The South-to-North Water Diversion Project (SNWDP) is a cross-basin large-scale water infrastructure, whose operational management faces many complex risks. This study constructs an operational safety risk analysis model based on fuzzy VIKOR-FMEA. First, the expert team used linguistic variables to evaluate the severity of each failure mode (S), frequency of occurrence (O), and difficulty of detection (D) in the failure mode and effects analysis (FMEA). Then, the fuzzy analytic hierarchy process (AHP) and the maximal deviation approach were integrated to carry out risk factor weights. The risk factor weight analysis matrix integrates the subjective and objective weights to obtain the comprehensive weights of the risk factors. Secondly, VIKOR is introduced to improve the traditional FMEA model and is used to calculate the risk priority number. The case study shows that untimely flood protection, irregular maintenance, and untimely emergency response are in the top order. Finally, it is compared with the traditional FMEA method, which verifies the feasibility and effectiveness of the proposed method, and provides a reference algorithm for risk analysis of operation management for the water diversion project.

  • FMEA is employed to assess the operational risks of the South-to-North Water Diversion Project.

  • The triangular fuzzy number is used to evaluate the severity (S), frequency of occurrence (O), and difficulty of detection (D) of each failure mode.

  • VIKOR is introduced to improve the traditional FMEA model.

  • Untimely flood control and irregular maintenance are the greatest risks.

Since the official operation of the South-to-North Water Diversion Project (SNWDP) in December 2014, the allocation of water resources along the route has been further optimized and has provided uninterrupted and safe water supply for about 1,700 days, playing a significant role in ensuring water security, restoring water ecology, and improving the water environment. The project has improved the water supply pattern in the receiving area and has become one of the main water sources for the receiving area (Zhang 2012). The operation and management of the SNWDP faces complex risk factors, and any risk in any part of the whole system will affect the safe operation of the whole system, resulting in huge economic losses and adverse social impacts. The study of the operation and management risks of the SNWDP can be used as a reference for the actual operation and management of the project to reduce the risks that may exist in the operation and management of the project, and is also of great importance for the scheduling and operation of the South–North Water Diversion Project and the innovation of the operation and management system (Liu & Geng 2010).

The SNWDP is leading in the international arena and is a major infrastructure indispensable to national economic development, and is a demonstration of universal significance for water infrastructure. Its operation management has received great attention from many scholars in China. Rong et al. (2012) compared it with the operation and management of traditional water conservancy projects, from theoretical and practical perspectives, to explore the operation and management of the South-to-North Water Diversion East Route Project, and provided useful research and thinking for the benefit of the project design. Jin et al. (2015) analyzed the situation and the main difficulties faced by the operation and management of the South-to-North Water Diversion Storage Reservoir, and the benefit of the first phase of the Middle Route Project and the optimal dispatch of water resources in the receiving area. Shi (2017) put forward optimization suggestions from the perspectives of emergency rescue, routine inspection, maintenance and pipe care, as well as annual age repair and overhaul of the SNWDP in terms of speeding up project inspection, improving pipe care efficiency, and reducing pipe care costs. A small number of scholars have conducted studies on the risk factors during the operation period of the SNWDP. Geng et al. (2012) identified the risks to the water transfer system from the external load, internal structure and operation and management, and used hierarchical-fuzzy analysis to calculate the risk level of each water transfer channel through cluster analysis. Hu et al. (2013) introduced intuitive fuzzy set theory and used the TOPSIS method to identify the operation risk of the South-to-North Water Transfer Main Canal in Chaohe River. Nie et al. (2019) fully considered the vagueness and randomness of the risk factors, used the gray correlation degree and Delphi method to build a risk evaluation index system based on the cloud model for project operation safety, and took the South-to-North Water Diversion Middle Route Project as an example for analysis, which played a reference role for the actual project operation safety risk management work. Most of the current studies on SNWDP operation management are limited to the management model itself, and less consideration is given to the risk factors of project operation. Moreover, many studies adopt methods that only consider objective risk factors, lacking consideration of both subjective and objective factors. Therefore, this study applies a combined subjective and objective approach to assess the important potential risk factors.

Traditional risk assessment methods only consider the probability and severity of the risk, but Failure Mode and Effects Analysis (FMEA) methods take into account the ease with which the risk can be detected, increasing the reliability of the assessment results. FMEA has been widely used in various fields such as engineering management to identify potential failure modes and causes so that failures can be predicted before they occur and prevented from occurring at the source. Traditionally, FMEA risk assessment is achieved by calculating the Risk Priority Number (RPN) for each failure mode, i.e., multiplying the severity (S), occurrence (O) and difficulty of detection (D) of the risk factors to obtain a final risk value, and the higher the failure mode score, the greater the risk. However, the vagueness of risk evaluation information, the determination of expert weights and risk factor weights, and risk prioritization issues are still flawed in practical applications. Therefore, in order to overcome the shortcomings of traditional FMEA methods and improve the validity of FMEA risk assessment results, the researchers have made some improvements. Song et al. (2013) used triangular fuzzy numbers to characterize the FMEA expert's assessment information in the risk assessment process of failure modes. An et al. (2016) used fuzzy rough numbers in the form of intervals to process the expert's assessment information in the FMEA process of the ambiguity. Emovon et al. (2015) proposed an integrated assignment method to determine risk factor weights based on a combination of variance and entropy weighting methods. FMEA can also be considered essentially as a multi-attribute group decision problem, so TODIM (Tomada de decisão interativa multicritério) (Li & Cao 2019), TOPSIS (Technique for Order Preference by Similarity to Solution) (Song et al. 2013), VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) (Liu et al. 2015), AHP (Analytic Hierarchy Process) (Ilangkumaran et al. 2014) and multi-attribute decision methods such as DEMATEL (Decision-Making and Trial Evaluation Laboratory) (Chang 2009) have been widely used in FMEA studies to improve their deficiencies. This study proposes a failure mode evaluation method based on the VIKOR model, which can not only effectively overcome the problem that the TOPSIS model cannot reflect the inadequate proximity of each scenario to the positive and negative ideal points, but can also fully consider the maximization of group benefits and minimization of individual regrets, and fully reflect the subjective preferences of decision makers.

