Improved FMEA method based on LINMAP, ELECTRE-VIKOR and mean shift clustering

Abstract

The application provides an improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering, and comprises the following steps: assigning weights to experts with different opinions by minimizing variance and and using majority voting method; calculating subjective and objective weights of risk factors by using LINMAP method and CRITIC method and calculating comprehensive weights of risk factors by using combination weighting based on uninorm operator; sorting failure modes by using ELECTRE-VIKOR, and finally analyzing the failure modes by using Mean shift clustering. The application provides an effective and reliable method for reliability and risk assessment of the MES system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of reliability analysis methods, and particularly relates to an improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering. BACKGROUND

[0002] Failure mode and effects analysis (FMEA) has been a risk assessment tool for assessing system reliability and risk, and identifying potential failures of a system. In the traditional FMEA, experts score the severity (S), occurrence (O) and detection (D) of failure modes based on their experience, and then multiply them to calculate the risk priority number (RPN) for ranking the failure modes. FMEA is widely used in reliability and risk management analysis in various fields. As a risk management tool, there are some shortcomings in the traditional FMEA process. First, the relative weights of various risk factors are not considered. It assumes that the weights of the three risk factors are the same and multiplies them. However, it is inaccurate when it comes to different situations and applications, ignoring the differences between risk factors. Second, the traditional FMEA always uses precise numbers to evaluate the risk factors of failure modes, and the evaluation is mainly based on the subjective opinions of experts. It is difficult for experts to give accurate risk assessment in an uncertain environment. Third, the calculated RPN values are sometimes the same, but the risk implications of failure modes can be completely different.

[0003] Multi-criteria compromise solution ordering method (VIKOR) is a compromise ordering method based on Lp-metric aggregation function, which determines the ranking of solutions by the closeness to the ideal solution. It can overcome the shortcomings of the approximation ideal solution ordering method, consider the maximization of group benefit and the minimization of individual regret against opinions, and fully consider the subjective preferences of decision makers.

[0004] Elimination and selection transformation method (ELECTRE) originated from Roy Company in the late 1960s, and is a comparison method of alternative solutions based on 2x2 scale. The consistent and inconsistent indexes of ERLCTRE method are used to represent the satisfaction and dissatisfaction of experts in determining the priority of two solutions.

[0005] Linear programming method of multi-dimensional preference analysis (LINMAP) is a multi-dimensional preference analysis method proposed by Srinivasan and Shocker in 1973. The basic concept of LINMAP method is to use the partial or complete comparison preference information between solutions given by decision makers to measure the consistency and inconsistency between solutions by distance, and construct the corresponding linear programming model.

[0006] The main idea of Mean shift clustering is to perform gradient ascent on the local density estimate for each data point in the feature space until convergence. The stationary points of this process represent the modes of the distribution. In addition, data points that are related (at least approximately) to the same fixed point are considered to be data points of the same cluster.

[0007] Therefore, it is an urgent technical problem to develop an improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering, which is of great significance to solve the deficiencies in the traditional FMEA process and the reliability and risk analysis of related systems. SUMMARY

[0008] The purpose of the present application is to provide an improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering, which is applied to the reliability and risk analysis of manufacturing execution systems, determines the importance of each failure mode in the manufacturing execution system and the key risk source, and verifies the reliability and effectiveness of the improved method. The technical scheme adopted is as follows:

[0009] An improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering, comprising the following steps:

[0010] Assigning weights to experts holding different opinions by minimizing variance and majority voting method;

[0011] Using LINMAP method and CRITIC (Criteria Importance Though Intercrieria Correlation) method to calculate the subjective and objective weights of risk factors and using combination weighting based on uninorm operator to calculate the comprehensive weight of risk factors;

[0012] Using ELECTRE-VIKOR to sort failure modes;

[0013] Finally, using Mean shift clustering to analyze failure modes.

[0014] Preferably, the step of assigning weights to experts holding different opinions specifically comprises:

[0015] Step S1, determining potential failure modes of the research object;

[0016] Step S2, obtaining failure mode evaluation table and expert subjective preference table;

[0017] Step S3, converting the failure mode evaluation table into an expert scoring table, and obtaining the risk priority number RPN of each failure mode based on the expert scoring tablei ;

[0018] Step S4, converting the language variables in the expert scoring table into corresponding triangular fuzzy numbers to obtain the fuzzy evaluation matrix of the kth expert

[0019] Step S5, based on the fuzzy evaluation matrix Step S2, the expert subjective preference table obtained is used to calculate the comprehensive expert weight λ k .

