CN112115561A - Improved FMEA method based on interval triangular fuzzy number and fuzzy VIKOR method - Google Patents

Improved FMEA method based on interval triangular fuzzy number and fuzzy VIKOR method Download PDF

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CN112115561A
CN112115561A CN202010990123.XA CN202010990123A CN112115561A CN 112115561 A CN112115561 A CN 112115561A CN 202010990123 A CN202010990123 A CN 202010990123A CN 112115561 A CN112115561 A CN 112115561A
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李国发
张微
何佳龙
霍津海
杨海吉
韩良晟
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Jilin University
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Abstract

The invention discloses an improved FMEA method based on an interval triangular fuzzy number and fuzzy VIKOR method. Firstly, the relative importance of the failure mode grade and the risk factor is evaluated by using linguistic variables, and the linguistic variables are expressed by interval triangular fuzzy numbers. Secondly, subjective weight of the risk factors is calculated by using a fuzzy analytic hierarchy process, objective weight of the risk factors is calculated by using an expanded VIKOR process, and comprehensive weight of the risk factors is calculated according to an improved game theory combination weighting process. And finally, sequencing the risk priority of the failure modes by using a fuzzy VIKOR method. The method is used for evaluating the workpiece box system of the numerical control gear milling machine, and the result verifies the applicability and the effectiveness of the method.

Description

Improved FMEA method based on interval triangular fuzzy number and fuzzy VIKOR method
Technical Field
The invention belongs to the technical field of reliability analysis, and particularly relates to an improved FMEA (Fuzzy algorithm) method based on an Interval Triangular Fuzzy Number and Fuzzy VIKOR (Fuzzy Number, IVF) method.
Prior Art
Failure Mode and Effect Analysis (FMEA) is a systematic activity of analyzing subsystems constituting a product or various processes constituting a process one by one in a product design stage or a process design stage, finding out all potential Failure modes, and taking necessary measures in advance, and was originally proposed by the national space agency (NASA) in the 20 th century and the 60 th century. Because of the characteristics of simplicity, convenience, high efficiency and the like, the method is widely applied to risk analysis in the fields of automobiles, aerospace, medical care and the like.
FMEA requires a cross-job team of FMEA members with different specialties who need to evaluate the degree of occurrence (O), severity (S), and degree of detection (D) for each failure mode based on past experience and judgment. In the traditional FMEA method, the score of each Risk factor is an integer of 1-10, the Risk Priority of a failure mode is determined according to the Risk Priority (RPN), the Risk Priority is obtained by multiplying the three Risk factors, and the larger the value of the RPN is, the more serious the influence of the failure mode is. Although the effectiveness of conventional FMEA methods based on RPN ranking has been variously demonstrated, there are still some drawbacks and shortcomings: (1) many fuzzy, complex or uncertain information can be generated in the FMEA evaluation process, and the FMEA member can hardly give accurate values of the three risk factors; (2) when failure modes are ranked, the weights of the three risk indicators are the same by default. However, when the evaluation is performed on different subjects, the weights of the three risk factors may have large differences; (3) the score combinations of different risk factors may result in the same RPN value, and the potential risk levels of these failure modes may be completely different, which may result in the failure to accurately find the most important failure mode;
(4) when calculating the RPN, only 120 numbers out of 1 to 1000 can be multiplied by three risk factors. This will result in a strong discontinuity in the RPN; (5) the calculation of the RPN is not scientifically based and is very sensitive to changes in the risk factors. Small changes in a certain risk factor may result in large differences in RPN.
The interval triangular fuzzy number is used for evaluating the relative importance of the grade of the failure mode and the risk factor, and is not used for a preset linguistic variable. The diversified view of the FMEA members can be flexibly and accurately expressed through the interval triangular fuzzy number.
The fuzzy VIKOR method is a multi-attribute decision method proposed by professor Opricovic of south Slave for complex systems. The fuzzy VIKOR method has the core content that on the basis of determining the positive and negative ideal solutions, the advantages and the disadvantages are ranked according to the proximity degree of each alternative scheme and the ideal scheme. The method considers the maximization of group benefit and the minimization of individual regret, and simultaneously also considers the subjective preference of a decision maker. And the VIKOR method obtains a compromise scheme with priority, and the compromise scheme is closer to an ideal scheme.
