Improved FMEA method based on LINMAP, ELCTRE-VIKOR and Mean shift clustering

Abstract

The invention provides an improved FMEA method based on LINMAP, ELCTRE-VIKOR and Mean shift clustering. The improved FMEA method comprises the following steps: distributing weights for experts with different viewpoints through a minimum variance sum and a majority voting method; calculating subjective and objective weights of the risk factors by using a LINMAP method and a CRITIC method, and calculating comprehensive weights of the risk factors by applying combined weighting based on a uninorm operator; and the failure modes are sorted by using the ELCTRE-VIKOR, and finally, the failure modes are analyzed by using Mean shift clustering. The invention provides an effective and reliable method for reliability and risk assessment of the MES system.

Description

Technical Field

[0001] The invention 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 Art

[0002] Failure Mode and Effects Analysis (FMEA) has always been a risk assessment tool for evaluating system reliability and risk and identifying potential failures of the system. In traditional FMEA, experts score the severity (S), occurrence (O) and detection (D) of failure modes based on their own experience, and then multiply them to calculate the risk priority number (RPN) to rank the failure modes. FMEA is widely used in reliability and risk management analysis in various fields. As a risk management tool, the traditional FMEA process has certain shortcomings. 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 together. However, it is inaccurate when it comes to different situations and applications, ignoring the differences between risk factors. Second, 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 assessments in an uncertain environment. Third, the calculated RPN values ​​are sometimes the same, but the risk meanings of failure modes may be completely different.

[0003] The multi-criteria compromise solution ranking method (VIKOR) is a compromise ranking method based on the Lp-metric aggregation function. The ranking of the alternative solutions is determined by the degree of proximity between the alternative solutions and the ideal solution. It can not only overcome the shortcomings of the ranking method that approximates the ideal solution, but also take into account the maximization of group benefits and the minimization of individual regrets of opposing opinions, and fully consider the subjective preferences of decision makers.

[0004] The Elimination and Selection Transformation (ELECTRE) method originated from Roy Company in the late 1960s and is a comparison method for alternatives based on a 2x2 scale. The ERLCTRE method obtains consistency and inconsistency indices to indicate the degree of satisfaction and dissatisfaction of experts in determining the priority of two options.

[0005] The Linear Programming Method for Multidimensional Preference Analysis (LINMAP) method is a multidimensional preference analysis method proposed by Srinivasan and Shocker in 1973. The basic concept of the LINMAP method is to use the two comparative preference information between some or all solutions given by the decision maker, use the distance to measure the consistency and inconsistency between the solutions, and construct the corresponding linear programming model.

[0006] The main idea of ​​mean shift clustering is to perform gradient ascent on the local estimated density for each data point in the feature space until convergence. The stationary point of this process represents the mode 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, developing an improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering is a technical problem that needs to be solved urgently, which is of great significance to solving the deficiencies in the traditional FMEA process and the reliability and risk analysis of related systems. Summary of the invention

[0008] The purpose of the present invention 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 the manufacturing execution system, determines the importance of each failure mode and key risk sources in the manufacturing execution system, and verifies the reliability and effectiveness of the improved method. The technical solution adopted is as follows:

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

[0010] Assign weights to experts holding different opinions by minimizing the sum of variances and majority voting;

[0011] The subjective and objective weights of risk factors are calculated using the LINMAP method and the CRITIC (Criteria Importance Through Intercrieria Correlation) method, and the combined weighting based on the uninorm operator is applied to calculate the comprehensive weight of risk factors.

[0012] Use ELECTRE-VIKOR to rank failure modes;

[0013] Finally, Mean shift clustering is used to analyze the failure mode.

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

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

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

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

[0018] Step S4: Convert the language variables in the expert rating 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 The expert subjective preference table obtained in step S2 is used to calculate the comprehensive expert weight λ k .