Traditional risk assessment methods cannot meet the operational needs of large-scale water infrastructure. The operational failure modes of SNWDP have not been fully considered in previous research. In order to overcome shortcomings in the traditional risk assessment and traditional FMEA method, this study proposes an improved FMEA risk assessment method based on VIKOR and combined weights in an uncertain environment. Firstly, the fuzzy AHP is used to construct the importance comparison matrix of risk factors, and the subjective weights of risk factors are obtained by optimizing the solution with the goal of minimum consistency. Secondly, the triangular fuzzy number is used to evaluate the risk factors of each failure mode, and the objective weight calculation based on the maximum deviation method is obtained, and the combined weights of risk factors are obtained by integrating the objective and subjective weights. The VIKOR method is introduced to evaluate the risk factors of traditional FMEA. The improved model is used for risk ranking. The feasibility and validity of the proposed method is verified by taking the analysis of the operation and management failure mode of the Huixian section of the SNWDP as an example. Finally, the evaluation results are analyzed and discussed using sensitivity analysis.

In this study, nine potential failure modes in operation and management were selected based on literature review and expert opinion: Irregular Operation and Scheduling (FM1), Inadequate Engineering Inspection (FM2), Irregular Maintenance (FM3), Power Supply System Failure (FM4), Untimely Flood Control (FM5), Inadequate Safety Protection (FM6), Emergence of Biological Hazards (FM7), Problems with Water Quality and Safety (FM8) and Untimely Emergency Response (FM9), as shown in Table 1.

Table 1

Failure modes and description

Serial numberFailure modeMain causes of failureEffects of the failureDocumentary sources
FM1 Irregular Operation and Scheduling Failure to follow dispatch protocols (or plans) for reasonable dispatch operations and inadequate dispatch mechanisms All levels of management staff cannot be connected in real time, and an alarm cannot be transmitted in a timely manner Geng et al. (2010) Nie et al. (2019)  
FM2 Inadequate Engineering Inspection Failure to comply with the standard or required inspection visits The presence of serious defects in the works that endanger safety, the presence of certain factors in the environment that endanger the safety of the works Sun (2018)  
FM3 Irregular Maintenance Failure to maintain works areas or facilities to standard or in a timely manner Failure of an engineering site or failure of a facility Zhu & Wang (2018) Geng et al. (2012)  
FM4 Power Supply System Failure Inappropriate personnel handling, failure to deal with malfunctions on time, failure to perform troubleshooting measures in a timely manner as required Inability to supply electricity properly, resulting in significant economic losses Chen et al. (2019) Nie et al. (2019)  
FM5 Untimely Flood Control Flood control measures are not taken on time or are poorly implemented Causing damage to works or likely to affect water supply Zhu & Wang (2018) Han et al. (2018)  
FM6 Inadequate Safety Protection Failure to regularly inspect, replace protective equipment (including firefighting supplies), inadequate protective equipment Casualties, major property damage, impact on the safety of works Zhu & Wang (2018) Jiang et al. (2010)  
FM7 The Emergence of Biological Hazards Termites and other organisms found in the embankment Threaten the safety of the levee, which can lead to dam failure Geng et al. (2010) Geng et al. (2012)  
FM8 Problems with Water Quality and Safety Leakage of hazardous objects, contaminants into dry canals, algal blooms Interruption of water supply at the diversion gate, (severely) affecting normal water delivery Xiao et al. (2010) Wang et al. (2009)  
FM9 Untimely Emergency Response Failure to address emergencies as they arise Interruption of water supply, major economic losses, casualties Wang & Huai (2019) Xiao et al. (2010)  
Serial numberFailure modeMain causes of failureEffects of the failureDocumentary sources
FM1 Irregular Operation and Scheduling Failure to follow dispatch protocols (or plans) for reasonable dispatch operations and inadequate dispatch mechanisms All levels of management staff cannot be connected in real time, and an alarm cannot be transmitted in a timely manner Geng et al. (2010) Nie et al. (2019)  
FM2 Inadequate Engineering Inspection Failure to comply with the standard or required inspection visits The presence of serious defects in the works that endanger safety, the presence of certain factors in the environment that endanger the safety of the works Sun (2018)  
FM3 Irregular Maintenance Failure to maintain works areas or facilities to standard or in a timely manner Failure of an engineering site or failure of a facility Zhu & Wang (2018) Geng et al. (2012)  
FM4 Power Supply System Failure Inappropriate personnel handling, failure to deal with malfunctions on time, failure to perform troubleshooting measures in a timely manner as required Inability to supply electricity properly, resulting in significant economic losses Chen et al. (2019) Nie et al. (2019)  
FM5 Untimely Flood Control Flood control measures are not taken on time or are poorly implemented Causing damage to works or likely to affect water supply Zhu & Wang (2018) Han et al. (2018)  
FM6 Inadequate Safety Protection Failure to regularly inspect, replace protective equipment (including firefighting supplies), inadequate protective equipment Casualties, major property damage, impact on the safety of works Zhu & Wang (2018) Jiang et al. (2010)  
FM7 The Emergence of Biological Hazards Termites and other organisms found in the embankment Threaten the safety of the levee, which can lead to dam failure Geng et al. (2010) Geng et al. (2012)  
FM8 Problems with Water Quality and Safety Leakage of hazardous objects, contaminants into dry canals, algal blooms Interruption of water supply at the diversion gate, (severely) affecting normal water delivery Xiao et al. (2010) Wang et al. (2009)  
FM9 Untimely Emergency Response Failure to address emergencies as they arise Interruption of water supply, major economic losses, casualties Wang & Huai (2019) Xiao et al. (2010)  
This study proposes a fuzzy VIKOR-based FMEA to assess the operational risk. In the traditional FMEA calculation, if is the failure mode to be evaluated in m and is the failure mode in i, the experts score the actual performance under occurrence (O), severity (S), and difficulty of detection (D), and the risk priority is calculated by Equation (1):
(1)