Disclosure of Invention
In order to solve the defects of the traditional FMEA, the invention provides an improved FMEA method based on an interval triangular fuzzy number and fuzzy VIKOR method. The method comprises the steps of firstly, evaluating the relative importance of the level of a failure mode and a risk factor by using a linguistic variable, wherein the linguistic variable is represented by an interval triangular fuzzy number. Secondly, subjective weight of the risk factors is calculated by using a fuzzy analytic hierarchy process, objective weight of the risk factors is calculated by using an expanded VIKOR process, and comprehensive weight of the risk factors is calculated according to an improved game theory combined weighting process. And finally, sequencing the risk priority of the failure modes by using a fuzzy VIKOR method. The method is used for evaluating the workpiece box system of the numerical control gear milling machine, and the result verifies the applicability and the effectiveness of the method.
The invention is realized by the following technical scheme:
the invention provides an improved FMEA method based on an interval triangular fuzzy number and fuzzy VIKOR method. Setting of l evaluators in an FMEA evaluation team TMk(k 1, 2.. times.l) for m failure modes FMi(i＝1,2, m) with n risk factors RFj(j ═ 1, 2.., n) was evaluated. The weight vector of the evaluators in the FMEA evaluation team is (lambda)1，λ2，……λl) And λk＞0，
Figure RE-GDA0002746306600000021
λkIndicating the relative importance of each evaluator in the evaluation team. Setting evaluator TMkGiven the evaluation result, n fuzzy decision matrixes are obtained
Figure RE-GDA0002746306600000031
And n fuzzy decision vectors
Figure RE-GDA0002746306600000032
i＝1,2,…,n；k＝1,2,3。
Figure RE-GDA0002746306600000033
And
Figure RE-GDA0002746306600000034
a matrix that evaluates the level of each failure mode and the relative importance of each risk factor using linguistic variables for FMEA members. Wherein
Figure RE-GDA0002746306600000035
Based on the setting, the method comprises the following steps:
step 1: and determining an evaluation target.
Step 2: potential failure modes are determined.
And step 3: the FMEA member evaluates the level of each failure mode and the relative importance of each risk factor using the linguistic variables in tables 1 and 2.
TABLE 1 linguistic variables for the level of failure modes
Figure BDA0002690581290000036
TABLE 2 linguistic variables for relative importance of risk factors
Figure BDA0002690581290000037
And 4, step 4: summarizing the evaluation results of each FMEA member to obtain n fuzzy decision matrixes
Figure RE-GDA0002746306600000038
And n fuzzy decision vectors
Figure RE-GDA0002746306600000039
Figure RE-GDA0002746306600000041
Figure RE-GDA0002746306600000042
And 5: determining a decision matrix
Figure RE-GDA0002746306600000043
And a decision vector Wk。
Figure RE-GDA0002746306600000044
Figure RE-GDA0002746306600000045
Wherein
Figure RE-GDA0002746306600000046
Step 6: computing a normalized decision matrix
Figure RE-GDA0002746306600000047
Figure BDA0002690581290000048
And 7: calculating subjective weight of risk factor using fuzzy analytic hierarchy process
Figure BDA0002690581290000049
The Fuzzy Analytic Hierarchy Process (FAHP) has the principle that a fuzzy consistent matrix and the analytic hierarchy process are fused, so that the fuzziness of a judgment matrix is reserved, and the consistency of the judgment matrix is guaranteed. The subjective weighting steps for calculating the risk factors by using the fuzzy analytic hierarchy process are as follows:
(1) will be provided with
Figure RE-GDA00027463066000000410
Expressed by 2 triangular fuzzy numbers, i.e.
Figure RE-GDA00027463066000000411
Figure RE-GDA00027463066000000412
k＝1,2,3。
(2) Defined in terms of triangular blur numbers, i.e. assuming any two triangular blur numbers
Figure RE-GDA00027463066000000413
And
Figure RE-GDA00027463066000000414
the degree of probability of (A) is shown in formula (6).