[0020] Preferably, step S5 specifically comprises the following steps:

[0021] Step S51, based on the fuzzy evaluation matrix Step S51, the variance-based weight λ of the kth expert is calculated k ′;

[0022] Step S52, based on the expert subjective preference table obtained in step S2, the voting-based expert weight λ is calculated k ″;

[0023] Step S53, based on the combination weighting method of the uninorm operator, λ k ′ and λ k ″, the comprehensive expert weight λ k .

[0024] Preferably, based on the comprehensive expert weight λ k and the fuzzy evaluation matrix , the comprehensive risk factor weight w j is calculated, and the specific steps include:

[0025] Step S61, the objective risk factor weight w j ′ calculated by the CRITIC method:

[0026] Step S61A, the fuzzy evaluation matrix is de-fuzzified to obtain the matrix

[0027] Step S61B, the matrix and λ k are weighted and added to obtain the decision matrix X;

[0028] Step S61C, the decision matrix X is standardized to obtain the standardized matrix R;

[0029] Step S61D, w j ′ is obtained;

[0030] Step S62, based on the expert subjective preference table obtained in step S2, the subjective risk factor weight w is calculated using the LINMAP methodj

[0031] Step S63, the combination weighting method based on uninorm operator, w j ′ and w j ″, to obtain the comprehensive risk factor weight w j .

[0032] Preferably, the specific steps of using ELECTRE-VIKOR to rank the failure modes include:

[0033] Step S7, based on the comprehensive risk factor weight w j and the normalized matrix R, the integrated dominance matrix E is calculated, and the most important failure mode is obtained based on the integrated dominance matrix E;

[0034] Step S8, the maximum group effect value S i , the minimum individual regret value R i of each failure mode is calculated, the maximum group utility weight value υ is solved, and the comprehensive evaluation value Q i is determined;

[0035] Step S9, the S i , R i , Q i values are sorted in ascending order to obtain three sequences, and after obtaining the ranking result, the most important failure mode is obtained.

[0036] Preferably, the specific steps of using Mean shift clustering to analyze the failure modes include:

[0037] S10, the RPN value and the Q value are taken as two characteristic values for describing the i th failure mode to obtain a description matrix F, and the Mean shift clustering method is used for clustering;

[0038] S11, according to the clustering result and the ranking result, the research object is analyzed, and the corresponding prevention and monitoring resource allocation and risk management are carried out for different failure modes.

[0039] Compared with the prior art, the advantages of the present application are:

[0040] By minimizing the variance sum and the majority voting method, the weights of experts holding different opinions are allocated, the subjective and objective weights of risk factors are calculated using the LINMAP method and the CRITIC method, the comprehensive weight of the risk factor is calculated based on the uninorm operator combination weighting, then the failure modes are ranked using ELECTRE-VIKOR, and finally the failure modes are analyzed using Mean shift clustering. The results show that the improved FMEA method provides an effective and reliable method for reliability and risk assessment of the manufacturing execution system. ​BRIEF DESCRIPTION OF DRAWINGS

[0041] Fig. 1 A schematic diagram of the improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering according to the present application;

[0042] Fig. 2 Mean shift clustering results of failure modes in a manufacturing execution system for the improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering according to the present application DETAILED DESCRIPTION

[0043] The improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering according to the present application will be described in more detail below with reference to the accompanying drawings, in which the preferred embodiments of the present application are shown, it being understood that the present application described herein can be modified by those skilled in the art, while still achieving the advantageous effects of the present application. Therefore, the following description should be understood as a broad knowledge for those skilled in the art, rather than as a limitation of the present application.

[0044] Reference Figs. 1-2 An improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering, comprising:

[0045] The present embodiment is analyzed and evaluated for a manufacturing execution system (MES).

[0046] Step S1, determining potential failure modes of the research object.

[0047] According to the requirements, an FMEA expert team is formed, the operation and structure of the research object are analyzed, and m potential failure modes of the research object are determined through brainstorming, literature review and expert interviews.

[0048] In the present embodiment, the FMEA team consists of an expert one for MES implementation consultant, an expert two for information technology consulting expert, an expert three for information technology project senior manager, and an expert four for university scholar in the field of intelligent manufacturing.

[0049] Determine the failure modes of the manufacturing execution system and analyze their effects.

[0050] At the same time, for convenience of expression, the above failure modes are represented by numbers FMi (i = 1, 2, …, 22), and the obtained failure modes are shown in Table 1.