The resulting RPNs are ranked from smallest to largest, from which the calculation of the final risk priority number can be obtained.

This study is based on an improved FMEA approach to assessing the safety risks of the operation and management of the SNWDP. Assuming that the FMEA expert team consists of s experts , different weights are assigned to the scores of the s experts according to their knowledge structure and domain experience. The expert team uses linguistic variables to evaluate the actual performance of m potential failure modes under n risk factors as well as the relative importance between risk factors, and converts the evaluation results into corresponding triangular fuzzy numbers, and the fuzzy AHP and maximum deviation methods are used to obtain the combined weights. Then the failure modes are ranked according to VIKOR, and the ranking results are evaluated and analyzed. The research framework of this paper is shown in Figure 1.

Figure 1

Research framework of FMEA model.

Figure 1

Research framework of FMEA model.

Close modal

Risk expression based on triangular fuzzy numbers

Definition 1: Let U be a theoretical domain, called a mapping:
(2)

Determine a fuzzy subset on U. Mapping is called the affiliation function of and is called the degree of 's affiliation to . The larger is, the greater the degree of x is in affiliation to .

Fuzzy logic uses different types of fuzzy affiliation functions, such as triangular fuzzy numbers and trapezoidal fuzzy numbers. The triangular fuzzy numbers are of high practical value due to their simplicity of computation and ease of processing and have good representation and information processing functions in fuzzy environments. Therefore, this study chooses triangular fuzzy numbers to express the language evaluation of experts.

Definition 2: A trigonometric fuzzy number can be expressed as: , whose subordinate function is as in Equation (3):
(3)
where l and u represent the upper and lower bounds of this triangular fuzzy number, and m is the modal value of the fuzzy number M.
Definition 3: Let and be two triangular fuzzy numbers, given any real numbers , , . The algebraic operation of triangular fuzzy numbers can be expressed as follows:
(4)
(5)
(6)
(7)
Definition 4: The distance between any two triangular fuzzy numbers and can be expressed as:
(8)

Determining risk factor weights based on fuzzy AHP and maximum deviation methods

Traditional FMEA methods consider the occurrence (O), severity (S) and difficulty of detection (D) of risk occurrence as equally important, and do not consider the risk factor weighting information, since it is difficult to determine the risk factor weights directly. There are many calculation methods to determine the FMEA risk factor weights, mainly including the objective assignment method, subjective assignment method, and integrated assignment method. Among them, the integrated assignment method can take both subjective and objective factors into account, which overcomes the limitation of calculating weights from unilateral methods and is widely used. In this study, by combining the fuzzy AHP and maximum deviation method, the integrated assignment method overcomes the shortcomings of traditional FMEA that does not take into account the risk factor weights by considering both subjective and objective factors.

Subjective weighting based on fuzzy AHP

Fuzzy hierarchy analysis is a method that combines fuzzy numbers and the Analytic Hierarchy Process (AHP) and is widely used in subjective evaluation to reflect the fuzzy thinking of people. Triangular fuzzy numbers are one of the most common forms of fuzzy numbers. Chang (1996) proposed the most widely used method of fuzzy hierarchy analysis, which converts experts' verbal judgments into triangular fuzzy numbers, constructs a judgment matrix for processing, and obtains subjective weights of risk factors.

The conversion relationship between the fuzzy triangle and the linguistic terms that team members can use to evaluate the subjective weight vector of risk factors is shown in Table 2.