Figure RE-GDA00027463066000000415
Will be provided with
Figure RE-GDA00027463066000000416
Degree of importance of two-by-twoComparing and constructing a fuzzy complementary judgment matrix B1＝{Puv}3×3U is 1,2, 3; v is 1,2, 3. Wherein
Figure RE-GDA00027463066000000417
And when u is equal to v,
Figure RE-GDA00027463066000000418
the fuzzy complementary judging matrix contains the possibility degree information of mutual comparison of all elements, and the proportion of each element is determined by calculating the sorting vector of each element.
Figure RE-GDA0002746306600000051
(3) According to the formula (8), calculating
Figure BDA0002690581290000052
Figure BDA0002690581290000053
(4) Repeating the steps (2) to (3) and calculating
Figure BDA0002690581290000054
(5) Calculating subjective weight of risk factor according to formula (9)
Figure BDA0002690581290000055
Figure BDA0002690581290000056
And 8: calculating objective weights for risk factors using extended VIKOR
Figure BDA0002690581290000057
(1) Determining an optimum value
Figure RE-GDA0002746306600000058
Sum worst value
Figure RE-GDA0002746306600000059
Calculating an optimum value
Figure RE-GDA00027463066000000510
To the worst value
Figure RE-GDA00027463066000000511
The distance of (c).
Figure RE-GDA00027463066000000512
(2) According to the formula (10), calculating
Figure RE-GDA00027463066000000513
To
Figure RE-GDA00027463066000000514
Distance.
Figure RE-GDA00027463066000000515
(3) According to equation (11), the standard blur distance is calculated.
Figure RE-GDA00027463066000000516
(4) Calculating subjective weight of risk factor according to equation (12)
Figure BDA00026905812900000517
Figure BDA00026905812900000518
And step 9: utilizing improved game theoryCalculating comprehensive weight of risk factor by combined weighting method
Figure BDA00026905812900000519
The game theory combined weighting method aims to find the maximized common points of interests among the subjective and objective weights, so that the deviation between the comprehensive weights and the subjective and objective weights is minimized. Assume that the weight vector obtained using the alpha methods is
Figure BDA00026905812900000520
Let an arbitrary linear combination of L weight vectors be:
Figure BDA00026905812900000521
in the formula:αin order to be a linear combination coefficient,α>0, W represents all possible weight vectors. With W and WαFor the L linear combination coefficients in the formula (13) with the minimum dispersion ofαAnd (6) optimizing. Constructing a strategy model:
Figure BDA0002690581290000061
the optimization condition for equation (14) is derived from the differential nature of the matrix:
Figure BDA0002690581290000062
the equivalent of equation (15) is:
Figure BDA0002690581290000063
solving equation (16) yields the linear combination coefficientsαBut cannot guaranteeα>0, which is clearly contrary to the assumption of equation (13).
By using the constraint conditions of the dispersion maximization objective weighting method for reference, the improved optimization model can be determined as follows:
Figure BDA0002690581290000064
establishing a Lagrange function to solve the model:
Figure BDA0002690581290000065
determining linear combination coefficientsαAnd toαAnd (3) performing normalization processing to determine a combination weight coefficient:
Figure BDA0002690581290000066
Figure BDA0002690581290000067
will be provided with
Figure BDA0002690581290000068
Substituting equation (13) results in the total weight:
Figure BDA0002690581290000069
step 10: s for each protocol was calculated using the fuzzy VIKOR methodj，RjAnd QjThe value of (c).
Calculating the group benefit optimal solution S according to the formula (22), the formula (23) and the formula (24)jRespectively regret worst solution RjAnd the comprehensive index QjSelecting
Figure BDA00026905812900000610
Figure BDA0002690581290000071
Figure BDA0002690581290000072
Figure BDA0002690581290000073
Step 11: according to Sj，RjAnd QjAnd sequencing the risk priority of each failure mode.
Step 12: a compromise is proposed.