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

[0021] Step S51: Based on the fuzzy evaluation matrix Calculate the variance-based weight λ of the kth expert k ′;

[0022] Step S52: Calculate the expert weight λ based on the voting based on the expert subjective preference table obtained in step S2. k ″;

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

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

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

[0026] Step S61A: Fuzzy evaluation matrix Defuzzification, get the matrix

[0027] Step S61B: Matrix and λ k After weighting, add them together to obtain the decision matrix X;

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

[0029] Step S61D, obtain w j ′;

[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 method.j ″;

[0031] Step S63: Combined weighting method based on uninorm operator, w j ′ and w j ″, and get the comprehensive risk factor weight w j .

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

[0033] Step S7: Based on the comprehensive risk factor weight w j and the standardized matrix R, calculate the integrated dominance matrix E, and obtain the most important failure modes based on the integrated dominance matrix E;

[0034] Step S8: Calculate the maximum group effect value S of each failure mode i , minimum personal regret value R i , solve the maximum group utility weight value υ to determine the comprehensive evaluation value Q i ;

[0035] Step S9: i , R i , Q i The values ​​are sorted in ascending order to obtain three sequences. After obtaining the sorted results, the most important failure mode is obtained.

[0036] Preferably, the specific steps of analyzing the failure mode using mean shift clustering include:

[0037] S10, taking the RPN value and the Q value as two eigenvalues ​​describing the i-th failure mode, obtaining a description matrix F, and clustering using the Mean shift clustering method;

[0038] S11. Analyze the research object based on the clustering and sorting results, and carry out corresponding prevention and monitoring resource allocation and risk management for different failure modes.

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

[0040] By minimizing the sum of variances and majority voting, weights are assigned to experts with different opinions. The subjective and objective weights of risk factors are calculated using the LINMAP method and the CRITIC method, and the combined weighting based on the uninorm operator is applied to calculate the comprehensive weight of risk factors. Then, ELECTRE-VIKOR is used to rank the failure modes, and finally Mean shift clustering is used to analyze the failure modes. The results show that the improved FMEA method provides an effective and reliable method for reliability and risk assessment of manufacturing execution systems. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0042] Figure 2 The mean shift clustering results of failure modes in manufacturing execution system according to the improved FMEA method based on LINMAP, ELECTRE-VIKOR and mean shift clustering of the present invention are presented. DETAILED DESCRIPTION

[0043] The improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering of the present invention will be described in more detail below in conjunction with the schematic diagram, wherein the preferred embodiment of the present invention is shown, and it should be understood that those skilled in the art can modify the present invention described herein, while still achieving the advantageous effects of the present invention. Therefore, the following description should be understood as being widely known to those skilled in the art, and not as a limitation of the present invention.

[0044] Reference Figure 1-2 , an improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering, including:

[0045] This embodiment analyzes and evaluates the Manufacturing Execution System (MES).

[0046] Step S1: determine the potential failure mode of the research object.

[0047] According to the needs, a FMEA expert team is formed to analyze the operation and structure of the research object. Through brainstorming, literature review and expert interviews, m potential failure modes of the research object are determined.

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

[0049] Identify failure modes of manufacturing execution systems and analyze their effects.

[0050] At the same time, for the 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 MES failure modes and their categories

[0052]

[0053] Step S2: Obtain a failure mode evaluation table and an expert subjective preference table.

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

[0055] Each expert in the FMEA expert team selects the most important and least important failure modes 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 evaluated the n risk factors of each failure mode, and used five linguistic variables to evaluate the risk factors of the failure mode, namely very low (VL), low (L), medium (M), high (H), and very high (VH). The failure mode evaluation table (Table 3) was obtained based on the evaluation criteria corresponding to the linguistic variables (the evaluation criteria of S, O, and D risk factors refer to Table 2), and the most important and least important failure modes were selected according to the classified failure modes to obtain the subjective preferences of the experts (Table 4).

