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

Info

Publication number
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
Authority
CN
China
Prior art keywords
fuzzy
calculating
vikor
fmea
formula
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010990123.XA
Other languages
Chinese (zh)
Other versions
CN112115561B (en
Inventor
李国发
张微
何佳龙
霍津海
杨海吉
韩良晟
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Jilin University
Original Assignee
Jilin University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Jilin University filed Critical Jilin University
Priority to CN202010990123.XA priority Critical patent/CN112115561B/en
Publication of CN112115561A publication Critical patent/CN112115561A/en
Application granted granted Critical
Publication of CN112115561B publication Critical patent/CN112115561B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]

Landscapes

  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

本发明公开了一种基于区间三角模糊数和模糊VIKOR法的改进FMEA方法，利用区间三角模糊数和模糊VIKOR法对传统FMEA进行改进。首先利用语言变量对失效模式的等级和风险因子的相对重要度进行评价，语言变量用区间三角模糊数表示。其次利用模糊层次分析法计算风险因子的主观权重，利用扩展的VIKOR法计算风险因子的客观权重，并根据改进博弈论组合赋权法计算风险因子的综合权重。最后利用模糊VIKOR法对失效模式的风险优先度进行排序。利用该方法对数控铣齿机工件箱系统进行评价，结果验证了该方法的适用性和有效性。

Figure 202010990123

The invention discloses an improved FMEA method based on the interval triangular fuzzy number and the fuzzy VIKOR method, and uses the interval triangular fuzzy number and the fuzzy VIKOR method to improve the traditional FMEA. Firstly, the level of failure mode and the relative importance of risk factors are evaluated by linguistic variables, which are represented by interval triangular fuzzy numbers. Secondly, the subjective weight of risk factors is calculated by the fuzzy analytic hierarchy process, the objective weight of risk factors is calculated by the extended VIKOR method, and the comprehensive weight of risk factors is calculated according to the improved game theory combination weighting method. Finally, the fuzzy VIKOR method is used to sort the risk priority of failure modes. The method is used to evaluate the workpiece box system of CNC gear milling machine, and the results verify the applicability and effectiveness of the method.

Figure 202010990123

Description

基于区间三角模糊数和模糊VIKOR法的改进FMEA方法Improved FMEA Method Based on Interval Triangular Fuzzy Number and Fuzzy VIKOR Method

技术领域technical field

本发明属于可靠性分析技术领域，具体涉及一种基于区间三角模糊数和模 糊VIKOR法的改进FMEA方法，利用区间三角模糊数(Interval-valued Triangular FuzzyNumber，IVF)和模糊VIKOR(VlseKriterijumska OptimizacijaⅠKompromisno Resenje)法对传统FMEA进行改进。The invention belongs to the technical field of reliability analysis, and in particular relates to an improved FMEA method based on an interval triangular fuzzy number and a fuzzy VIKOR method. Improvements to traditional FMEA.

现有技术current technology

失效模式和影响分析(Failure Mode and Effect Analysis，FMEA) 是在产品设计阶段或过程设计阶段，对构成产品的子系统，或构成过程的各个 工序逐一进行分析，找出所有潜在的失效模式，并预先采取必要的措施的一种 系统化活动，最早是由美国国家宇航局(NASA)在20世纪60年代提出。因其具 有简便、高效等特点，目前已广泛应用于汽车、航空航天、医疗保健等领域的 风险分析。Failure Mode and Effect Analysis (FMEA) is to analyze the subsystems that make up the product or the processes that make up the process one by one in the product design stage or process design stage to find out all potential failure modes, and A systematic activity of taking necessary measures in advance was first proposed by NASA in the 1960s. Because of its simplicity and efficiency, it has been widely used in risk analysis in automotive, aerospace, medical care and other fields.

FMEA需要一个由具有不同专业的FMEA成员组成的跨职能团队，FMEA成员 需要根据以往的经验和判断对每种失效模式下的发生度(O)、严重度(S)和 检测度(D)进行评价。传统FMEA方法中，每个风险因子的分值为1-10的整 数，失效模式的风险优先度是根据风险优先数(Risk Priority Number,RPN) 来确定的，风险优先数由三种风险因子相乘得到，RPN的值越大，说明失效模 式的影响越严重。虽然基于RPN排序的传统FMEA方法的有效性已经得到不同 证明，但仍然存在一些不足与缺陷：(1)在FMEA评价过程中会产生许多模糊、复杂或不确定的信息，FMEA成员很难给出三种风险因子的精确数值；(2)对失 效模式进行排序时，默认三个风险指标的权重相同。然而针对不同对象进行评 价时，三种风险因子的权重可能会有较大的差异；(3)不同风险因子的分值组 合可能会得到相同的RPN值，而这些失效模式的潜在风险程度可能完全不同， 这会导致无法准确找到最为重要的失效模式；FMEA requires a cross-functional team composed of FMEA members with different specialties. FMEA members need to evaluate the occurrence (O), severity (S) and detection (D) of each failure mode based on past experience and judgment. Evaluation. In the traditional FMEA method, the score of each risk factor is an integer from 1 to 10, and the risk priority of the failure mode is determined according to the Risk Priority Number (RPN), which is determined by the three risk factors. Multiply, the larger the value of RPN, the more serious the influence of the failure mode. Although the effectiveness of the traditional FMEA method based on RPN ranking has been proved differently, there are still some deficiencies and defects: (1) Many vague, complex or uncertain information will be generated during the FMEA evaluation process, which is difficult for FMEA members to give The exact values of the three risk factors; (2) When sorting failure modes, the default weights of the three risk indicators are the same. However, when evaluating different objects, the weights of the three risk factors may be quite different; (3) the combination of scores of different risk factors may obtain the same RPN value, and the potential risk degree of these failure modes may be completely different, which can lead to an inability to accurately find the most important failure mode;