Table 2

Language variables for risk factor weighting

Linguistic termsTriangular fuzzy numbers
Absolutely strong (AS) (2,5/2,3) 
Very strong (VS) (3/2,2,5/2) 
Fairly strong (FS) (1,3/2,2) 
Slightly strong (SS) (1,1, 3/2) 
Equal (EI) (1,1,1) 
Slightly weak (SW) (2/3,1,1) 
Fairly weak (FW) (1/2,2/3,1) 
Very weak (VW) (2/5,1/2,2/3) 
Absolutely weak (AW) (1/3,2/5,1/2) 
Linguistic termsTriangular fuzzy numbers
Absolutely strong (AS) (2,5/2,3) 
Very strong (VS) (3/2,2,5/2) 
Fairly strong (FS) (1,3/2,2) 
Slightly strong (SS) (1,1, 3/2) 
Equal (EI) (1,1,1) 
Slightly weak (SW) (2/3,1,1) 
Fairly weak (FW) (1/2,2/3,1) 
Very weak (VW) (2/5,1/2,2/3) 
Absolutely weak (AW) (1/3,2/5,1/2) 
Let be a set of objects and be a set of targets. For each object , perform a degree analysis for each target . You can obtain m range analysis values for each object with the following notation:
where is a triangular fuzzy number and then the steps to obtain the subjective weights of the three risk factors S, O and D are as follows:
Step 1: Calculate the value of the degree of fuzzy integration concerning the th target according to Equation (9):
(9)
where can be calculated by fuzzy addition of m range analysis values of a particular matrix:
(10)
The reciprocal of is calculated as in Equation (11):
(11)
Step 2: The degree of likelihood between the two fuzzy integrated intervals of A and B is defined by Equation (12):
(12)
The above formula can also be described as:
(13)

In Equation (13), the point D located between and is at the coordinates of the highest point of the intersecting part, as shown in Figure 2. In order to compare the sizes of and , the sizes of and are required.

Figure 2

Intersection of S1 and S2.

Figure 2

Intersection of S1 and S2.

Close modal
Step 3: The degree of likelihood that the number of convex ambiguities is greater than k convex ambiguities can be calculated from Equation (14) as follows:
(14)
Step 4: Subjective weights for risk factors can be calculated from Equation (15):
(15)
Assumptions:
(16)
where denotes the number of elements.
After normalization, the normalized subjective weight vector for each risk factor is expressed as Equation (17), where is the non-fuzzy number:
(17)

Objective weights based on maximum deviation method

In order to determine the objective weights of risk factors S, O and D, a model for calculating risk factor weights based on the maximum deviation method is developed in a fuzzy environment. According to the idea of the maximum deviation method, if the degree of difference in the assessed values of all the scenarios under an attribute is not significant, i.e., the attribute does not play a significant role in the overall decision process, the attribute should be assigned a smaller weight value; conversely, if the degree of difference is significant, the attribute should be assigned a larger weight value.

Safety Failure Mode is set as , the evaluation index of failure mode as , and the expert for . The evaluation group composed of experts makes the semantic evaluation of the evaluation index of each failure mode, and quantifies the evaluation result by using a triangular fuzzy number, as shown in Table 3; represents the evaluation value of expert on the evaluation indicator in failure mode . The arithmetic means algorithm is used to find the group decision value for the evaluation value given by different experts, and constitutes the fuzzy evaluation matrix .

Table 3

Semantic evaluation form for failure modes

Language variablesTriangular fuzzy number
Very low (VL) (0,0,0.1) 
Low (L) (0,0.1,0.3) 
Moderately low (ML) (0.1,0.3,0.5) 
Moderate (M) (0.3,0.5,0.7) 
Moderately high (MH) (0.5,0.7,0.9) 
High (H) (0.7,0.9,1) 
Very high (VH) (0.9,1,1) 
Language variablesTriangular fuzzy number
Very low (VL) (0,0,0.1) 
Low (L) (0,0.1,0.3) 
Moderately low (ML) (0.1,0.3,0.5) 
Moderate (M) (0.3,0.5,0.7) 
Moderately high (MH) (0.5,0.7,0.9) 
High (H) (0.7,0.9,1) 
Very high (VH) (0.9,1,1) 
Step 1: De-blurring of the assessment value :
(18)
In Equation (18), in order to determine the weight of decision indicators by the maximum deviation method, the evaluation value in the fuzzy evaluation matrix should be de-fuzzified first. In this paper, the fuzzy evaluation number de-fuzzification rule is used to de-fuzzify , , , . The exact evaluation value after de-fuzzifying each evaluation value in the fuzzy evaluation matrix is as follows:
(19)
Step 2: Normalization of the matrix. The evaluation matrix is composed of . For the evaluation index , the highest value of m failure modes is and the lowest value is . The matrix is normalized to obtain a standardized matrix. The matrix R is normalized to obtain the standardized matrix .
(20)
Step 3: Develop a model for calculating the evaluation indicator importance based on the maximum deviation method.
(21)
The model is solved as follows:
(22)
Step 4: Based on the above solution, the objective weight for the evaluation indicator is obtained as follows:
(23)

Determine the combined weights

In this study, the comprehensive weighting method is proposed, which introduces a risk factor weight adjustment factor (usually ) as the relative importance of the subjective and objective weights. The comprehensive weight is as follows:
(24)

Fuzzy VIKOR-based FMEA approach for risk ranking

The VIKOR method is proposed by Opricovic's formula-criteria optimization of complex systems (Opricovic 1998), which identifies compromise solutions to problems with conflicting criteria and helps experts to make final decisions. In this section, an improved fuzzy method is proposed for dealing with uncertain data and solving fuzzy multi-criteria problems with conflicting criteria. The proposed fuzzy VIKOR method provides a more rational way to calculate the distance between the state of the failure mode and the ideal failure point.

Suppose a failure mode risk ranking problem has k experts , m failure modes and n criteria , and is evaluated against the n criteria; and order to be the th fuzzy rating of the th failure mode provided by the experts, and to be the relative importance weight of the k experts, both of them are satisfying and . The improved VIKOR method is as follows:

Step 1: Aggregate the opinions of experts to obtain a pooled fuzzy evaluation of the failure modes and construct a fuzzy decision matrix. The pooled fuzzy evaluation () of each failure mode relative to each criterion can be calculated as:
(25)
where
A failure mode risk ranking problem can be succinctly expressed in matrix format as follows:
where is the score of failure mode relative to criterion , , , .
Step 2: Determine the fuzzy best and fuzzy worst values for all evaluation indicators:
(26)
(27)

It is worth emphasizing that all the methods used in the literature to determine non-fuzzy values also apply to ranking fuzzy numbers. For simplicity, this study recommends using the gravity method to rank the fuzzy composite scores and to determine the fuzzy best and fuzzy worst scores.