[0051] Table 1 Failure modes of MES and their categories

[0052]

[0053] Step S2, obtaining the failure mode evaluation table and the expert subjective preference table.

[0054] Each expert in the FMEA expert team evaluates the n risk factors of each failure mode to obtain the failure mode evaluation table;

[0055] Each expert in the FMEA expert team selects the most important and the least important failure mode under each category to obtain the expert subjective preference table.

[0056] The specific process of step S2 is as follows:

[0057] Each expert in the FMEA expert team evaluates the n risk factors of each failure mode, and uses five language variables to evaluate the risk factors of the failure mode, i.e. very low (VL), low (L), medium (M), high (H), and very high (VH). Based on the language variable corresponding to the evaluation standard (wherein the evaluation standard of S, O, and D risk factors is shown in Table 2), the failure mode evaluation table (Table 3) is obtained, and the most important and the least important failure mode is selected according to the category to obtain the expert subjective preference (Table 4).

[0058] Table 2 Evaluation standard reference table

[0059]

[0060] Four experts in the field of intelligent manufacturing scored each failure mode risk factor according to the evaluation standard (as shown in Table 2). The four experts belong to different fields of manufacturing execution system and judge the same failure mode from different angles.

[0061] The failure mode evaluation table of the FMEA team members for the failure mode is shown in Table 3, and the preference is selected among the failure modes in the same category (the most important and the least important failure mode is selected in the same category), and the expert preference table is shown in Table 4.

[0062] Table 3 Failure mode evaluation table

[0063]

[0064] Table 4 Expert preference table

[0065]

[0066] In Table 4, the failure modes FM1 and FM3 under the category "resource allocation and state management" are taken as examples to explain Table 4:

[0067] Expert 1 subjectively considers that FM1 is the most important failure mode, and experts 2-4 subjectively consider that FM1 is neither the most important failure mode nor the least important failure mode.

[0068] Experts 1-4 subjectively consider that FM3 is the least important failure mode.

[0069] Step S3, converting the failure mode evaluation table into an expert score table, and obtaining the risk priority number RPN of each failure mode based on the expert score table i .

[0070] Specifically, according to the correspondence between the fuzzy language variable and the traditional FMEA score value, the language variables of the severity (S), occurrence (O), and detectability (D) of the failure mode evaluation table are converted into the score values of each expert for each risk factor in the traditional FMEA according to table 2, that is, the failure mode evaluation table is converted into an expert score table.

[0071] The arithmetic mean of all expert score values of each risk factor is calculated and taken as the numerical value of each risk factor in the traditional FMEA;

[0072] The numerical values of the three risk factors are multiplied to obtain the risk priority number RPN of each failure mode in the traditional FMEA method i .

[0073] Taking the failure mode FM1 in the expert score table as an example, the calculation process of the corresponding risk priority number RPN1 is described:

[0074] The scores of severity S by expert 1 (DM1), expert 2 (DM2), expert 3 (DM3), and expert 4 (DM4) are 4, 3, 2, and 3, respectively, and the arithmetic mean of severity S is 3.

[0075] Similarly, the arithmetic means of occurrence O and detectability D are calculated.

[0076] Then RPN1 = arithmetic mean of severity S * arithmetic mean of occurrence O * arithmetic mean of detectability D.

[0077] Step S4, converting the language variables in the expert score table into corresponding triangular fuzzy numbers There are l experts in the FMEA team, and the fuzzy evaluation matrix of the kth expert is

[0078] Where i represents the number of the failure mode;

[0079] j represents the number of the risk factor under the failure mode i;

[0080] m represents the number of failure modes; n' represents the number of risk factors*3.

[0081] Taking the failure mode FM1 corresponding to expert 1 in the expert scoring table as an example, the calculation process of the triangular fuzzy number corresponding thereto is described.

[0082] The expert DM1 language variables corresponding to the failure mode FM1 are H, M, and L in turn, and the corresponding triangular fuzzy numbers are (6, 8, 10), (3, 5, 7), and (0, 2, 4). For example, the triangular fuzzy number corresponding to H is (6, 8, 10).

[0083] Finally, the fuzzy evaluation matrix of the kth member, such as expert 1, is as follows:

[0084] Table 5 Fuzzy evaluation matrix of expert 1

[0085]

[0086]

[0087] Step S5, based on the fuzzy evaluation matrix Based on the expert subjective preference table obtained in step S2, the comprehensive expert weight λ is calculated k . Wherein, k = 1 ~ l.