Advantageous effects
(1) It is more advantageous in handling uncertain information. The diversified viewpoints of the FMEA members can be expressed flexibly and accurately through interval triangular fuzzy numbers. (2) The method comprises the steps of calculating subjective weight of the risk factors by using a fuzzy analytic hierarchy process, calculating objective weight of the risk factors by using an extended VIKOR process, and obtaining comprehensive weight of the risk factors by using an improved game theory combination weighting process. The method can give consideration to the advantages of subjective and objective weights and avoid information loss to a certain extent. (3) The failure modes are sorted using the fuzzy VIKOR method. The method fully considers the maximization of group benefit and the minimization of individual regret, and simultaneously also considers the subjective preference of a decider.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment evaluates a workpiece box system of the numerical control gear milling machine.
In this embodiment, the FMEA team consists of 1 machine tool designer, 1 assembly engineer, 1 quality inspector, and 1 operation engineer, and the number and weight thereof are TM1(λ 1)1＝0.2)、TM2(λ2＝0.35)、 TM3(λ30.15) and TM4(λ)40.3). The risk factors are RF 1: degree of occurrence (O); RF 2: severity (S); RF 3: a detected degree (D).
Step 1: and determining an evaluation target. The evaluation target is a numerical control gear milling machine workpiece box system. The inside of the gear box body is provided with a worm gear transmission mechanism which adopts oil-immersed lubrication. The clamping mode of the workpiece is hydraulic clamping. One servo motor drives the workpiece shaft to rotate, and the other servo motor drives the workpiece box system to do arc reciprocating motion. During machining, the nozzle sprays the cutting fluid to a machining area.
Step 2: potential failure modes are determined. The 10 potential failure modes were identified, FM 1: oil leaks from the gear box body; FM 2: the hydraulic cylinder leaks oil; FM 3: insufficient lubrication of the bearing; FM 4: insufficient clamping force; FM 5: gear wear; FM 6: insufficient lubrication of the gears; FM 7: the motor temperature is too high; FM 8: the precision of the workpiece shaft is reduced; FM 9: the flow of cutting fluid is insufficient; FM 10: the bearing wears.
And step 3: the FMEA member evaluates the relative importance of the level of failure mode and risk factor using the linguistic variables in tables 1 and 2.
And 4, step 4: summarizing the evaluation results of each FMEA member to obtain 4 fuzzy decision matrixes
Figure RE-GDA0002746306600000081
And 4 fuzzy decision vectors
Figure RE-GDA0002746306600000082
The results are shown in tables 3 and 4.
TABLE 3 evaluation results of failure mode grades
Figure BDA0002690581290000083
TABLE 4 evaluation results of the relative importance of the Risk factors
Figure BDA0002690581290000091
And 5: determining a decision matrix
Figure RE-GDA0002746306600000092
And decision vector
Figure RE-GDA0002746306600000093
The results are shown in Table 5.
TABLE 5 comprehensive evaluation of failure mode grade and relative importance of risk factors
Figure BDA0002690581290000094
Step 6: computing a normalized decision matrix
Figure RE-GDA0002746306600000095
The results are shown in Table 6.
TABLE 6 normalized decision matrix
Figure BDA0002690581290000096
Figure BDA0002690581290000101
And 7: calculating subjective weight of risk factor using fuzzy analytic hierarchy process
Figure BDA0002690581290000102
(1) Will be provided with
Figure RE-GDA0002746306600000103
Represented by 2 triangular blur numbers.
Figure RE-GDA0002746306600000104
Figure RE-GDA0002746306600000105
Figure RE-GDA0002746306600000106
(2) Constructing a fuzzy complementary judgment matrix B1And B2。
Figure BDA0002690581290000107
Figure BDA0002690581290000108
(3) Computing
Figure BDA0002690581290000109
And
Figure BDA00026905812900001010
the value of (c).
Figure BDA00026905812900001011
Figure BDA00026905812900001012
(4) Calculating subjective weights for risk factors
Figure BDA00026905812900001013
Figure BDA00026905812900001014
And 8: calculating objective weights for risk factors using extended VIKOR
Figure BDA00026905812900001015
(1) Computing
Figure RE-GDA00027463066000001016
To
Figure RE-GDA00027463066000001017
The results are shown in Table 7.
