

[0182] (ix) Determining the overall weight

[0183] The initial comprehensive weight matrix for reliability allocation of this system is calculated according to formula (1). W*=[11.5794,12.9759,12.4875,12.5768,11.9076,10.5789,18.0384] T (x) Reliability Allocation

[0184] The initial composite matrix is ​​normalized according to formula (6) to obtain: W = [0.1284, 0.1439, 0.1385, 0.1395, 0.1321, 0.1173, 0.2001] T

[0185] Reliability allocation is carried out according to formula (11), taking into account a margin during allocation, and the system reliability index is R. S Reliability allocation was performed using a value of 0.92. The allocation results are shown in Table 6.

[0186] Table 6 Reliability Allocation Results of a Certain System

[0187] <![CDATA[R j ]]> 0.9865 0.9849 0.9855 0.9854 0.9862 0.9877 0.9791

[0188] (xi) Verification of allocation results

[0189] The allocation results were verified according to formula (12), and the calculations were performed.

[0190]

[0191] The system reliability requirements have been met, and the allocation is complete.

[0192] The parts of this invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A method for allocating reliability indicators considering multiple dimensions, characterized in that... include: (1) Determine the attribute matrix and the number of levels; the attribute matrix includes the factor matrix. and scaling matrix Factor matrix Scale matrix This indicates a cross-influence relationship; (2) Determine the rating scale among factors; (3) Determine the indirect judgment matrix; (4) Determine the weight judgment matrix; (5) Determine the relative importance of each factor to determine the factor matrix. ; (6) Construct a factor matrix based on consistency indicators. Consistency check; (7) Obtain the evaluation scale set to determine the scaling matrix. ; (8) Determine the overall weight ; (9) Assign reliability indicators; The evaluation criteria among the determining factors are specifically as follows: The degree of influence on system reliability indicators is determined by factor weights. i The weights of all factors form a factor matrix. The evaluation scale is defined based on the importance of the contribution of each reliability index to the reliability. The evaluation scale is a relatively symmetrical discrete interval. The determination of the indirect judgment matrix is ​​specifically as follows: The factor matrix is ​​obtained by comparing each pair of the determined evaluation criteria. Indirect judgment matrix : In the formula, ix For the first i The factor and the first x A comparison of several factors to evaluate reliability; The determination of the weight judgment matrix is ​​specifically as follows: definition Ranking index of the relative importance of each factor: In the formula, I represents the total number of selected factors. Then the weights of each factor for: In the formula: r max The maximum sorting index; r min The minimum sorting index; x m The relative importance score is calculated using the median value of the ranking index. The acquisition of the evaluation scale set specifically involves: Define evaluation scale b ij , mark j The unit in the first i Scale values ​​on each factor; The rating scale is selected within a certain positive integer interval, based on the first... i The factor affects the first j When a higher reliability index is assigned to a unit, that unit's first... i The rating scale for each factor is lower, and the evaluation scale is lower. K The scaling evaluation in the next iteration evaluates each component of the system for different factors, resulting in a set of initial scaling matrices for the initial scaling set. The initial scaling matrices are as follows: Add the initial scaling matrices together to obtain the final scaling matrix. : 。 2. The reliability index allocation method considering multiple dimensions as described in claim 1, characterized in that: Based on the characteristics of complex aerospace systems and their constituent units, appropriate reliability indicators are selected, influencing factors are allocated, and a factor matrix is ​​constructed. Factors influencing the allocation of reliability metrics include: a) The simpler the unit, the higher the reliability index assigned to it; b) The more mature the unit technology, the higher the reliability index assigned to it; c) The shorter the unit's working time, the higher the reliability index assigned to it; d) The more severe the consequences of the failure, the higher the reliability index assigned to it; e) The more favorable the unit's operating conditions, the higher the reliability index assigned to it; f) The worse the unit reachability, the higher the reliability index assigned to it; g) The higher the economic value of a unit, the higher the reliability index assigned to it; h) The better the manufacturability of a unit, the higher the reliability index assigned to it.

3. The reliability index allocation method considering multiple dimensions as described in claim 1, characterized in that: The scaling matrix It is an evaluation scale for all factors. b ij The set of evaluation scales b ij For the first j The unit in the first i The higher the reliability index assigned to a factor, the lower the rating scale.

4. The reliability index allocation method considering multiple dimensions as described in claim 1, characterized in that: The determination of the relative importance of each factor is specifically as follows: The relative weights are calculated using the root method. : right After normalization, the relative importance weights of each element can be obtained. : Then we can obtain the matrix. .

5. The reliability index allocation method considering multiple dimensions according to claim 4, characterized in that: Consistency verification is performed based on consistency metrics, specifically as follows: If consistency index If the factor matrix is ​​≤0.10, then the factor matrix is ​​considered to be... Consistency is good, meaning the relative importance of each factor is acceptable; (7) In the formula, λ max For matrix [ The largest eigenvalue of ].

6. The reliability index allocation method considering multiple dimensions according to claim 1, characterized in that: The determination of comprehensive weight Specifically: according to Obtain the initial synthesis matrix ,matrix The values ​​in the matrix represent the initial comprehensive weights. By normalizing the initial comprehensive weights in this matrix, we can obtain the comprehensive matrix and its comprehensive weights. or .

7. A reliability index allocation method considering multiple dimensions as described in claim 6, characterized in that: Reliability metrics are assigned in the following manner: In the formula: For the first j The overall weight of each unit; To be assigned to the j The reliability of each unit; This is a reliability indicator for the system.

Images