[0058] Table 2 Evaluation standard reference table

[0059]

[0060] Four experts in the field of intelligent manufacturing scored the risk factors of each failure mode according to the evaluation criteria (as shown in Table 2). The four experts belonged to different fields of manufacturing execution systems and judged the same failure mode from different perspectives.

[0061] The failure mode evaluation table of the FMEA team members for the failure modes is shown in Table 3, and they make preference choices in the failure modes of the same category (selecting the most important and least important failure modes 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, 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 believes that FM1 is the most important failure mode, while experts 2 to 4 all subjectively believe that FM1 is neither the most important failure mode nor the least important failure mode.

[0068] Experts 1 to 4 all subjectively believe that FM3 is the least important failure mode.

[0069] Step S3: convert the failure mode evaluation table into an expert scoring table, and obtain the risk priority number RPN of each failure mode based on the expert scoring table i .

[0070] Specifically, according to the fuzzy linguistic variables corresponding to the traditional FMEA scoring values, the linguistic variables of the three risk factors, severity (S), occurrence (O), and detectability (D) in the failure mode assessment table are converted into the scoring values ​​of each expert for each risk factor in the traditional FMEA according to Table 2, that is, the failure mode assessment table is converted into an expert scoring table.

[0071] Calculate the arithmetic mean of all expert scores for each risk factor and use this value as the value of each risk factor in traditional FMEA;

[0072] Multiply the values ​​of the three risk factors 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 scoring table as an example, the calculation process of its corresponding risk priority number RPN1 is explained:

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

[0075] By analogy, the arithmetic mean of the occurrence degree O and the detectability D is calculated.

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

[0077] Step S4: Convert the language variables in the expert scoring table into corresponding triangular fuzzy numbers There are l experts in the FMEA team. 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 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 its corresponding triangular fuzzy number is explained:

[0082] The expert DM1 language variables corresponding to failure mode FM1 are: H, M, L, and the corresponding triangular fuzzy numbers are: (6, 8, 10), (3, 5, 7), (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:

[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, calculate the comprehensive expert weight λ k . Wherein, k=1~l.

[0088] Step S51: Based on the fuzzy evaluation matrix Calculate the variance-based weight λ of the kth expert k ′.

[0089] The specific steps include:

[0090] Step S51A: Based on the fuzzy evaluation matrix Calculate the average fuzzy evaluation matrix Variance matrix of the kth expert.

[0091]

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

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

[0094] The number of rows of failure modes in Table 6 is 22, and the number of columns of risk factors*3 is 9, that is, the fuzzy evaluation matrix The number of rows m=22, the number of columns n′=9.

[0095] Table 6 Average fuzzy evaluation matrix

[0096]

[0097]

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

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

[0100] The sum of the experts' variances is calculated to be V1=515.0625, V2=539.5625, V3=1318.5630, and V4=483.5625.

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

[0102]

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

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

[0105] Step S52: Calculate the expert weight λ based on the voting based on the expert subjective preference table obtained in step S2. k ″.

[0106] The specific steps include:

[0107] Step S52A: Count the number of voters who voted for the most important and least important votes for any failure mode in the expert subjective preference table, and use the number of voters as the score of the failure mode.

[0108] Specifically, suppose that among l experts, there are t people who choose a certain failure mode as the most important failure mode, then this failure mode is set to have t points in the most important vote; suppose that among l experts, there are t' people who choose a certain failure mode as the least important failure mode, then this failure mode is set to have t' points in the least important vote.

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

[0110] In FM1, the most important vote is 1, i.e., expert 1, and the least important vote is 0.

[0111] Step S52B, calculate the score of the kth expert for the most important vote as T k ' points, the sum of the least important votes is T k "point.

[0112] Taking expert 1 as an example, expert 1 believes that FM1, FM4, FM8, FM13, FM14, FM16, FM18, and FM21 are the most important failure modes, and combined with the votes of other experts on the above most important failure modes, the scores of the above most important failure modes are 1, 2, 3, 2, 2, 4, 4, and 2, respectively, and the sum is T1′=20. Expert 1 believes that FM3, FM6, FM9, FM12, FM15, FM17, FM19, and FM20 are the least important failure modes, and combined with the votes of other experts on the above least important failure modes, the scores of the above least important failure modes are 4, 4, 4, 4, 2, 4, 4, and 2, respectively, and the sum is T1″=28.