TABLE 7
Figure RE-GDA00027463066000001018
To
Figure RE-GDA00027463066000001019
Is a distance of
Figure RE-GDA00027463066000001020
Figure BDA0002690581290000111
And
Figure BDA0002690581290000112
the value of (c).
Figure BDA0002690581290000113
Figure BDA0002690581290000114
(3) Calculating objective weights for risk factors
Figure BDA0002690581290000115
Figure BDA0002690581290000116
And step 9: comprehensive weight for calculating risk factor by using improved game theory combined weighting method
Figure BDA0002690581290000117
(1) And calculating a combination weight coefficient.
Figure BDA0002690581290000118
(2) Calculating composite weights for risk factors
Figure BDA0002690581290000119
Figure BDA00026905812900001110
Figure BDA00026905812900001111
Figure BDA00026905812900001112
Step 10: s for each protocol was calculated using the fuzzy VIKOR methodj，RjAnd QjThe results are shown in Table 8, Table 9 and Table 10.
TABLE 8 failure mode SjValue of
Figure BDA00026905812900001113
TABLE 9 failure mode RjValue of
Figure BDA00026905812900001114
TABLE 10 failure mode QjValue of
Figure BDA00026905812900001115
Step 11: according to Sj，RjAnd QjAnd sequencing the risk priority of each failure mode.
(1) As can be seen from Table 11, according to Sj，RjAnd QjThe risk priorities of the failure modes are ranked, FM2 is the most severe failure mode and should be given the highest risk priority, and the risk priority order of 10 failure modes is FM2>FM4>FM8>FM3>FM1>FM10>FM6>FM5>FM7>FM9。
TABLE 11 order of failure mode Risk prioritization
Figure BDA0002690581290000121
Step 12: a compromise is proposed.
The compromise herein corresponds to the lowest risk priority scheme. According to the rule described in the fuzzy VIKOR method,
Figure BDA0002690581290000122
FM9 as Sj、RjAnd QjThe ranking is the scheme with the lowest risk priority, and the condition 1 and the condition 2 are met. Thus. Compromise FM9 for failure mode. The present invention is not limited to the above embodiments, and any person skilled in the art can substitute or change the technical solution and the inventive concept of the present invention within the technical scope of the present invention.

Claims (4)

1. The improved FMEA method based on the interval triangular fuzzy number and fuzzy VIKOR method is characterized by comprising the following steps of:
step 1: determining an evaluation target;
step 2: determining a potential failure mode;
and step 3: the FMEA member evaluates the level of each failure mode and the relative importance of each risk factor using the linguistic variables in tables 1 and 2:
TABLE 1 linguistic variables for the level of failure modes
Figure RE-FDA0002746306590000011
TABLE 2 linguistic variables for relative importance of risk factors
Figure RE-FDA0002746306590000012
And 4, step 4: summarizing the evaluation results of each FMEA member to obtain n fuzzy decision matrixes
Figure RE-FDA0002746306590000021
And n fuzzy decision vectors
Figure RE-FDA0002746306590000022
Figure RE-FDA0002746306590000023
Figure RE-FDA0002746306590000024
And 5: determining a decision matrix
Figure RE-FDA0002746306590000025
And a decision vector Wk；
Figure RE-FDA0002746306590000026
Figure RE-FDA0002746306590000027
Wherein
Figure RE-FDA0002746306590000028
Step 6: computing a normalized decision matrix
Figure RE-FDA0002746306590000029
Figure RE-FDA00027463065900000210
And 7: calculating subjective weight of the risk factors by using a fuzzy analytic hierarchy process;
and 8: calculating objective weights for risk factors using extended VIKOR
Figure RE-FDA00027463065900000211
And step 9: comprehensive weight for calculating risk factor by using improved game theory combined weighting method
Figure RE-FDA00027463065900000212
Step 10: s for each protocol was calculated using the fuzzy VIKOR methodj，RjAnd QjA value of (d);
step 11: according to Sj，RjAnd QjRanking the risk priority of each failure mode;
step 12: a compromise is proposed.