Step 3: Calculate the normalized fuzzy distances :
(28)
Step 4: Calculate the maximum group utility and the minimum individual regret by Equations (29–30), :
(29)
(30)
where is the combined weight of the evaluation criteria, and represents the relative importance of the subjective and objective weights; denotes decision-making based on maximizing group utility, denotes decision-making based on minimizing individual regret mechanisms, and denotes decision-making based on negotiated consensus mechanisms. In this study, both weights are considered equally important and .
Step 5: Calculate according to Equation (31):
(31)
where , v is introduced as the weight of the maximum group utility strategy, while is the weight of individual regret. In this study, the value of v is set to 0.5.

Step 6: Rank the failure modes in descending order of S, R, and Q values, with lower values indicating less risk.

Step 7: Determine the compromise failure mode risk ranking. That is, failure mode (), which measures this risk ordering as Q (maximum) is best if the following two conditions are met:

  • , where n is the total number of failure modes.

  • ②  Failure mode risk ranking based on and ranking is also the optimal risk ranking, then is judged to be the stable maximum risk ranking.

If the above conditions are not met simultaneously, then the two compromise risk rankings are obtained, with the following two situations:

  • (1)

    If condition ① is satisfied but condition ② is not satisfied, there are two compromise risk rankings: , .

  • (2)

    If condition ① is not satisfied but condition ② is satisfied, there are M compromise risk rankings: , , …, , where M is the maximized M value determined from .

Case description

This study selects the Huixian section of the Middle Route of the South-to-North Water Diversion Project as an example for operation risk evaluation. The Huixian section is located within Huixian City, Henan Province. The total length of the channel section is 48.951 km, including 43.631 km of open channel, 5.320 km of hydraulic structures. The total waterway is mainly an open canal, and 26 rivers are crossed by the vertical intersection of the canal line. The designed flow of the channel is 260 m3/s, and the increased flow is 310 m3/s.

Step 1: Evaluate the Occurrence (O), Severity (S), and Difficulty detection (D) using the linguistic variables. There are four experts in the FMEA evaluation team, namely a scientific expert, engineering design expert, engineering operation manager, and engineering site inspector. They are prioritized according to their knowledge structure and domain experience, with weights of 0.25, 0.30, 0.28, and 0.17. The four experts evaluated the actual situation of nine potential failure modes under the three risk factors of Occurrence (O), Severity (S), and Difficulty detection (D) using the linguistic variables in Table 2, and the results of the evaluation are shown in Table 4. The experts' semantic evaluation information is transformed into the corresponding triangular fuzzy number, and the comprehensive fuzzy level of the failure mode is calculated to determine the fuzzy decision matrix, which constitutes the triangular fuzzy evaluation matrix of the failure mode, as shown in Table 5.

Table 4

Evaluation information of expert language variables

Failure modesSeverity (S)
Occurrence (O)
Difficulty detection (D)
DM1DM2DM3DM4DM1DM2DM3DM4DM1DM2DM3DM4
FM1 MH MH MH ML ML 
FM2 MH MH ML ML MH ML MH 
FM3 MH MH MH MH ML MH 
FM4 MH MH MH ML ML 
FM5 VH VH VH MH ML ML ML 
FM6 MH MH ML ML MH 
FM7 MH MH MH VL MH MH MH 
FM8 MH VL MH MH 
FM9 VH VH VH VL VL VL ML 
Failure modesSeverity (S)
Occurrence (O)
Difficulty detection (D)
DM1DM2DM3DM4DM1DM2DM3DM4DM1DM2DM3DM4
FM1 MH MH MH ML ML 
FM2 MH MH ML ML MH ML MH 
FM3 MH MH MH MH ML MH 
FM4 MH MH MH ML ML 
FM5 VH VH VH MH ML ML ML 
FM6 MH MH ML ML MH 
FM7 MH MH MH VL MH MH MH 
FM8 MH VL MH MH 
FM9 VH VH VH VL VL VL ML 
Table 5