[0113] Step S52C: Based on T k ′ and T k ″, calculate λ k ″.

[0114]

[0115] The expert weights obtained by majority voting are:

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

[0117] Step S53: Combined weighting method based on uninorm operator, λ k ′ and λ k ″, get the comprehensive expert weight λ k .

[0118] Let g′=1 / n, there are generally the following situations;

[0119] In the first case, both weights are greater than 0 and less than g′, then λ k ″′=λ k ′λ k ″ / g′;

[0120] In the second case, both weights are greater than g′ and less than 1;

[0121] At this time 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] The final lambda k ″′ is normalized to obtain the comprehensive expert weight λ k .

[0124] Among them, n represents the number of weights that need to be combined.

[0125] Finally, the comprehensive weights of the four experts are obtained based on the uninorm operator combined weighting method:

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

[0127] Step S6: Based on comprehensive expert weight λ k and fuzzy evaluation matrix Calculate the comprehensive risk factor weight w j . Wherein, j=1~n.

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

[0129] Step S61A: Fuzzy evaluation matrix Defuzzification, get the matrix

[0130]

[0131] The collection is

[0132] Step S61B: Matrix and λ k After weighting, add them together to obtain the decision matrix X.

[0133]

[0134] X=(x ij ) m×n

[0135] Where m represents the number of failure modes and n represents the number of risk factors.

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

[0137] Table 7 Decision matrix

[0138]

[0139]

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

[0141]

[0142] R=(r ij ) m×n

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

[0144] Table 8 Standardized matrix R

[0145]

[0146]

[0147] Step S61D, obtain w j ′.

[0148] Calculate the correlation coefficient

[0149] in and is the arithmetic mean of the sum of the failure mode scores of the jth and pth 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 value for each risk factor

[0152] calculate

[0153] calculate

[0154] The weights calculated by the CRITIC method are normalized to obtain the weights of objective risk factors: (0.3881, 0.3441, 0.2678).

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

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

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

[0158] Among them, A g ≥A h Indicates that the g-th failure mode is more important than the h-th failure mode.

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

[0160] The preferences of the experts corresponding to Table 4 are transformed into preference sets:

[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 and 6 expert preference sets in Table 4 is that when the expert preferences are the same under the same failure mode, there is no need to convert the expert preferences into preference sets.

[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 + The Euclidean distance S′ from the negative ideal solution - :

[0167] Positive ideal solution

[0168] The Euclidean distance of the i-th 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] Constructing an inconsistency index based on preference sets (S h -S g ) - :

[0172]

[0173] Overall consistency index and overall inconsistency index

[0174] S h ' + represents the Euclidean distance of the h-th failure mode from the positive ideal solution; S h ' - Represents the Euclidean distance of the h-th failure mode from the negative ideal solution.

[0175] Step S62C: Establish a linear programming model to minimize B′ and solve w j ″.

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

[0177] The linear programming equations are obtained as follows:

[0178] min{B'}

[0179]

[0180] The subjective weights of risk factors obtained by the LINMAP method solved by LINGO11 are (0.2757, 0.4487, 0.2757).

[0181] Step S63: Combined weighting method based on uninorm operator, w j ′ and w j ″, and get the comprehensive risk factor weight w j .

[0182] The comprehensive weight of risk factors obtained by the combined weighting method based on the uninorm operator is (0.3283, 0.4526, 0.2191).

[0183] Step S7: Based on the comprehensive risk factor weight w j The integrated dominance matrix E is calculated based on the standardized matrix R, and the most important failure modes are obtained based on the integrated dominance matrix E.