[0088] Step S51, based on the fuzzy evaluation matrix The variance-based weight λ of the kth expert is calculated k ′.

[0089] Specifically, the following steps are included:

[0090] Step S51A, based on the fuzzy evaluation matrix The average fuzzy evaluation matrix The variance matrix of the kth expert is calculated.

[0091]

[0092] The elements in the variance matrix are variances.

[0093] The average fuzzy evaluation matrix As shown in Table 6.

[0094] The number of rows of the failure mode in Table 6 is 22, and the number of columns of the risk factor*3 is 9, i.e. the number of rows m = 22 and the number of columns n' = 9 of the fuzzy evaluation matrix .

[0095] Table 6 Average fuzzy evaluation matrix

[0096]

[0097]

[0098] Step S51B, calculate the sum of variance of the kth expert V k .

[0099] V k is the sum of all elements in the variance matrix.

[0100] The sum of variance of the experts is calculated as V1=515.0625, V2=539.5625, V3=1318.5630, V4=483.5625.

[0101] Step S51C, based on V k , calculate λ k ′.

[0102]

[0103] The expert weights based on variance are calculated as:

[0104] λ1′=0.27323, λ2′=0.27038, λ3′=0.17948, λ4′=0.27691.

[0105] Step S52, based on the expert subjective preference table obtained in step S2, calculate the expert weights based on voting λ k ″.

[0106] Specifically, the following steps are included:

[0107] Step S52A, count the number of votes for the most important and the least important failure mode in the expert subjective preference table, and take the number as the score of the failure mode.

[0108] Specifically, if t experts in the l experts select a certain failure mode as the most important failure mode, then the failure mode is set as t points in the most important vote, and if t' experts in the l experts select a certain failure mode as the least important failure mode, then the failure mode is set as t' points in the least important vote.

[0109] Taking the failure modes FM1 and FM3 in the expert subjective preference table as examples, the calculation process of the score of the failure mode is described:

[0110] In FM1, the number of votes for the most important failure mode is 1, i.e., expert 1, and the number of votes for the least important failure mode is 0.

[0111] Step S52B, calculate the sum of scores of the most important vote of the kth expert T k ′ points, and the sum of scores of the least important vote T k ″ points.

[0112] Taking expert 1 as an example, expert 1 considers FM1, FM4, FM8, FM13, FM14, FM16, FM18 and FM21 as the most important failure modes, and the scores of the above most important failure modes are 1, 2, 3, 2, 2, 4, 4 and 2 respectively, which are added to obtain T1' = 20. Expert 1 considers FM3, FM6, FM9, FM12, FM15, FM17, FM19 and FM20 as the least important failure modes, and the scores of the above least important failure modes are 4, 4, 4, 4, 2, 4, 4 and 2 respectively, which are added to obtain T1'' = 28.

[0113] Step S52C, based on T k ' and T k '', calculate λ k ''.

[0114]

[0115] The expert weights obtained according to the majority voting method are as follows:

[0116] λ1'' = 0.2449, λ2'' = 0.2551, λ3'' = 0.2449, λ4'' = 0.2551.

[0117] Step S53, based on the combination weighting method of the uninorm operator, λ k ' and λ k '', obtain the comprehensive expert weight λ k .

[0118] Let g' = 1 / n, and there are generally the following several cases:

[0119] The first case is that both weights are greater than 0 and less than g', and λ k '''= λ k ' λ k '' / g';

[0120] The second case is that both weights are greater than g' and less than 1.

[0121] At this time, λ k '''= (λ k ' + λ k '' - λ k ' λ k '' - g') / (1-g');

[0122] For the remaining cases, λ k '''= (λ k ' + λ k) / 2,

[0123] Finally λ k "normalized to get the comprehensive expert weight λ k .

[0124] Wherein, n represents the number of weights need to be combined.

[0125] Finally, the comprehensive weights of the four experts obtained by the uninorm operator-based combination weighting method are:

[0126] λ1=0.2671, λ2=0.2753, λ3=0.1755, λ4=0.2820.

[0127] Step S6, based on the comprehensive expert weight λ k and the fuzzy evaluation matrix The comprehensive risk factor weight w j is calculated, wherein j=1~n.

[0128] Step S61, the objective risk factor weight w j ′ calculated by the CRITIC method.

[0129] Step S61A, the fuzzy evaluation matrix is de-fuzzified to obtain the matrix

[0130]

[0131] The set of

[0132] Step S61B, the matrix and λ k are weighted and added to obtain the decision matrix X.