(4)计算RPN时，1到1000中仅有120个数字可以通过三个风险因子相乘得到。 这将导致RPN具有很强的不连续性；(5)RPN的计算方式没有科学依据，并且 对风险因子的变化非常敏感。某一个风险因子发生微小变化可能会导致RPN 的巨大不同。(4) When calculating RPN, only 120 numbers from 1 to 1000 can be obtained by multiplying three risk factors. This will lead to a strong discontinuity in RPN; (5) RPN is calculated in a way that has no scientific basis and is very sensitive to changes in risk factors. Small changes in one risk factor can lead to large differences in RPN.

区间三角模糊数是对失效模式的等级和风险因子的相对重要性进行评价， 而不是利用预先规定好的语言变量。FMEA成员的多样化观点可以通过区间三 角模糊数灵活准确的表达出来。Interval triangular fuzzy numbers are used to evaluate the relative importance of failure mode levels and risk factors, rather than using pre-specified linguistic variables. The diverse views of FMEA members can be expressed flexibly and accurately through interval triangular fuzzy numbers.

模糊VIKOR法是南斯拉夫Opricovic教授针对复杂系统提出的一种多属性 决策方法。模糊VIKOR方法的核心内容是在确定正、负理想解的基础上，依据 各备选方案与理想方案的接近程度进行优劣排序。该方法考虑了群体效益最大 化和个体遗憾最小化，同时也考虑了决策者的主观偏好。并且VIKOR法得到的 是带有优先级的折中方案，更加逼近理想方案。Fuzzy VIKOR method is a multi-attribute decision-making method proposed by Yugoslav Professor Opricovic for complex systems. The core content of the fuzzy VIKOR method is to rank the pros and cons of the alternatives according to the closeness of each alternative to the ideal on the basis of determining the positive and negative ideal solutions. The method takes into account group benefit maximization and individual regret minimization, as well as the subjective preferences of decision makers. And the VIKOR method obtains a compromise solution with priority, which is closer to the ideal solution.

发明内容SUMMARY OF THE INVENTION

为了解决传统FMEA的缺点，本发明提出了一种基于区间三角模糊数与模 糊VIKOR方法的改进FMEA方法。该方法首先利用语言变量对失效模式的等级 和风险因子的相对重要度进行评价，语言变量用区间三角模糊数表示。其次利 用模糊层次分析法计算风险因子的主观权重，利用扩展的VIKOR法计算风险因 子的客观权重，并根据改进博弈论组合赋权法计算风险因子的综合权重。最后 利用模糊VIKOR法对失效模式的风险优先度进行排序。利用该方法对数控铣齿 机工件箱系统进行评价，结果验证了该方法的适用性和有效性。In order to solve the shortcomings of traditional FMEA, the present invention proposes an improved FMEA method based on interval triangular fuzzy numbers and fuzzy VIKOR method. The method first uses linguistic variables to evaluate the level of failure modes and the relative importance of risk factors. The linguistic variables are represented by interval triangular fuzzy numbers. Secondly, the subjective weight of risk factors is calculated by the fuzzy analytic hierarchy process, the objective weight of risk factors is calculated by the extended VIKOR method, and the comprehensive weight of risk factors is calculated according to the improved game theory combination weighting method. Finally, the fuzzy VIKOR method is used to sort the risk priority of failure modes. The method is used to evaluate the workpiece box system of CNC gear milling machine, and the results verify the applicability and effectiveness of the method.