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

[0185] R′=w j ·R

[0186] Step S72: Calculate the consistency index c αβ , get the consistency matrix C; calculate the inconsistency index d αβ , and get the inconsistency matrix D.

[0187]

[0188] C=(c αβ ) m×m

[0189]

[0190] D=(d αβ ) m×m

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

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

[0193] J is the set of j.

[0194] C 21 For example, in the weighted standard matrix R′, for the same risk factor j, r2′ j >r1′ j , then j is a set C 21 The elements in .

[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 C 21 The elements in a collection.

[0196] Step S73, calculate the consistent dominant matrix from the consistency matrix C; calculate the contradictory dominant matrix from the consistency matrix D.

[0197] Compute threshold value of uniformly dominated matrix When the elements in the consistency matrix are greater than or equal to the threshold, the corresponding consistent dominance matrix f αβ =1, otherwise 0, thus we get the uniformly dominant matrix F = (f αβ ) m×m ;

[0198] Calculate the threshold of the contradiction dominance matrix When the elements in the consistency matrix are less than or equal to the threshold, the corresponding consistent dominance matrix g αβ =1, otherwise 0, thus we get the contradiction dominant matrix G = (g αβ ) m×m ;

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

[0200] Calculate e αβ =f αβ ·g αβ , we get the integrated dominant matrix E = (e αβ ) m×m

[0201]

[0202] In this matrix, a value of 1 means that the failure mode corresponding to the row of the element is more important than the failure mode corresponding to the column. Compared with other failure modes, the sum of the element values ​​in the row corresponding to FM7 is the largest. It can be concluded that FM7 is the most important failure mode. In steps S8 to S9, the ELECTRE method is used to solve and verify the maximum group utility weight value υ in the VIKOR method.

[0203] Step S8: Calculate the maximum group effect value S of each failure mode i , minimum personal regret value R i , solve the maximum group utility weight value υ to determine the comprehensive evaluation value Q i .

[0204]

[0205] Where S + =maxS i , S - =minS i , R + =maxR i , R - =minRi , υ is the maximum group utility weight value, and is the set value.

[0206] represents the positive ideal solution for the j-th failure mode.

[0207] represents the negative ideal solution of the j-th failure mode.

[0208] R i represents the minimum personal regret value.

[0209] In order to determine the optimal maximum group utility weight value, the integrated dominance matrix obtained by the ELECTRE method is αβ =1, it means that the αth failure mode should be more important than the βth failure mode. Since the comprehensive evaluation value is sorted in ascending order, the smaller the Q i The more important;

[0210] Therefore, the comprehensive evaluation value of the αth failure mode and the βth failure mode should satisfy

[0211]

[0212] Through this relationship, the υ value that meets the conditions is obtained. The final υ generally has the following three situations:

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

[0214] (2) If there are multiple values ​​that satisfy the optimal matrix for integration, then the value closest to 0.5 is taken (the accuracy depends on the specific situation and can be 0.1, 0.01, etc.), because υ is usually set to 0.5 in VIKOR to represent a compromise between individual minimum regret and maximum group utility;

[0215] The υ value obtained satisfies the situation that there are multiple values ​​that meet the integrated optimal matrix, so the value closest to 0.5 is 0.7 (the accuracy is set to 0.1 according to the specific situation). Finally, υ = 0.7 is selected as the comprehensive evaluation value Q in the VIKOR method. i The weight of the maximum group utility when calculating.

[0216] (3) If no value satisfies the optimal matrix of the integration, then 0.5 is taken;

[0217] Step S9: i , R i , Q i The values ​​are sorted in ascending order to obtain three sequences. After obtaining the sorted results, the most important failure mode is obtained.

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

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

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

[0221] If the above conditions cannot be met at the same time, a compromise solution can be obtained. Generally, there are two situations as follows:

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

[0223] (B) If condition (1) is not satisfied but condition (2) is satisfied, a set of compromise solutions is obtained: A(1), ..., A(M), which are all the most important failure modes, where M is the value of [Q A (M)-Q A (1)]<1 / (m-1) to determine the maximum M value.