[0133]

[0134] X=(x ij ) m×n

[0135] Wherein, m represents the number of failure modes; n represents the number of risk factors.

[0136] The decision matrix X is shown in Table 7.

[0137] Table 7 Decision matrix

[0138]

[0139]

[0140] Step S61C: Standardize the decision matrix X to obtain the standardized matrix R.

[0141]

[0142] R = (r ij ) m×n

[0143] The standardized matrix R is shown in Table 8.

[0144] Table 8 Standardization Matrix R

[0145]

[0146]

[0147] Step S61D, Obtain w j ′.

[0148] Calculate the correlation coefficient

[0149] in and It is the arithmetic mean of the sum of the failure mode scores of the j-th and p-th risk factors;

[0150] by For example, the arithmetic mean of the sum of the failure mode scores of the first risk factor (i.e., risk factor S) is...

[0151] Calculate the standard deviation of each risk factor.

[0152] calculate

[0153] calculate

[0154] The weights calculated using the CRITIC method, after normalization, yield the objective risk factor weights as (0.3881, 0.3441, 0.2678).

[0155] Step S62: Based on the expert subjective preference table obtained in step S2, calculate the subjective risk factor weights w using the LINMAP method. j ″.

[0156] Step S62A: Convert the expert's preference table into a preference set.

[0157] According to the preferences of the expert team for each category of failure modes, the expert team selects the most important and the least important for each category of failure modes for m failure modes, thereby obtaining the expert preference set Ω = {(g, h) | A g ≥ A h (g, h = 1, 2,..., m)}.

[0158] Wherein, A g ≥ A h represents that the gth failure mode is more important than the hth failure mode.

[0159] Each category corresponds to an expert preference set.

[0160] The preferences of the corresponding experts in Table 4 are converted into the preference set as follows:

[0161] Ω = {(g, h) | A g ≥ A3(g, h = 1, 2, 3)} Ω = {(g, h) | A g ≥ A6(g, h = 4, 5, 6, 7)}

[0162] Ω = {(g, h) | A g ≥ A9(g, h = 8, 9, 10)} Ω = {(g, h) | A g ≥ A 12 (g, h = 11, 12, 13)}

[0163] Ω = {(g, h) | A g ≥ A 17 (g, h = 16, 17)} Ω = {(g, h) | A g ≥ A 19 (g, h = 18, 19)}

[0164] The reason why there are 9 categories in Table 4 and 6 expert preference sets is that when the expert preferences are the same under the same failure mode, the expert preferences do not need to be converted into the preference set.

[0165] Step S62B, calculate the overall consistency index G' and the overall inconsistency index B'.

[0166] Calculate the Euclidean distance S' of each failure mode from the positive ideal solution + and the Euclidean distance S' from the negative ideal solution - :

[0167] Positive ideal solution

[0168] Euclidean distance of the ith failure mode from the positive ideal solution

[0169] Based on the preference set Ω = {(g, h) | A g ≥ A h (g, h = 1, 2, …, m)} to construct the consistency index (S h ′- S g ′) +

[0170]

[0171] Based on the preference set to construct the inconsistency index (S h -S g ) - :

[0172]

[0173] The overall consistency index and the overall inconsistency index

[0174] S h ′ + represents the Euclidean distance between the hth failure mode and the positive ideal solution; S h ′ - represents the Euclidean distance between the hth failure mode and the negative ideal solution.

[0175] Step S62C, a linear programming model is established to minimize B', and w j ″ is solved.

[0176] In the mathematical model in the LINMAP method, h' = 0.1, ε1 = 0.1, and ε2 = 1 are set according to the previously obtained weights.

[0177] The linear programming equation set is obtained as:

[0178] min{B'}

[0179]

[0180] The subjective weight of the risk factor obtained by the LINMAP method solved by LINGO11 is (0.2757, 0.4487, 0.2757).

[0181] Step S63, based on the uninorm operator combination weighting method, w j ′ and w j ″, the comprehensive risk factor weight w j is obtained.

[0182] The comprehensive weight of the risk factor obtained by the uninorm operator combination weighting method is (0.3283, 0.4526, 0.2191).

[0183] Step S7, based on the comprehensive risk factor weight w j and the normalized matrix R, the integrated dominant matrix E is calculated, and the most important failure mode is obtained based on the integrated dominant matrix E.

[0184] Step S71, the weighted standard matrix R' is calculated.