本发明是通过以下的技术方案来实现的：The present invention is achieved through the following technical solutions:

本发明提出了一种基于区间三角模糊数与模糊VIKOR法的改进FMEA方法。 设定FMEA评估团队中有l个评估人员TMk(k＝1,2,...,l)对m个失效模式 FMi(i＝1,2,...,m)就n个风险因子RFj(j＝1,2,...,n)进行评估。FMEA评估 团队中评估人员的权重向量为(λ1，λ2，……λl)，且λk＞0，

Figure RE-GDA0002746306600000021
λk表示每 个评估人员在评估团队中的相对重要程度。设定评估人员TMk给出的评价结果 的，得到n个模糊决策矩阵
Figure RE-GDA0002746306600000031
和n个模糊决策向量
Figure RE-GDA0002746306600000032
i＝1,2,…,n；k＝1,2,3。
Figure RE-GDA0002746306600000033
与
Figure RE-GDA0002746306600000034
为FMEA成员利用语言变量对各失效模式的等级和各风险因子的相对重要度进行评价的矩阵。其中
Figure RE-GDA0002746306600000035
The invention proposes an improved FMEA method based on interval triangular fuzzy numbers and fuzzy VIKOR method. It is assumed that there are l assessors TM k (k=1,2,...,l) in the FMEA assessment team, and m failure modes FM i (i=1,2,...,m) are n risks The factor RF j (j=1,2,...,n) is evaluated. The weight vector of the evaluators in the FMEA evaluation team is (λ 1 , λ 2 , ... λ l ), and λ k > 0,
Figure RE-GDA0002746306600000021
λk represents the relative importance of each evaluator in the evaluation team. If the evaluation results given by the evaluator TM k are set, n fuzzy decision matrices 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 for FMEA members to use linguistic variables to evaluate the level of each failure mode and the relative importance of each risk factor. in
Figure RE-GDA0002746306600000035

基于上述设定，该方法包括以下步骤：Based on the above settings, the method includes the following steps:

步骤1：确定评价目标。Step 1: Determine the evaluation objectives.

步骤2：确定潜在的失效模式。Step 2: Identify potential failure modes.

步骤3：FMEA成员利用表1和表2中的语言变量对各失效模式的等级和各 风险因子的相对重要度进行评价。Step 3: FMEA members use the linguistic variables in Tables 1 and 2 to evaluate the level of each failure mode and the relative importance of each risk factor.

表1失效模式的等级的语言变量Table 1. Linguistic variables for the rank of failure modes

Figure BDA0002690581290000036
Figure BDA0002690581290000036

表2风险因子的相对重要度的语言变量Table 2 Linguistic variables of relative importance of risk factors

Figure BDA0002690581290000037
Figure BDA0002690581290000037

步骤4：汇总各FMEA成员的评价结果，得到n个模糊决策矩阵

Figure RE-GDA0002746306600000038
和 n个模糊决策向量
Figure RE-GDA0002746306600000039
Step 4: Summarize the evaluation results of each FMEA member to obtain n fuzzy decision matrices
Figure RE-GDA0002746306600000038
and n fuzzy decision vectors
Figure RE-GDA0002746306600000039

Figure RE-GDA0002746306600000041
Figure RE-GDA0002746306600000041

Figure RE-GDA0002746306600000042
Figure RE-GDA0002746306600000042

步骤5：确定决策矩阵

Figure RE-GDA0002746306600000043
和决策向量Wk。Step 5: Determine the Decision Matrix
Figure RE-GDA0002746306600000043
and the decision vector W k .

Figure RE-GDA0002746306600000044
Figure RE-GDA0002746306600000044

Figure RE-GDA0002746306600000045
Figure RE-GDA0002746306600000045

其中

Figure RE-GDA0002746306600000046
in
Figure RE-GDA0002746306600000046

步骤6：计算归一化决策矩阵

Figure RE-GDA0002746306600000047
Step 6: Calculate the normalized decision matrix
Figure RE-GDA0002746306600000047

Figure BDA0002690581290000048
Figure BDA0002690581290000048

步骤7：利用模糊层次分析法计算风险因子的主观权重

Figure BDA0002690581290000049
Step 7: Calculate the subjective weights of risk factors using fuzzy AHP
Figure BDA0002690581290000049

所述的模糊层次分析法(FAHP)的原理是将模糊一致矩阵和层次分析法相 融合，这样既保留了判断矩阵的模糊性，又保证了判断矩阵的一致性。利用模 糊层次分析法计算风险因子的主观权重步骤如下：The principle of the Fuzzy Analytic Hierarchy Process (FAHP) is to integrate the fuzzy consistency matrix and the analytic hierarchy process, which not only retains the ambiguity of the judgment matrix, but also ensures the consistency of the judgment matrix. The steps for calculating the subjective weight of risk factors using the fuzzy analytic hierarchy process are as follows:

(1)将

Figure RE-GDA00027463066000000410
用2个三角模糊数表示，即
Figure RE-GDA00027463066000000411
(1) will
Figure RE-GDA00027463066000000410
It is represented by 2 triangular fuzzy numbers, namely
Figure RE-GDA00027463066000000411

Figure RE-GDA00027463066000000412
k＝1,2,3。
Figure RE-GDA00027463066000000412
k=1,2,3.

(2)根据三角模糊数定义，即假设任意两个三角模糊数

Figure RE-GDA00027463066000000413
和
Figure RE-GDA00027463066000000414
的可能度见公式(6)。(2) According to the definition of triangular fuzzy numbers, that is, assuming any two triangular fuzzy numbers
Figure RE-GDA00027463066000000413
and
Figure RE-GDA00027463066000000414
The possibility of , see formula (6).