[0224] S i , R i , Q i The values ​​are sorted in ascending order to obtain three sequences, as shown in Table 9.

[0225] Among them, FM7 is in S i , R i , Q i The values ​​are sorted by the smallest value.

[0226] And satisfy Q A (2)-Q A (1) = 0.3833 ≥ 1 / 21, FM7 can be confirmed as the most important failure mode again.

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

[0228]

[0229]

[0230] S10. Use the RPN value and the Q value as two eigenvalues ​​describing the i-th failure mode to obtain a description matrix F, and perform clustering using the Mean shift clustering method.

[0231] Calculate the offset vector

[0232] Translate the density estimation window:

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

[0234] The description matrix F is:

[0235] Table 10 Description matrix

[0236]

[0237]

[0238] S11. Analyze the research object based on the clustering and sorting results, and carry out corresponding prevention and monitoring resource allocation and risk management for different failure modes.

[0239] In order to better compare the difference between the improved FMEA method and the traditional FMEA and the direct calculation using only a multi-criteria decision making (MCDM) method, the present invention example calculates and compares the results of the four methods of the traditional FMEA method, the VIKOR-FMEA method, the entropy weight method-FMEA method and the improved method of the present application. The results and comparisons obtained by the four methods are shown in Table 11.

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

[0241]

[0242]

[0243] Improved RPN and Q in FMEA i The values ​​are normalized and clustered as the coordinate values ​​of the failure modes.

[0244] After modifying the experimental Mean shift bandwidth value, the bandwidth in Mean shift was finally set to 0.5. The clustering results are as follows Figure 2 shown.

[0245] Figure 2 The clustering results of Mean-shift clustering are described, and 5 clusters are obtained.

[0246] Among them, Cluster 1 only contains FM7, which is the most important among all failure modes, indicating that it has a great impact on the operation of the manufacturing execution system and a lot of resources should be invested in prevention and monitoring;

[0247] Cluster 2 includes FM6, FM11, and FM12. These failure modes are more important than other failure modes except FM7, which means that they have a greater impact on the operation of the manufacturing execution system and more resources should be invested in prevention and monitoring.

[0248] Among all failure modes; Cluster 3 includes FM1, FM2, FM3, FM4, FM5, FM13, FM15, FM16, FM19, and FM21. After tracing back the causes of the failure modes, these failure modes are of medium importance among all failure modes, which means that they have a medium impact on the operation of the manufacturing execution system and medium resources should be invested for prevention and monitoring;

[0249] Cluster 4 includes FM8, FM10, FM14, FM18, and FM20. After tracing back the causes of the failure modes, these failure modes are less important than all the failure modes, which means that they have little impact on the operation of the manufacturing execution system and less resources should be invested in prevention and monitoring.

[0250] Cluster 5 includes FM9, FM17, and FM22. After tracing back the causes of the failure modes, these failure modes are the least important among all failure modes, which means that they have the least impact on the operation of the manufacturing execution system and a small amount of resources should be invested in prevention and monitoring.

[0251] In summary, "Cluster 1" is the most important failure mode cluster, "Cluster 2" is a relatively important failure mode cluster, "Cluster 3" is a generally important failure mode cluster, "Cluster 4" is a relatively unimportant failure mode cluster, and "Cluster 5" is the least important failure mode cluster. This clustering result is relatively reasonable.

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

[0253] In summary, this embodiment aims at the defects of the traditional FMEA method in the process of 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 calculated risk priority values ​​may be the same, but the risk meanings of failure modes are completely different. By minimizing the sum of variances and the majority voting method, weights are assigned to experts with different opinions, the LINMAP method and the CRITIC method are used to calculate the subjective and objective weights of risk factors, and the combined weighting based on the uninorm operator is applied to calculate the comprehensive weights of risk factors. Then, ELECTRE-VIKOR is used to sort the failure modes, and finally Mean shift clustering is used to analyze the failure modes. The results show that the improved FMEA method provides an effective and reliable method for reliability and risk assessment of MES systems.