[0185] R'=w j ·R

[0186] Step S72, the consistency index c αβ is calculated, and the consistency matrix C is obtained; the inconsistency index d αβ is calculated, and the inconsistency matrix D is obtained.

[0187]

[0188] C=(c αβ ) m×m

[0189]

[0190] D=(d αβ ) m×m

[0191] wherein C αβ ={j|r αj ′≥r βj ′},α,β∈{1,2,...,m},j∈{1,2,...,n}

[0192] D αβ ={j|r αj ′<r βj ′}=J-C αβ ,α,β∈{1,2,...,m},j∈{1,2,...,n}

[0193] J is the set of j.

[0194] Taking C 21 as an example, in the weighted standard matrix R', for the same risk factor j, r2′ j >r1′ j , then j is an element in the set C 21 .

[0195] In the S failure mode, r2′1=0.259981 (weighted by 0.7919 in Table 8), r1′1=0.17482 (weighted by 0.5325 in Table 8), r2′1 is greater than r1′1, so j=1 is an element in the set C 21 .

[0196] Step S73, calculating the consistent dominance matrix from the consistency matrix C and the contradictory dominance matrix from the consistency matrix D.

[0197] Threshold for calculating the consistent dominance matrix The corresponding consistent dominance matrix f is 1 when the element in the consistency matrix is greater than or equal to the threshold value, and 0 otherwise. αβ αβ m×m ;

[0198] Threshold for calculating the contradictory dominance matrix The corresponding consistent dominance matrix g is 1 when the element in the consistency matrix is less than or equal to the threshold value, and 0 otherwise. αβ αβ m×m ;

[0199] Step S74, calculating the integrated dominance matrix E based on the consistent dominance matrix and the contradictory dominance matrix.

[0200] Calculating e αβ = f αβ · g αβ , to obtain the integrated dominance matrix E = (e αβ ) m×m

[0201]

[0202] In this matrix, the value of 1 represents that the failure mode corresponding to the row is more important than the failure mode corresponding to the column, and the sum of the element values of the corresponding row of FM7 is the largest among other failure modes. It can be concluded that FM7 is the most important failure mode, and the maximum group utility weight value υ in the ELECTRE method is solved and verified in steps S8-S9.

[0203] Step S8, calculating the maximum group effect value S i , the minimum individual regret value R i , solving the maximum group utility weight value υ to determine the comprehensive evaluation value Q i .

[0204]

[0205] Where S + = max S i , S - = min S i , R + = max R i , R - = min R​​​​i , u is the maximum group utility weight value, and is a set value.

[0206] is the positive ideal solution of the jth failure mode.

[0207] is the negative ideal solution of the jth failure mode.

[0208] R i is the minimum individual regret value.

[0209] To confirm the optimal maximum group utility weight value, according to the integrated dominance matrix obtained by the ELECTRE method, if e αβ = 1, it indicates that the ath failure mode should be more important than the βth failure mode, and since the comprehensive evaluation value is in ascending order, the smaller the Q i is, the more important it is;

[0210] Therefore, the comprehensive evaluation values of the ath failure mode and the βth failure mode should satisfy

[0211]

[0212] Through this relationship, the value of u that satisfies the condition is obtained, and the final u generally exists in the following three cases:

[0213] (1) If there is only one value of u that satisfies the integrated optimal matrix, that is, the value of u is substituted into the comprehensive evaluation values Q α and Q β , if the value Q α > Q β , the corresponding integrated optimal matrix element e αβ = 1, indicating that the value of u satisfies the integrated optimal matrix, then the value of u is determined, but usually more than one value satisfies the integrated optimal matrix;

[0214] (2) If there are multiple values that satisfy the integrated optimal matrix, then take the value closest to 0.5 (the precision depends on the specific situation, and the precision can be 0.1, 0.01, etc.), because u is usually set to 0.5 in VIKOR, which represents a compromise between individual minimum regret and maximum group utility;

[0215] Among the obtained values of u, if there are multiple values that satisfy the integrated optimal matrix, then take the value closest to 0.5, which is 0.7 (the precision is 0.1 depending on the specific situation). Finally, u = 0.7 is selected as the weight of the maximum group utility in the calculation of the comprehensive evaluation value Q i .

[0216] (3) If there is no value that satisfies the integrated optimal matrix, then take 0.5;

[0217] Step S9, S i , R i , Q i values are sorted in ascending order, three sequences are obtained, after obtaining the sorting result, the most important failure mode is determined.