Figure RE-GDA00027463066000000415
Figure RE-GDA00027463066000000415

将

Figure RE-GDA00027463066000000416
两两进行重要程度比较，构建模糊互补判断矩阵 B1＝{Puv}3×3,u＝1,2,3；v＝1,2,3。其中
Figure RE-GDA00027463066000000417
且当u＝v时，
Figure RE-GDA00027463066000000418
模糊互补判断矩阵包含了所有元素相互比较的可能度信息，通过计算各元素的 排序向量来确定每个元素的占比。Will
Figure RE-GDA00027463066000000416
Comparing the importance levels in pairs, construct a fuzzy complementary judgment matrix B 1 ={P uv } 3×3 , u=1,2,3; v=1,2,3. in
Figure RE-GDA00027463066000000417
And when u=v,
Figure RE-GDA00027463066000000418
The fuzzy complementary judgment matrix contains the possibility information of all elements compared with each other, and the proportion of each element is determined by calculating the sorting vector of each element.

Figure RE-GDA0002746306600000051
Figure RE-GDA0002746306600000051

(3)根据公式(8)，计算

Figure BDA0002690581290000052
(3) According to formula (8), calculate
Figure BDA0002690581290000052

Figure BDA0002690581290000053
Figure BDA0002690581290000053

(4)重复步骤(2)-(3)，计算

Figure BDA0002690581290000054
(4) Repeat steps (2)-(3) to calculate
Figure BDA0002690581290000054

(5)根据公式(9)，计算风险因子的主观权重

Figure BDA0002690581290000055
(5) According to formula (9), calculate the subjective weight of the risk factor
Figure BDA0002690581290000055

Figure BDA0002690581290000056
Figure BDA0002690581290000056

步骤8：利用扩展VIKOR法计算风险因子的客观权重

Figure BDA0002690581290000057
Step 8: Calculate the objective weights of risk factors using the extended VIKOR method
Figure BDA0002690581290000057

(1)确定最佳值

Figure RE-GDA0002746306600000058
和最差值
Figure RE-GDA0002746306600000059
计算最佳值
Figure RE-GDA00027463066000000510
到最差值
Figure RE-GDA00027463066000000511
的距离。(1) Determine the best value
Figure RE-GDA0002746306600000058
and worst
Figure RE-GDA0002746306600000059
Calculate the best value
Figure RE-GDA00027463066000000510
to the worst
Figure RE-GDA00027463066000000511
the distance.

Figure RE-GDA00027463066000000512
Figure RE-GDA00027463066000000512

(2)根据公式(10)，计算

Figure RE-GDA00027463066000000513
到
Figure RE-GDA00027463066000000514
距离。(2) According to formula (10), calculate
Figure RE-GDA00027463066000000513
arrive
Figure RE-GDA00027463066000000514
distance.

Figure RE-GDA00027463066000000515
Figure RE-GDA00027463066000000515

(3)根据公式(11)，计算标准模糊距离。(3) According to formula (11), calculate the standard blur distance.

Figure RE-GDA00027463066000000516
Figure RE-GDA00027463066000000516

(4)根据公式(12)，计算风险因子的主观权重

Figure BDA00026905812900000517
(4) According to formula (12), calculate the subjective weight of the risk factor
Figure BDA00026905812900000517

Figure BDA00026905812900000518
Figure BDA00026905812900000518

步骤9：利用改进博弈论组合赋权法计算风险因子的综合权重

Figure BDA00026905812900000519
Step 9: Calculate the comprehensive weights of risk factors using the improved game theory portfolio weighting method
Figure BDA00026905812900000519

所述的博弈论组合赋权法旨在寻找主客观权重之间最大化的利益共同点， 使得综合权重与主客观权重之间的偏差最小。假设利用α种方法所得的权重向 量为

Figure BDA00026905812900000520
记L个权重向量的任意线性组合为：The described game-theoretic combined weighting method aims to find the maximal common point of interests between the subjective and objective weights, so that the deviation between the comprehensive weights and the subjective and objective weights is minimized. Assuming that the weight vector obtained by using α methods is
Figure BDA00026905812900000520
Denote any linear combination of L weight vectors as:

Figure BDA00026905812900000521
Figure BDA00026905812900000521

式中：εα为线性组合系数，εα>0，W表示所有可能出现的权重向量。以W 与Wα的离差最小为目标，对公式(13)中的L个线性组合系数εα进行优化。构建 对策模型：In the formula: ε α is the linear combination coefficient, ε α >0, W represents all possible weight vectors. The L linear combination coefficients εα in formula (13) are optimized with the aim of minimizing the dispersion between W and W α . Build a game model:

Figure BDA0002690581290000061
Figure BDA0002690581290000061

根据矩阵的微分性质得出公式(14)的最优化条件为：According to the differential properties of the matrix, the optimization condition of formula (14) is obtained as:

Figure BDA0002690581290000062
Figure BDA0002690581290000062

公式(15)的等价形式为：The equivalent form of formula (15) is:

Figure BDA0002690581290000063
Figure BDA0002690581290000063

求解公式(16)可得线性组合系数εα，但不能保证εα>0，这显然是与公式(13) 的假设是相悖的。Solving formula (16) can obtain the linear combination coefficient ε α , but it cannot guarantee that ε α >0, which is obviously contrary to the assumption of formula (13).