[0254] The above is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any technician in the relevant technical field, without departing from the scope of the technical solution of the present invention, makes any form of equivalent replacement or modification to the technical solution and technical content disclosed in the present invention, which does not depart from the content of the technical solution of the present invention and still falls within the protection scope of the present invention.

Claims

1. An improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering, characterized in that: The following steps are involved: Assign weights to experts holding different opinions by minimizing the sum of variances and majority voting; The subjective and objective weights of risk factors are calculated using the LINMAP method and the CRITIC method, and the combined weighting based on the uninorm operator is applied to calculate the comprehensive weight of risk factors; Use ELECTRE-VIKOR to rank failure modes; Finally, Mean shift clustering is used to analyze the failure mode.

2. The improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering according to claim 1, characterized in that: The steps to assign weights to experts with different opinions include: Step S1, determining the potential failure mode of the research object; Step S2, obtaining a failure mode evaluation table and an expert subjective preference table; Step S3: convert the failure mode evaluation table into an expert scoring table, and obtain the risk priority number RPN of each failure mode based on the expert scoring table i ; Step S4: Convert the language variables in the expert rating table into corresponding triangular fuzzy numbers to obtain the fuzzy evaluation matrix of the kth expert. Step S5: Based on the fuzzy evaluation matrix The expert subjective preference table obtained in step S2 is used to calculate the comprehensive expert weight λ k .

3. The improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering according to claim 2, characterized in that: Step S5 specifically includes the following steps: Step S51: Based on the fuzzy evaluation matrix Calculate the variance-based weight λ of the kth expert k ′; Step S52: Calculate the expert weight λ based on the voting based on the expert subjective preference table obtained in step S2. k ″; Step S53: Combined weighting method based on uninorm operator, λ k ′ and λ k ″, get the comprehensive expert weight λ k .

4. The improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering according to claim 3, characterized in that: Based on comprehensive expert weight λ k and fuzzy evaluation matrix Calculate the comprehensive risk factor weight w j The specific calculation steps include: Step S61: The objective risk factor weight w calculated by the CRITIC method j ′: Step S61A: Fuzzy evaluation matrix Defuzzification, get the matrix Step S61B: Matrix and λ k After weighting, add them together to obtain the decision matrix X; Step S61C, standardize the decision matrix X to obtain a standardized matrix R; Step S61D, obtain w j ′; Step S62: Based on the expert subjective preference table obtained in step S2, the subjective risk factor weight w is calculated using the LINMAP method. j ″; Step S63: Combined weighting method based on uninorm operator, w j ′ and w j ″, and get the comprehensive risk factor weight w j .

5. The improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering according to claim 4, characterized in that: The specific steps for using ELECTRE-VIKOR to rank failure modes include: Step S7: Based on the comprehensive risk factor weight w j and the standardized matrix R, calculate the integrated dominance matrix E, and obtain the most important failure modes based on the integrated dominance matrix E; Step S8: Calculate the maximum group effect value S of each failure mode i , minimum personal regret value R i , solve the maximum group utility weight value υ to determine the comprehensive evaluation value Q i ; Step S9: i , R i , Q i The values ​​are sorted in ascending order to obtain three sequences. After obtaining the sorted results, the most important failure mode is obtained.

6. The improved FMEA method based on LINMAP, ELECTRE-VIKOR and Mean shift clustering according to claim 1, characterized in that: The specific steps of using Mean shift clustering to analyze failure modes include: S10, taking the RPN value and the Q value as two eigenvalues ​​describing the i-th failure mode, obtaining the description matrix F, and clustering using the Meanshift clustering method; S11. Analyze the research object based on the clustering and sorting results, and carry out corresponding prevention and monitoring resource allocation and risk management for different failure modes.

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