[0218] The optimal solution needs to satisfy the following two conditions:

[0219] (1) Q A (2) -Q A (1) ≥ 1 / (m-1), wherein Q A (1) is the smallest Q i value in the sorting result, Q A (2) is the second smallest Q i value in the sorting result, and m is the number of failure modes;

[0220] (2) The S i value or R i value of the solution with the smallest Q i value is also optimal, so that the solution with the smallest Q value is determined as the optimal solution;

[0221] If the above conditions cannot be met at the same time, a compromise solution can be obtained, and there are generally the following two cases:

[0222] (A) If condition (1) is met, a set of compromise solutions A(1), A(2) is obtained, that is, all are the most important failure modes;

[0223] (B) If condition (1) is not met but condition (2) is met, a set of compromise solutions A(1),..., A(M) is obtained, that is, all are the most important failure modes, wherein M is the maximum M value determined according to the formula [Q A (M) - Q A (1)] < 1 / (m-1).

[0224] S i , R i , Q i values are sorted in ascending order, three sequences are obtained, as shown in Table 9,

[0225] wherein FM7 is the minimum value in the S i , R i , Q i value sorting,

[0226] and satisfies Q A (2) - Q A (1) = 0.3833 ≥ 1 / 21, that is, FM7 is determined again as the most important failure mode.

[0227] Table 9 Failure mode S i , Ri Q i value

[0228]

[0229]

[0230] S10. Using the RPN value and Q value as two feature values ​​to describe the i-th failure mode, we obtain the description matrix F, and then use the Mean shift clustering method for clustering.

[0231] Calculate the offset vector

[0232] Translation density estimation window:

[0233] Repeat the above two steps (calculate the offset vector and translation density estimation window) until convergence.

[0234] The description matrix F is:

[0235] Table 10 Description Matrix

[0236]

[0237]

[0238] S11. Analyze the research objects based on the clustering and ranking results, and allocate resources and manage risks for prevention and monitoring according to different failure modes.

[0239] To better compare the differences between the improved FMEA method and the traditional FMEA method and the method calculated directly using only one multi-criteria decision-making (MCDM), this invention will calculate and compare the results of four methods: the traditional FMEA method, the VIKOR-FMEA method, the entropy weight-FMEA method, and the improved method of this application. The results and comparisons of the four methods are shown in Table 11.

[0240] Table 11 Ranking results of the improved FMEA method, traditional FMEA method, VIKOR-FMEA method, and entropy weight method-FMEA method

[0241]

[0242]

[0243] RPN and Q in the improved FMEA i After value normalization, the coordinate values ​​are used as the failure mode coordinates for clustering.

[0244] After modifying the test Mean shift band value, finally set the bandwidth setting in Mean shift to 0.5, and the clustering result obtained is as shown in Fig. 2

[0245] Fig. 2 The clustering result of Mean-shift clustering is described, and 5 clusters are obtained.

[0246] Among them, Cluster1 only contains FM7, and FM7 is the most important in all failure modes, which indicates that it has a great impact on the operation of the manufacturing execution system, and a large amount of resources should be invested for prevention and monitoring;

[0247] Cluster2 contains FM6, FM11 and FM12, which are more important than other failure modes except FM7, which indicates that they have a greater impact on the operation of the manufacturing execution system, and more resources should be invested for prevention and monitoring.

[0248] Among all failure modes, Cluster3 contains FM1, FM2, FM3, FM4, FM5, FM13, FM15, FM16, FM19 and FM21, and after tracing analysis of the causes of failure modes, these failure modes are moderately important in all failure modes, which indicates that they have a moderate impact on the operation of the manufacturing execution system, and moderate resources should be invested for prevention and monitoring;

[0249] Cluster4 contains FM8, FM10, FM14, FM18 and FM20, and after tracing analysis of the causes of failure modes, these failure modes are less important in all failure modes, which indicates that they have a small impact on the operation of the manufacturing execution system, and less resources should be invested for prevention and monitoring;

[0250] Cluster5 contains FM9, FM17 and FM22, and after tracing analysis of the causes of failure modes, these failure modes are the least important in all failure modes, which indicates that they have the smallest impact on the operation of the manufacturing execution system, and a small amount of resources should be invested for prevention and monitoring.

[0251] In summary, Cluster1 is the most important failure mode cluster, Cluster2 is the relatively important failure mode cluster, Cluster3 is the generally important failure mode cluster, Cluster4 is the relatively unimportant failure mode cluster, and Cluster5 is the least important failure mode cluster, and the clustering result is reasonable.