通过借鉴离差最大化客观赋权法的约束条件，可以确定改进的最优化模型 为：By referring to the constraints of the objective weighting method of maximizing dispersion, the improved optimization model can be determined as:

Figure BDA0002690581290000064
Figure BDA0002690581290000064

建立拉格朗日函数求解该模型：Set up a Lagrangian function to solve the model:

Figure BDA0002690581290000065
Figure BDA0002690581290000065

确定线性组合系数εα的解，并对εα进行归一化处理，即可确定组合权重系 数：Determine the solution of the linear combination coefficient ε α and normalize ε α to determine the combined weight coefficient:

Figure BDA0002690581290000066
Figure BDA0002690581290000066

Figure BDA0002690581290000067
Figure BDA0002690581290000067

将

Figure BDA0002690581290000068
带入公式(13)，即可求得综合权重为：Will
Figure BDA0002690581290000068
Bringing into formula (13), the comprehensive weight can be obtained as:

Figure BDA0002690581290000069
Figure BDA0002690581290000069

步骤10：利用模糊VIKOR法计算每个方案的Sj，Rj和Qj的值。Step 10: Calculate the values of S j , R j and Q j for each scheme using the fuzzy VIKOR method.

根据公式(22)，公式(23)和公式(24)计算群体效益最优解Sj，个别 遗憾最劣解Rj和综合指标Qj，选取

Figure BDA00026905812900000610
According to formula (22), formula (23) and formula (24), calculate the group benefit optimal solution S j , the individual regret worst solution R j and the comprehensive index Q j , select
Figure BDA00026905812900000610

Figure BDA0002690581290000071
Figure BDA0002690581290000071

Figure BDA0002690581290000072
Figure BDA0002690581290000072

Figure BDA0002690581290000073
Figure BDA0002690581290000073

步骤11：根据Sj，Rj和Qj对各失效模式的风险优先度进行排序。Step 11: Rank the risk priority of each failure mode according to S j , R j and Q j .

步骤12：提出折中方案。Step 12: Come up with a compromise.

有益效果beneficial effect

(1)它在处理不确定信息方面更有优势。FMEA成员的多样化观点可以通 过区间三角模糊数灵活准确的表达出来。(2)提出利用模糊层次分析法计算风 险因子的主观权重，利用扩展VIKOR法计算风险因子的客观权重，并利用改进 博弈论组合赋权法得到风险因子的综合权重。该方法能够兼顾主客观权重的优 点，在一定程度上避免了信息的丢失。(3)利用模糊VIKOR法对失效模式进行 排序。该方法充分考虑了群体效益最大化和个体遗憾最小化，同时也考虑了决 策者的主观偏好。(1) It has more advantages in dealing with uncertain information. The diverse views of FMEA members can be expressed flexibly and accurately through interval triangular fuzzy numbers. (2) It is proposed to use the fuzzy analytic hierarchy process to calculate the subjective weight of risk factors, use the extended VIKOR method to calculate the objective weight of risk factors, and use the improved game theory combined weighting method to obtain the comprehensive weight of risk factors. This method can take into account the advantages of subjective and objective weights and avoid the loss of information to a certain extent. (3) Use fuzzy VIKOR method to sort the failure modes. The method fully considers group benefit maximization and individual regret minimization, as well as the subjective preferences of decision makers.

附图说明Description of drawings

图1是本发明所提方法的流程图。Fig. 1 is the flow chart of the method proposed by the present invention.

具体实施方式Detailed ways

下面结合附图和实施例对本发明进一步说明。显然，所描述的实施例仅仅 是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领 域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属 于本发明保护的范围。The present invention will be further described below in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are only some, but not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.

本实施例对数控铣齿机工件箱系统进行评价。This embodiment evaluates the workpiece box system of the CNC gear milling machine.

本实施例中，FMEA团队由1名机床设计人员、1名装配工程师、1名质检 人员及1名操作工程师组成，其编号和权重分别为TM1(λ1＝0.2)、TM2(λ2＝0.35)、 TM3(λ3＝0.15)和TM4(λ4＝0.3)。风险因子为RF1：发生度(O)；RF2：严重度(S)； RF3：检测度(D)。In this embodiment, the FMEA team is composed of 1 machine tool designer, 1 assembly engineer, 1 quality inspector and 1 operation engineer, whose numbers and weights are TM1 (λ 1 =0.2) and TM2 (λ 2 = 0.35), TM3 (λ 3 =0.15) and TM4 (λ 4 =0.3). The risk factors are RF1: Occurrence (O); RF2: Severity (S); RF3: Detection (D).