2. The improved FMEA method based on interval triangular ambiguity and ambiguity VIKOR method of claim 1, wherein the step 7 of calculating the subjective weight of the risk factor using ambiguity hierarchy analysis comprises the steps of:
(1) will be provided with
Figure RE-FDA0002746306590000031
Expressed by 2 triangular fuzzy numbers, i.e.
Figure RE-FDA0002746306590000032
Figure RE-FDA0002746306590000033
(2) Defined in terms of triangular blur numbers, i.e. assuming any two triangular blur numbers
Figure RE-FDA0002746306590000034
And
Figure RE-FDA0002746306590000035
Figure RE-FDA0002746306590000036
the degree of possibility of (A) is shown in formula (6);
Figure RE-FDA0002746306590000037
will be provided with
Figure RE-FDA0002746306590000038
Comparing the importance degrees of every two to construct a fuzzy complementary judgment matrix B1＝{Puv}3×3U is 1,2, 3; v is 1,2, 3. Wherein
Figure RE-FDA0002746306590000039
And when u is equal to v,
Figure RE-FDA00027463065900000310
the fuzzy complementary judgment matrix comprises the possibility degree information of mutual comparison of all elements, and the proportion of each element is determined by calculating the sequencing vector of each element;
Figure RE-FDA00027463065900000311
(3) according to the formula (8), calculating
Figure RE-FDA00027463065900000312
Figure RE-FDA00027463065900000313
(4) Repeating the steps (2) to (3) and calculating
Figure RE-FDA00027463065900000314
(5) Calculating subjective weight of risk factor according to formula (9)
Figure RE-FDA00027463065900000315
Figure RE-FDA00027463065900000316
3. The improved FMEA method based on interval triangular fuzzy number and fuzzy VIKOR method according to claim 1, wherein said step 8 calculates objective weights for risk factors using extended VIKOR method
Figure RE-FDA00027463065900000317
The method comprises the following steps:
(1) determining an optimum value
Figure RE-FDA00027463065900000318
Sum worst value
Figure RE-FDA00027463065900000319
Calculating an optimum value
Figure RE-FDA00027463065900000320
To the worst value
Figure RE-FDA00027463065900000321
The distance of (d);
Figure RE-FDA00027463065900000322
(2) according to the formula (10), calculating
Figure RE-FDA00027463065900000323
To
Figure RE-FDA00027463065900000324
A distance;
Figure RE-FDA0002746306590000041
(3) calculating a standard fuzzy distance according to the formula (11);
Figure RE-FDA0002746306590000042
(4) calculating subjective weight of risk factor according to equation (12)
Figure RE-FDA0002746306590000043
Figure RE-FDA0002746306590000044
4. The improved FMEA method based on interval triangular fuzzy number and fuzzy VIKOR method as claimed in claim 1, wherein the S of each scheme is calculated by fuzzy VIKOR method in step 10j，RjAnd QjThe implementation mode is as follows: calculating the group benefit optimal solution S according to the formula (22), the formula (23) and the formula (24)jRespectively regret worst solution RjAnd the comprehensive index QjSelecting
Figure RE-FDA0002746306590000045
Figure RE-FDA0002746306590000046
Figure RE-FDA0002746306590000047
Figure RE-FDA0002746306590000048
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ALESSANDRA COLLI: "Failure mode and effect analysis for photovoltaic systems", 《RENEWABLE AND SUSTAINABLE ENERGY REVIEWS》 *
GUO-FA LI等: "Advanced FMEA method based on interval 2-tuple linguistic variables and TOPSIS", 《QUALITY ENGINEERING》 *
N. FOROOZESH等: "ustainable-supplier selection for manufacturing services:a failuremode and effects analysismodel based on interval-valued fuzzy group decision-making", 《JOURNAL OF INTELLIGENT & FUZZY SYSTEMS》 *
YONGFENG LI等: "Risk analysis of human error in interaction design by using a hybrid approach based on FMEA, SHERPA, and fuzzy TOPSIS", 《 QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL》 *
荆树伟等: "基于FMEA和模糊VIKOR的煤炭开采企业风险识别", 《工业工程》 *

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