[0252] Through example analysis, the application is applicable and effective in reliability analysis.

[0253] ​In summary, the embodiment is aimed at the defects of the traditional FMEA method in use, such as using precise numbers to evaluate the risk factors of failure modes, not considering the relative weights of various risk factors, and the risk priority number calculated may be the same, but the risk implications of failure modes are completely different, etc. The minimum variance sum and majority voting method are used to assign weights to experts with different views, the LINMAP method and CRITIC method are used to calculate the subjective and objective weights of risk factors, and the uninorm operator-based combination weighting is used to calculate the comprehensive weight of risk factors. Then, the failure modes are sorted by using ELECTRE-VIKOR, and finally, the failure modes are analyzed by using Mean shift clustering. The results show that the improved FMEA method provides an effective and reliable method for the reliability and risk assessment of the MES system.

[0254] The above is only the preferred embodiment of the present application, and does not limit the present application in any way. Any person skilled in the art can make any form of equivalent replacement, modification or change to the technical solutions and technical contents disclosed in the present application without departing from the scope of the technical solutions of the present application, and still falls within the protection scope of the present application.

Claims

1. An improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering, characterized in that, The method comprises the following steps: assigning weights to experts holding different opinions by minimizing variance sum and and majority voting; calculating subjective and objective weights of risk factors by using LINMAP and CRITIC methods and calculating comprehensive weights of risk factors by using combination weighting based on uninorm operator; ranking failure modes by using ELECTRE-VIKOR; finally, analyzing the failure modes by using Mean shift clustering; the step of assigning weights to experts holding different opinions specifically comprises: S1, determining potential failure modes of the research object; S2, obtaining a failure mode evaluation table and an expert subjective preference table; Step S3, converting the failure mode assessment table into an expert scoring table, and obtaining a risk priority number of each failure mode based on the expert scoring table ; Step S4, converting the language variables in the expert scoring table into corresponding triangular fuzzy numbers to obtain the fuzzy evaluation matrix of the expert ; and ; Step S5, calculating the comprehensive expert weight based on the fuzzy evaluation matrix , the expert subjective preference table obtained in step S2 Step S5 specifically includes the following steps: Step S51, based on the fuzzy evaluation matrix , the first weight of the expert based on the variance ; Step S52, based on the expert subjective preference table obtained in step S2, calculate the voting-based expert weight ; Step S53, combination weighting method based on uninorm operator, and , obtain comprehensive expert weight ; based on the comprehensive expert weight and the fuzzy evaluation matrix , the comprehensive risk factor weight is calculated , and the specific steps include: Step S61, the objective risk factor weight calculated by CRITIC method : Step S61A, blurring the evaluation matrix Deblurring, obtaining the matrix ; Step S61B, adding the matrices and after weighting, obtaining a decision matrix ; Step S61C, obtaining a decision matrix normalization, obtaining a normalized matrix ; Step S61D, acquiring ; Step S62, based on the expert subjective preference table obtained in step S2, the subjective risk factor weight is calculated by using the LINMAP method ; Step S63, combination weighting method based on uninorm operator, and , to obtain the comprehensive risk factor weight The specific steps of using ELECTRE-VIKOR to rank the failure modes include: Step S7, calculating the integrated risk factor weight based on the integrated risk factor and the normalized matrix , the integrated dominant matrix is calculated based on the integrated dominant matrix to obtain the most important failure mode; Step S8, calculating the maximum group effect value of each failure mode , the minimum individual regret value , solving the maximum group utility weight value , to determine the comprehensive evaluation value ; ； ； ； wherein , , , , is a maximum group utility weight value, and is a set value; represents the positive ideal solution of the risk factor; represents the negative ideal solution for the risk factor; represents the weight of the composite risk factor; denotes the element in the normalized matrix denotes the element in the normalized matrix a number indicating the failure mode; indicates the number of risk factors under the failure mode indicates the number of risk factors under the failure mode Step S9, obtaining , , The values are sorted in ascending order to obtain three sequences. After obtaining the sorted results, the most important failure mode is determined.

2. The improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering of claim 1, wherein, the specific steps of analyzing the failure modes by using Mean shift clustering comprise: S10, the RPN value is compared with values as two characteristic values describing the first failure mode, a description matrix F is obtained, and the Meanshift clustering method is used for clustering. S11, analyzing the research object according to the clustering result and the ranking result, and allocating resources for prevention and monitoring and managing risks for different failure modes.

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