Aggregated fuzzy ratings of failure modes

Risk factorSeverity (S)Occurrence (O)Difficulty detection (D)
FM1 (0.54,0.74,0.92) (0.27,0.47,0.67) (0.26,0.46,0.66) 
FM2 (0.47,0.67,0.845) (0.19,0.39,0.59) (0.37,0.57,0.77) 
FM3 (0.42,0.62,0.82) (0.34,0.54,0.74) (0.31,0.51,0.71) 
FM4 (0.42,0.62,0.82) (0.02,0.14,0.34) (0.04,0.18,0.38) 
FM5 (0.82,0.96,1) (0.33,0.53,0.73) (0.08,0.26,0.46) 
FM6 (0.39,0.59,0.79) (0.22,0.42,0.62) (0.25,0.45,0.65) 
FM7 (0.47,0.67,0.87) (0,0.085,0.27) (0.46,0.66,0.86) 
FM8 (0.62,0.82,0.96) (0,0.085,0.27) (0.41,0.61,0.81) 
FM9 (0.82,0.96,1) (0,0.02,0.14) (0.02,0.14,0.34) 
Risk factorSeverity (S)Occurrence (O)Difficulty detection (D)
FM1 (0.54,0.74,0.92) (0.27,0.47,0.67) (0.26,0.46,0.66) 
FM2 (0.47,0.67,0.845) (0.19,0.39,0.59) (0.37,0.57,0.77) 
FM3 (0.42,0.62,0.82) (0.34,0.54,0.74) (0.31,0.51,0.71) 
FM4 (0.42,0.62,0.82) (0.02,0.14,0.34) (0.04,0.18,0.38) 
FM5 (0.82,0.96,1) (0.33,0.53,0.73) (0.08,0.26,0.46) 
FM6 (0.39,0.59,0.79) (0.22,0.42,0.62) (0.25,0.45,0.65) 
FM7 (0.47,0.67,0.87) (0,0.085,0.27) (0.46,0.66,0.86) 
FM8 (0.62,0.82,0.96) (0,0.085,0.27) (0.41,0.61,0.81) 
FM9 (0.82,0.96,1) (0,0.02,0.14) (0.02,0.14,0.34) 

Step 2: The integrated assignment method solves for the combined weights. The FMEA team members used linguistic variables to assess the relative importance of the risk factors. The results of the four experts' evaluations using a two-comparison approach are shown in Table 6. For example, when comparing the severity and frequency of occurrence of risk factors, the four experts' responses were fairly strong (FS), slightly strong (SS), slightly strong (SS), and fairly strong (FS), respectively. Team members can convert the linguistic variables into triangular fuzzy numbers using the method in Table 1, as shown in Table 7; a weighted average is performed to obtain subjective weights for the risk factors, as shown in Table 8.

Table 6

Scoring of subjective weights of risk factors

Risk factorSeverity (S)Occurrence (O)Difficulty detection (D)
Severity (SE,E,E,E FS,SS,SS,FS FS,SS,FS,FS 
Occurrence (O– E,E,E,E SS,E,SS,S 
Difficulty detection (D– – E,E,E,E 
Risk factorSeverity (S)Occurrence (O)Difficulty detection (D)
Severity (SE,E,E,E FS,SS,SS,FS FS,SS,FS,FS 
Occurrence (O– E,E,E,E SS,E,SS,S 
Difficulty detection (D– – E,E,E,E 
Table 7

Fuzzy pairwise comparison matrix of subjective weights of risk factors

Risk factorSeverity (S)Occurrence (O)Difficulty detection (D)
Severity (S(1,1,1) (1,3/2,2) (1,3/2,2) 
 (1,1,3/2) (1,1,3/2) 
 (1,1,3/2) (1,3/2,2) 
  (1,3/2,2) (1,3/2,2) 
Occurrence (O(1/2,2/3,1) (1,1,1) (1,1,3/2) 
(2/3,1,1)  (1,1,1) 
(2/3,1,1)  (1,1,3/2) 
 (1/2,2/3,1)  (1,1,3/2) 
Difficulty detection (D(1/2,2/3,1) (2/3,1,1) (1,1,1) 
(2/3,1,1) (1,1,1)  
(1/2,2/3,1) (2/3,1,1)  
 (1/2,2/3,1) (2/3,1,1)  
Risk factorSeverity (S)Occurrence (O)Difficulty detection (D)
Severity (S(1,1,1) (1,3/2,2) (1,3/2,2) 
 (1,1,3/2) (1,1,3/2) 
 (1,1,3/2) (1,3/2,2) 
  (1,3/2,2) (1,3/2,2) 
Occurrence (O(1/2,2/3,1) (1,1,1) (1,1,3/2) 
(2/3,1,1)  (1,1,1) 
(2/3,1,1)  (1,1,3/2) 
 (1/2,2/3,1)  (1,1,3/2) 
Difficulty detection (D(1/2,2/3,1) (2/3,1,1) (1,1,1) 
(2/3,1,1) (1,1,1)  
(1/2,2/3,1) (2/3,1,1)  
 (1/2,2/3,1) (2/3,1,1)  
Table 8

Weighted average of subjective weight matrix for risk factors

Risk factorSeverity (S)Occurrence (O)Difficulty detection (D)
Severity (S(1,1,1) (1,1.13,1.63) (1,1.25,1.75) 
Occurrence (O(0.63,0.92,1) (1,1,1) (1,1,1.38) 
Difficulty detection (D(0.58,0.83,1) (0.75,1,1) (1,1,1) 
Risk factorSeverity (S)Occurrence (O)Difficulty detection (D)
Severity (S(1,1,1) (1,1.13,1.63) (1,1.25,1.75) 
Occurrence (O(0.63,0.92,1) (1,1,1) (1,1,1.38) 
Difficulty detection (D(0.58,0.83,1) (0.75,1,1) (1,1,1) 
Equations (8)–(10) are used to calculate the degree of fuzzy integration for each risk factor:

Subjective weight vector based on Equations (11–16): .

According to Equation (3), the fuzzy evaluation values in Table 1 are de-fuzzyified, and then the maximum deviation method is used, that is, according to Equations (18–23). The objective weight for each evaluation indicator is calculated; and , that is, assuming that the objective and subjective weights are equally important, the combined weight of the risk factors is determined to be .

Step 3: VIKOR-based FMEA. Occurrence, Severity, and Difficulty detection are all cost-based risk factors, and fuzzy best and fuzzy worst are obtained from Equations (26–27).