步骤1：确定评价目标。评价目标为评价目标为数控铣齿机工件箱系统。 齿轮箱体内部为蜗轮蜗杆传动机构，采用油浸式润滑。工件的夹紧方式为液压 夹紧。其中一伺服电机驱动工件轴进行旋转运动，另一伺服电机驱动工件箱系 统进行弧形往复运动。加工时，喷嘴将切削液喷射至加工区域。Step 1: Determine the evaluation objectives. The evaluation target is the workpiece box system of CNC gear milling machine. The inside of the gear box is a worm gear transmission mechanism, which is lubricated by oil immersion. The clamping method of the workpiece is hydraulic clamping. One of the servo motors drives the workpiece shaft to rotate, and the other servo motor drives the workpiece box system to perform arc reciprocating motion. During machining, the nozzle sprays cutting fluid into the machining area.

步骤2：确定潜在的失效模式。确定了10种潜在的失效模式，FM1：齿轮 箱体漏油；FM2：液压缸漏油；FM3：轴承润滑不足；FM4：夹紧力不足；FM5： 齿轮磨损；FM6：齿轮润滑不足；FM7：电机温度过高；FM8：工件轴精度降低； FM9：切削液流量不足；FM10：轴承磨损。Step 2: Identify potential failure modes. 10 potential failure modes were identified, FM1: Gearbox oil leakage; FM2: Hydraulic cylinder oil leakage; FM3: Insufficient bearing lubrication; FM4: Insufficient clamping force; FM5: Gear wear; FM6: Insufficient gear lubrication; FM7: Motor temperature is too high; FM8: workpiece shaft accuracy is reduced; FM9: insufficient cutting fluid flow; FM10: bearing wear.

步骤3：FMEA成员利用表1和表2中的语言变量对失效模式的等级和风险 因子的相对重要度进行评价。Step 3: The FMEA members use the linguistic variables in Tables 1 and 2 to evaluate the level of failure modes and the relative importance of risk factors.

步骤4：汇总各FMEA成员的评价结果，得到4个模糊决策矩阵

Figure RE-GDA0002746306600000081
和 4个模糊决策向量
Figure RE-GDA0002746306600000082
结果如表3和表4。Step 4: Summarize the evaluation results of each FMEA member to obtain 4 fuzzy decision matrices
Figure RE-GDA0002746306600000081
and 4 fuzzy decision vectors
Figure RE-GDA0002746306600000082
The results are shown in Table 3 and Table 4.

表3失效模式等级的评价结果Table 3 Evaluation results of failure mode grades

Figure BDA0002690581290000083
Figure BDA0002690581290000083

表4风险因子相对重要度的评价结果Table 4 Evaluation results of the relative importance of risk factors

Figure BDA0002690581290000091
Figure BDA0002690581290000091

步骤5：确定决策矩阵

Figure RE-GDA0002746306600000092
和决策向量
Figure RE-GDA0002746306600000093
结果如表5。Step 5: Determine the Decision Matrix
Figure RE-GDA0002746306600000092
and decision vector
Figure RE-GDA0002746306600000093
The results are shown in Table 5.

表5失效模式等级和风险因子相对重要度的综合评价结果Table 5 Comprehensive evaluation results of failure mode level and relative importance of risk factors

Figure BDA0002690581290000094
Figure BDA0002690581290000094

步骤6：计算归一化决策矩阵

Figure RE-GDA0002746306600000095
结果如表6。Step 6: Calculate the normalized decision matrix
Figure RE-GDA0002746306600000095
The results are shown in Table 6.

表6归一化决策矩阵Table 6 Normalized decision matrix

Figure BDA0002690581290000096
Figure BDA0002690581290000096

Figure BDA0002690581290000101
Figure BDA0002690581290000101

步骤7：利用模糊层次分析法计算风险因子的主观权重

Figure BDA0002690581290000102
Step 7: Calculate the subjective weights of risk factors using fuzzy AHP
Figure BDA0002690581290000102

(1)将

Figure RE-GDA0002746306600000103
用2个三角模糊数表示。(1) will
Figure RE-GDA0002746306600000103
It is represented by 2 triangular fuzzy numbers.

Figure RE-GDA0002746306600000104
Figure RE-GDA0002746306600000104

Figure RE-GDA0002746306600000105
Figure RE-GDA0002746306600000105

Figure RE-GDA0002746306600000106
Figure RE-GDA0002746306600000106

(2)构建模糊互补判断矩阵B1和B2。(2) Constructing fuzzy complementary judgment matrices B 1 and B 2 .

Figure BDA0002690581290000107
Figure BDA0002690581290000107

Figure BDA0002690581290000108
Figure BDA0002690581290000108

(3)计算

Figure BDA0002690581290000109
和
Figure BDA00026905812900001010
的值。(3) Calculation
Figure BDA0002690581290000109
and
Figure BDA00026905812900001010
value of .

Figure BDA00026905812900001011
Figure BDA00026905812900001011

Figure BDA00026905812900001012
Figure BDA00026905812900001012

(4)计算风险因子的主观权重

Figure BDA00026905812900001013
(4) Calculate the subjective weight of risk factors
Figure BDA00026905812900001013

Figure BDA00026905812900001014
Figure BDA00026905812900001014

步骤8：利用扩展VIKOR法计算风险因子的客观权重

Figure BDA00026905812900001015
Step 8: Calculate the objective weights of risk factors using the extended VIKOR method
Figure BDA00026905812900001015

(1)计算

Figure RE-GDA00027463066000001016
到
Figure RE-GDA00027463066000001017
的距离，结果如表7。(1) Calculation
Figure RE-GDA00027463066000001016
arrive
Figure RE-GDA00027463066000001017
distance, the results are shown in Table 7.

表7

Figure RE-GDA00027463066000001018
到
Figure RE-GDA00027463066000001019
的距离Table 7
Figure RE-GDA00027463066000001018
arrive
Figure RE-GDA00027463066000001019
the distance

Figure RE-GDA00027463066000001020
Figure RE-GDA00027463066000001020

Figure BDA0002690581290000111
和
Figure BDA0002690581290000112
的值。
Figure BDA0002690581290000111
and
Figure BDA0002690581290000112
value of .

Figure BDA0002690581290000113
Figure BDA0002690581290000113

Figure BDA0002690581290000114
Figure BDA0002690581290000114

(3)计算风险因子的客观权重

Figure BDA0002690581290000115
(3) Calculate the objective weight of risk factors
Figure BDA0002690581290000115

Figure BDA0002690581290000116
Figure BDA0002690581290000116

步骤9：利用改进博弈论组合赋权法计算风险因子的综合权重

Figure BDA0002690581290000117
Step 9: Calculate the comprehensive weights of risk factors using the improved game theory portfolio weighting method
Figure BDA0002690581290000117

(1)计算组合权重系数。(1) Calculate the combined weight coefficient.

Figure BDA0002690581290000118
Figure BDA0002690581290000118

(2)计算风险因子的综合权重

Figure BDA0002690581290000119
(2) Calculate the comprehensive weight of risk factors
Figure BDA0002690581290000119

Figure BDA00026905812900001110
Figure BDA00026905812900001110

Figure BDA00026905812900001111
Figure BDA00026905812900001111

Figure BDA00026905812900001112
Figure BDA00026905812900001112

步骤10：利用模糊VIKOR法计算每个方案的Sj，Rj和Qj的值，结果如表8， 表9和表10。Step 10: Calculate the values of S j , R j and Q j for each scheme using the fuzzy VIKOR method. The results are shown in Table 8, Table 9 and Table 10.

表8失效模式的Sj值Table 8 Sj values for failure modes

Figure BDA00026905812900001113
Figure BDA00026905812900001113

表9失效模式的Rj值Table 9 Rj values for failure modes

Figure BDA00026905812900001114
Figure BDA00026905812900001114

表10失效模式的Qj值Table 10 Q j values for failure modes

Figure BDA00026905812900001115
Figure BDA00026905812900001115

步骤11：根据Sj，Rj和Qj对各失效模式的风险优先度进行排序。Step 11: Rank the risk priority of each failure mode according to S j , R j and Q j .

(1)从表11可知，按照据Sj，Rj和Qj对失效模式的风险优先度进行排序， FM2都是最严重的失效模式，应该被给予最高的风险优先度，10种失效模式的 风险优先度顺序为FM2>FM4>FM8>FM3>FM1>FM10>FM6>FM5>FM7>FM9。(1) It can be seen from Table 11 that according to the risk priority of failure modes according to S j , R j and Q j , FM2 is the most serious failure mode and should be given the highest risk priority. There are 10 failure modes. The risk priority order of FM2>FM4>FM8>FM3>FM1>FM10>FM6>FM5>FM7>FM9.

表11失效模式风险优先度的顺序Table 11 Sequence of Failure Mode Risk Priority

Figure BDA0002690581290000121
Figure BDA0002690581290000121

步骤12：提出折中方案。Step 12: Come up with a compromise.