For each of the failure modes identified in the FMEA, the normalized fuzzy distance can be calculated using Equation (27), as shown in Table 9. Then, the S, and Q values are calculated for all the fault modes, as shown in Table 10.

Table 9

Normalized fuzzy distance for failure modes

Risk factorSeverity (S)Occurrence (O)Difficulty detection (D)
FM1 0.431 0.777 0.573 
FM2 0.233 0.682 0.799 
FM3 0.154 1.000 0.646 
FM4 0.154 0.274 0.000 
FM5 1.000 0.992 0.167 
FM6 0.000 0.788 0.714 
FM7 0.138 0.107 1.000 
FM8 0.644 0.107 0.927 
FM9 1.000 0.000 0.019 
Risk factorSeverity (S)Occurrence (O)Difficulty detection (D)
FM1 0.431 0.777 0.573 
FM2 0.233 0.682 0.799 
FM3 0.154 1.000 0.646 
FM4 0.154 0.274 0.000 
FM5 1.000 0.992 0.167 
FM6 0.000 0.788 0.714 
FM7 0.138 0.107 1.000 
FM8 0.644 0.107 0.927 
FM9 1.000 0.000 0.019 
Table 10

S, Q, R values of failure modes

Failure modesFM1FM2FM3FM4FM5FM6FM7FM8FM9
S 0.583 0.540 0.567 0.148 0.759 0.458 0.375 0.552 0.397 
R 0.250 0.229 0.322 0.088 0.392 0.254 0.287 0.266 0.392 
Q 0.623 0.553 0.728 0.000 1.000 0.527 0.513 0.624 0.704 
Failure modesFM1FM2FM3FM4FM5FM6FM7FM8FM9
S 0.583 0.540 0.567 0.148 0.759 0.458 0.375 0.552 0.397 
R 0.250 0.229 0.322 0.088 0.392 0.254 0.287 0.266 0.392 
Q 0.623 0.553 0.728 0.000 1.000 0.527 0.513 0.624 0.704 

Step 4: Risk priorities of the failure modes. Based on the decreasing order of S, R, and Q, the risk priorities of the failure modes are derived as shown in Table 11.

Table 11

Failure modes in descending order of S, R and Q

Failure modesFM1FM2FM3FM4FM5FM6FM7FM8FM9
S 
R 
Q 
Failure modesFM1FM2FM3FM4FM5FM6FM7FM8FM9
S 
R 
Q 

From Table 11, in descending order of Q, FM5 > FM3 > FM9 > FM8 > FM1 > FM2 > FM6> FM7 > FM4. In addition, , so condition 1 is satisfied. In the descending order of S and R, FM5 is in the first place, so condition 2 is satisfied. That is, it is the optimal risk ranking scheme according to the descending order of Q values.

In summary, the combined risk ranking for the nine failure modes is: FM5 > FM3 > FM9> FM8 > FM1 > FM2 > FM6 > FM7 > FM4. Among all the failure modes, the highest risk is caused by untimely flood control.

In the operation safety risks of SNWDP, rainfall concentrated in July and August each year, is very likely to cause flooding. In actual operation and management, new flood control work mechanisms are still in the run-in period, coupled with the existence of project flood control pressure, and task complexity. So flood control is of great significance to protect the smooth operation of the SNWDP. The second place in the risk ranking is the maintenance of non-standard maintenance. In the operation of the SNWDP, this risk will be affected by many factors. In order to promote the improvement of the overall quality of the project, it is necessary to focus on maintenance, project structure, and mechanical and electrical equipment on-time maintenance.

Sensitivity analysis

A sensitivity analysis is performed on the risk assessment results of the FMEA method proposed in this study, where takes 0, 0.5, and 1 as the raw weights obtained by the objective, combined, and subjective assignment methods, respectively. From Figure 3, it can be found that as the value of increases progressively from 0 to 1, the failure mode order of FM4, FM5, and FM6 does not change. The changes in the weights of the risk factors greatly impact the final risk ranking of the failure modes. When , the integrated weight , when the risk factor Occurrence (O) and Difficulty Detection (D) weight are higher, the Severity (S) weight is lower, the risk ranking of FM9 is eighth, the risk is lower. When , the integrated weight , the risk factor Occurrence (O) and Difficulty Detection (D) weight are lower and the Severity (S) weight is higher. FM9 ranking rises sharply to second place. If it is not handled in time, extremely serious consequences would be caused. The risk ranking of FM1, FM2, and FM7 remains stable after a small decrease, because the severity of irregular operation and scheduling, inadequate engineering inspection, and biohazard are lower than other failure modes. Therefore, it is particularly important to select an appropriate method to determine the weight of risk factors. The comprehensive assignment method proposed in this study can fully consider the role of expert opinion and evaluation information itself. It makes the risk ranking of failure modes more realistic. In addition, the comprehensive weighting approach is used in this study, and can be determined by the decision-maker regarding the actual situation. When the FMEA expert team is less certain or it is difficult to evaluate the weighting information for the risk factors, should be assumed. When the expert team is more certain about the weighting information for the risk factors, should be assumed.

Figure 3

Sensitivity analysis results.

Figure 3

Sensitivity analysis results.

Close modal

This study constructed nine typical failure modes: Irregular Operation and Scheduling (FM1), Inadequate Engineering Inspection (FM2), Irregular Maintenance (FM3), Power Supply System Failure (FM4), Untimely Flood Control (FM5), Inadequate Safety Protection (FM6), Emergence of Biological Hazards (FM7), Problems with Water Quality and Safety (FM8) and Untimely Emergency Response (FM9). All of those failure modes are common in the water division project (Nie et al. 2019). This output makes a good foundation for theoretical and practical research on cross-basin large-scale water division infrastructure.

This study proposed an improved FMEA risk assessment method based on VIKOR and combined weights in a fuzzy environment. This assessment model is a theoretical framework for the operational risk management of large-scale infrastructure. In order to further illustrate the validity of the constructed model, the risk ranking results of the failure model in this study are compared with the calculation results of RPN in traditional FMEA, as well as comparing the weighting calculation method using only fuzzy AHP and the weighting calculation method using only the maximum deviation method. Based on the calculation results in Table 12, the superiority of the FMEA method proposed in this paper relative to other methods can be seen, and the comparison results can be summarized as follows:

  • (1)

    When only the subjective or objective weights of the risk factors are considered, the failure modes can also be ranked, but the ranking results may be biased or even misleading. When takes 0, 0.5, and 1, respectively, six of the nine failure modes (66.7%) show different degrees of variation in the risk ranking, indicating that the differences in risk ranking can vary greatly under the constraints of different risk factor weights.

  • (2)

    Compared with the traditional RPN method, the risk ranking of the proposed risk assessment model is inconsistent except for FM4 and FM5. FM4 and FM5 represent the power supply system failure and flood control delay respectively, which correspond to the minimum risk value and maximum risk value, and in the traditional FMEA model, the results calculated by tend to vary widely, and there are higher requirements for the accuracy of expert scoring.

  • (3)

    The traditional FMEA method uses real numbers for calculation, and there is the same risk value ranking situation. For example, FM1 and FM6 correspond to irregular operation and scheduling and incomplete safety protection respectively, and the expert scores are inconsistent in Severity (S), Occurrence (O) and Difficulty Detection (D), but the calculated RPN value appears with the same value, so the risk ranking is the same. It is difficult to determine the risk order of the two failure modes, because of the information loss.

Table 12

Comparison of failure mode rankings

Failure modes


Traditional FMEA method
QRankingQRankingQRankingSODRPNRanking
FM1 0.741 0.591 0.471 120 
FM2 0.702 0.519 0.378 168 
FM3 0.908 0.680 0.489 75 
FM4 0.000 0.000 0.000 54 
FM5 0.995 1.000 1.000 288 
FM6 0.675 0.488 0.331 120 
FM7 0.687 0.473 0.302 90 
FM8 0.758 0.603 0.600 105 
FM9 0.580 0.715 0.769 72 
Failure modes


Traditional FMEA method
QRankingQRankingQRankingSODRPNRanking
FM1 0.741 0.591 0.471 120 
FM2 0.702 0.519 0.378 168 
FM3 0.908 0.680 0.489 75 
FM4 0.000 0.000 0.000 54 
FM5 0.995 1.000 1.000 288 
FM6 0.675 0.488 0.331 120 
FM7 0.687 0.473 0.302 90 
FM8 0.758 0.603 0.600 105 
FM9 0.580 0.715 0.769 72 

In this study, the comprehensive weighting method is used to consider the weight of risk factors in both subjective and objective aspects, which makes the risk analysis results more consistent with the actual situation (Song et al. 2013). The fuzzy VIKOR method is used to evaluate the failure mode, which improves the robustness of the existing FMEA results (Emovon et al. 2015). From the above analysis, it can be concluded that the proposed method is better than the traditional FMEA method.

The geographical span of the SNWDP is large, the operational reliability requirements are high, the management is difficult, and the operational management safety risk has a significant impact on the operational reliability of the project. This study proposes a risk assessment model for the operational management safety of the SNWDP based on the integrated empowerment method and fuzzy VIKOR-FMEA.

The main contributions of this paper are:

  • (1)

    The established risk assessment framework for project operation and management is an effective method for identifying project risks and is capable of identifying key risk factors in the operation of water division projects.

  • (2)

    The extended fuzzy VIKOR-FMEA risk assessment method proposed in this study makes up for the shortcomings of traditional risk assessment methods such as single perspective and easy loss of important information in the process of information fusion, and provides a theoretical algorithm for operation and management risk analysis of similar engineering projects.

The research results have a certain reference effect on actual engineering operation safety risk management. Only by identifying the important risk factors in the project operation process in advance can we take correct operation and management measures to better ensure the safe and stable operation of the project.

At present, there is no comprehensive and reasonable diagnostic method for the key risk sources faced in the operation of water transfer projects, therefore, the way of thinking about the identification of risk factors in the operation of water transfer projects in this paper is not comprehensive enough, and a detailed theoretical framework for conducting scientific identification and assessment of important risk factors in the operation management of water transfer projects is expected to be constructed in the future.

The authors acknowledge with gratitude the National Key R&D Program of China (No.2018YFC0406905); MOE (Ministry of Education in China) Project of Humanities and Social Sciences (No. 19YJC630078), Youth Talents Teachers Scheme of Henan Province Universities (No. 2018GGJS080), the National Natural Science Foundation of China (No. 71974056 and 71302191), the Foundation for Distinguished Young Talents in Higher Education of Henan (Humanities & Social Sciences), China (No. 2017-cxrc-023), China Scholarship Council (No. 201908410388), 2018 Henan Province Water Conservancy Science and Technology Project (GG201828). This study would not have been possible without their financial support.

The authors declare that they have no conflicts of interest.

Data cannot be made publicly available; readers should contact the corresponding author for details.

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