本文的折中方案对应于风险优先度最低的方案。根据所述的模糊VIKOR 法中所述的规则，

Figure BDA0002690581290000122
FM9按照Sj、Rj和Qj排序均是风险 优先度最低的方案，满足条件1和条件2。因此。失效模式的折中方案FM9。 本实施例仅为本发明较佳的具体实施方式，但本发明的保护范围并不局限于 此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，根据本发明 的技术方案及其发明构思加以等同替换或改变，都应涵盖在本发明的保护范围 之内。The compromise in this paper corresponds to the one with the lowest risk priority. According to the rules stated in the said fuzzy VIKOR method,
Figure BDA0002690581290000122
FM9 ranked according to S j , R j and Q j is the scheme with the lowest risk priority, which satisfies conditions 1 and 2. therefore. Compromise of failure modes FM9. The present embodiment is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited thereto. The equivalent replacement or modification of its inventive concept shall be included within the protection 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
CN202010990123.XA 2020-09-18 2020-09-18 Improved FMEA Method Based on Interval Triangular Fuzzy Number and Fuzzy VIKOR Method Active CN112115561B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010990123.XA CN112115561B (en) 2020-09-18 2020-09-18 Improved FMEA Method Based on Interval Triangular Fuzzy Number and Fuzzy VIKOR Method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010990123.XA CN112115561B (en) 2020-09-18 2020-09-18 Improved FMEA Method Based on Interval Triangular Fuzzy Number and Fuzzy VIKOR Method

Publications (2)

Publication Number Publication Date
CN112115561A true CN112115561A (en) 2020-12-22
CN112115561B CN112115561B (en) 2022-04-22

Family

ID=73799940

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010990123.XA Active CN112115561B (en) 2020-09-18 2020-09-18 Improved FMEA Method Based on Interval Triangular Fuzzy Number and Fuzzy VIKOR Method

Country Status (1)

Country Link
CN (1) CN112115561B (en)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140200699A1 (en) * 2013-01-17 2014-07-17 Renesas Electronics Europe Limited Support system
CN104992281A (en) * 2015-06-29 2015-10-21 中国信息安全研究院有限公司 Method for achieving electronic product reliability evaluation
CN107688912A (en) * 2017-09-22 2018-02-13 南京信息工程大学 One kind mixing sustainable chemical industry evaluation method of conflict type
CN108985554A (en) * 2018-06-05 2018-12-11 上海大学 A method of the improvement FMEA based on interval-valued intuitionistic fuzzy set and mixing multiple criteria decision making (MCDM) model

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140200699A1 (en) * 2013-01-17 2014-07-17 Renesas Electronics Europe Limited Support system
CN104992281A (en) * 2015-06-29 2015-10-21 中国信息安全研究院有限公司 Method for achieving electronic product reliability evaluation
CN107688912A (en) * 2017-09-22 2018-02-13 南京信息工程大学 One kind mixing sustainable chemical industry evaluation method of conflict type
CN108985554A (en) * 2018-06-05 2018-12-11 上海大学 A method of the improvement FMEA based on interval-valued intuitionistic fuzzy set and mixing multiple criteria decision making (MCDM) model

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
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》 *

Also Published As

Publication number Publication date
CN112115561B (en) 2022-04-22

Similar Documents

Publication Publication Date Title
Altan et al. The effect of kernel values in support vector machine to forecasting performance of financial time series
CN110782164A (en) Power distribution equipment state evaluation method based on variable weight and fuzzy comprehensive evaluation
CN110007652B (en) A method and system for predicting the deterioration trend interval of a hydroelectric unit
CN109495296B (en) Evaluation method of communication network status of intelligent substation based on clustering and neural network
Li A fuzzy closeness approach to fuzzy multi-attribute decision making
CN108305014A (en) A kind of failure model and effect analysis method based on reliability room and Rough Ideals point method
CN110717654B (en) Product Quality Evaluation Method and System Based on User Reviews
CN108256763A (en) Nonstandard components supplying quotient manufacturing capacity analysis method and device based on analytic hierarchy process (AHP)
Araghinejad et al. Application of data-driven models in drought forecasting
Sadabadi et al. A new index for TOPSIS based on relative distance to best and worst points
US8463678B2 (en) Generating method for transaction models with indicators for option
CN110782157A (en) Maintenance mode making method based on importance of power generation equipment
CN111814728A (en) Recognition method and storage medium for tool wear state of CNC machine tools
CN108920806A (en) A kind of heavy machine tool reliability allocation methods based on Trapezoid Fuzzy Number and ranking method
Yang et al. Constructing novel operational laws and information measures for proportional hesitant fuzzy linguistic term sets with extension to PHFL-VIKOR for group decision making
CN108319776B (en) Simulation parameter selection decision method based on group generalized interval intuitive fuzzy soft set
CN112115561B (en) Improved FMEA Method Based on Interval Triangular Fuzzy Number and Fuzzy VIKOR Method
Jiang et al. TOPSIS with belief structure for group belief multiple criteria decision making
CN113469370B (en) Industrial Internet of things data sharing method based on federal incremental learning
CN106529799A (en) Sustainable design index evaluation method for machine tool
CN112415894A (en) Control method for safe operation of dense medium coal preparation process based on active learning and BN
CN117522208A (en) Method for constructing index evaluation system based on electric power spot market
CN104850711A (en) Mechanical and electrical product design standard selecting method
CN115796693A (en) Beer production enterprise energy efficiency determination method and system and electronic equipment
Zhang Research of default risk of commercial bank's personal loan based on rough sets and neural network

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant