Honghua Sun is an associate professor in the School of Mechanical Engineering at Inner Mongolia University of Technology. She received her M.S. degree from Harbin Institute of Technology in 2008. Her current research interests include reliability data analysis and reliability evaluation.
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Hongxia Chen is an associate professor in the School of Mechanical Engineering at Inner Mongolia University of Technology. She received her M.S. degree in 2008. Her current research interests include reliability data analysis and reliability evaluation.
, E-mail: chenhx@imut.edu.cn.
Qingyang Li is a postgraduate student in the School of Mechanical Engineering at Inner Mongolia University of Technology. He received his bachelor’s degree from Inner Mongolia University of Technology in 2016. His current research interests include reliability data analysis and reliability evaluation.
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Xudong Chen is a postgraduate student in the School of Mechanical Engineering at Inner Mongolia University of Technology. He received his bachelor’s degree from Inner Mongolia University of Technology in 2016. His current research interests include reliability data analysis and reliability evaluation.
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Abstract
Building a fault tree and calculating the sequence of bottom events importance degree are key steps in fault diagnosis. Two improvements are made to the fuzzy fault tree in this study. The first is building the fault tree using Interpretive Structure Modeling (ISM)technology. The second is transforming triangular fuzzy numbers into binary connection numbers (BCN)through the uncertainty theory of set pair analysis, where the certainty coefficient is determined by the median of the triangular fuzzy number and the uncertainty coefficient is determined by the interval value described bythe upper and lower limitations. The formula of failure probability of the top event and the formula of probability importance of the bottom event are deduced with the binary connection number. This method reduces the calculation amount. A case studyis carried out to verify the feasibility and effectiveness of the method.
Honghua Sun, Hongxia Chen, Qingyang Li, and Xudong Chen. Fuzzy Fault Tree Analysis based on Interpretive Structure Model and Binary Connection Numbers. International Journal of Performability Engineering, 2019, 15(1): 45-55 doi:10.23940/ijpe.19.01.p5.4555
1. Introduction
A fault tree is an analysis method to improve system reliability. The logic relation diagram is drawn by analyzing the factors that affect a system’s failures (including hardware, software, environment, human factors, etc.).The fault tree analysis method can determine the possible combinations cause and failure probability of the system failure, and then measures can be taken to prevent system failures. Fault trees describe the logical relationship between the basic events that lead to the failure of the system by using prescribed events, logic gates, and other symbols.
Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11].
Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21].
Fault treesare used to analyze the causality between faults, and the ISM is also used to establish the hierarchy between causality, so this paper applies the method of ISM to the establishment of fault trees. There are many methods for ordering the probability importance of bottom events. BCN is applied to conduct evaluation problems, but no one has applied BCN to the solution of probability importance of fuzzy fault trees previously. Hence, this paper studies the following two aspects:using the ISM to build fault trees and applying the BCN to triangular fuzzy numbers to calculate the probability importance of the bottom event.
This paper is organized as follows.Section 2 introduces the basic principle and steps of the interpretive structure modeling.In Section 3, the binary connection number is defined, the procedure of how to transform triangle fuzzy numbers into binary connection numbers is described, and the reliability formula by binary connection numberis deduced.In Section 4, a case study is given to verify the effectiveness of using ISM and BCN.Section 5 providesthe conclusions and future works.
2. The Steps to Build aModel by ISM
The ISM is a determining technology of the whole structure of the system based on various creative techniques. By exploring the elements of the system and defining the significance of the correlation between the elements, the concrete relationship between the elements based on the binary relation is given. Moreover, the structure model of a complex system is established by digraph and matrix, which are easy to understand and easy to deal with. The technology of interpretive structure modeling was developed by Warfield in 1973 to analyze complex socio-economic problems [22]. The flow chart of the fault tree is set up by using ISM, as shown in Figure 1.The modeling steps are as follows.
Figure 1.
Applying ISM to establish a fault tree flow chart
Step 1 Establish the adjacency matrix A of direct binary relations between elements. “1” in a matrix denotes the binary relationship between row elements and column elements. The binary relationship includes influence, causality, inclusion, membership, or comparison. The binary relationship is defined as causality when applied to a fault tree. The adjacency matrix $A$ and the unit matrix $I$ are combined to form the $(A+I)$ matrix:
${{a}_{ij}}=1$ means $i$ element has binary relation to $j$ element, and ${{a}_{ij}}=0$ Means $i$ element has no binary relation to $j$ element..
Step 2 The reachable matrix $M$ is calculated according to the ($A+I$) matrix. The $M$ matrix contains direct, indirect, and self to self-binary relations.
Step 3 According to the reachable matrix $M$, the number of “1”in each row is calculated. The position of the elements is rearranged according to the number of row “1” from less to more, and the unit matrix of the largest order is drawn.
Step 4 Remove the binary relation of the leap frogging, and transform the multi-hierarchical digraph into interpretive structure modeling on the basis of understanding the practical meaning of the elements.
Step 5 Transform the interpretive structure modeling into a fault tree.
3. Transform Triangular Fuzzy Number into Connection Numbers
3.1. Triangular Fuzzy Number
In general, the probability of a bottom event is obtained from a reliability manual or an empirical manual, but in some practical systems there are a large number of uncertainties, such as natural climate and human operations, which have an impact on the probability of the bottom event. Therefore, the probability of these bottom events does not have accurate values that can be counted. Even if the probability of the bottom event is obtained, these values are not certain because of the incidental complexity of the fault. If there is no statistical data, the determination of the probability of bottom events is generally based on the method of expert group scoring.All tables should be numbered with Arabic numerals. Captions should be placed above tables, center justified. Tables must be embedded into the text and not supplied separately. Below is an example that authors may find useful.
There are many kinds of models of fuzzy numbers, which are mainly divided into triangular fuzzy numbers, trapezoidal fuzzy numbers, normal fuzzy numbers, parabolic fuzzy numbers, etc.In this paper, we mainly study the triangular fuzzy number, so we choose the triangular fuzzy number to describe the probability of occurrence of thebottom event. Triangular fuzzy numbe r$A.=[\alpha , m,\beta ]$, where m is the median and $\alpha$ and $\beta$ are the upper and lower of the triangular fuzzy number.In the absence of statistical data, $n$ experts estimate the probability of the occurrence of the basic events in the fault tree, and the results are expressed as ${{p}_{1}},\text{ }{{p}_{2}},\text{ }{{p}_{3}},\text{ }\cdots \text{, }{{p}_{n}}$.A triangular fuzzy number is constructed by the mean value and the variance of the estimated probability, shown as Equations (2) and (3) where $\mu $ represents the mean value and $\sigma $ represents the variance.
Suppose the expert estimates the probability value to follow the normal statistical rule. According to the $3\sigma $ rule, the basic event whose probability exceeds 99.74% should fall in $[u-3\sigma , u+3\sigma ]$.Therefore, we can set $m=u$, $\alpha =u-3\sigma $, and $\beta =u+3\sigma .$ Obviously, the $m$ is determined, while the number between the lower$\alpha $ and the upper$\beta $ of the triangular fuzzy number is indefinite, and $\alpha $ and $\beta $ give the range of values. From this perspective, the triangular fuzzy number is the unity of certainty and uncertainty. It is confirmed that if the estimates are accurate, the upper and lower bounds of the fuzzy trigonometry can be determined using $u\pm \gamma \sigma $, which is determined by the investigators, $0<\gamma \le 3.$
3.2. The Basic Principle of Connection Number
SPA (set pair analysis) was put forward by Zhao in 1989 [18].SPA is a new theory of uncertainty. The core idea of SPA is to analyze the deterministic and uncertainty measures of objective things as a system, dealing with mixed uncertainty problems caused by fuzzy, random, unascertained, and mediating. The connection number is the main mathematical tool in the SPA. As a kind of connection number, the binary connection number is defined as follows:
Definition 1 Set R as a real number set, then the binary connection number $0<a$,$b\in R$,$i\in \left[ -1, 1 \right].$
Definition 2 Addition operation, let two connection numbers ${{L}_{1}} = {{a}_{1}} + {{b}_{1}}i $ and ${{L}_{2}}={{a}_{2}}+{{b}_{2}}i$ define the sum of two connection numbers $L={{L}_{1}}+{{L}_{2}}$, which is denoted as Equation(4).
Definition 3 Multiplication operation, let two connection numbers ${{L}_{1}} = {{a}_{1}} + {{b}_{1}}i $ and ${{L}_{2}}={{a}_{2}}+{{b}_{2}}i$ define two connection numbers $L={{L}_{1}}\times {{L}_{2}}$, which is denoted as Equation (5).
According to the theory of set pair analysis, without considering the level of uncertainty orthe product of two connection numbers, the different powers of “i” can be treated as a power, e.g.:
Let $a={{a}_{1}}{{a}_{2}},\text{ }b={{a}_{1}}{{b}_{2}}+{{a}_{2}}{{b}_{1}}+{{b}_{1}}{{b}_{2}}$, then $L\text{=}a+bi$. It can be proven that when there are three or more binary connection numbers multiplied, the product is still the binary number.
Definition 4 Division operation, it is known that $L=a+bi$ is the product of two binary connection numbers, one of which is ${{L}_{1}}={{a}_{1}}+{{b}_{1}}i$, and the other is
Let ${{a}_{2}}=a/{{a}_{1}},\text{ }{{b}_{2}}=(b-{{a}_{2}}{{b}_{1}})/({{a}_{1}}+{{b}_{1}})$, then ${{L}_{2}}={{a}_{2}}+{{b}_{2}}i$. It can be proven that when there are threeor more binary connection numbers divided, the quotient is still the binary connection number.
3.3. Transform Triangular Fuzzy Number into Binary Connection Number
The triangular fuzzy numberhas the characteristics of certainty and uncertainty. The median of the triangular fuzzy number corresponds to the determined quantity of the connection number with $a=m$, the lengthof interval($\beta -\alpha $)inthe triangular fuzzy number corresponds to the uncertainty of the connection number with $b=\beta -\alpha $, andthen the triangular fuzzy number $L$ can be transformed into ($a+bi$) type connection number. The formula is shown as Equation (8).
$L=m+(\beta -\alpha )i=a+bi$
Equation (8) is called the conversion of transforming the triangular fuzzy number into the binary conversion number. $b=\beta -\alpha $ is called the difference degree of the connection number. The value range of $i$ is $[(\alpha -m)/(\beta -\alpha ),(\beta -m)/(\beta -\alpha )]$.The connection number can be used to indicate the probability of occurrence of the bottom event.
Once the probability of occurrence of the bottom event and the structure function of the top event are given, using the logic gate operator to calculate the probability of occurrence of the basic event, the failure probability of the top event is obtained. The calculation of the AND gate and OR gate represented by the connection number is shown in Equations(10) and (11), respectively.
The probability importance of the bottom event means that when only the $j$ event changes from the normal state to the failed state, therate change of the probability of occurrence of the top event is:
In Equation(12), $h(p)=h({{p}_{1}},{{p}_{2}},\cdots ,{{p}_{n}})$ is the top event fuzzy fault function and ${{p}_{j}}$ is the fuzzy probability of the ${{X}_{j}}$ bottom event. This paper uses the contact number to describe the probability of occurrence of the bottom event to analyze the importance of the fuzzy probability of the basic event.The built fuzzy fault tree is composed of only the OR gate; therefore, the formula is shown as Equations (13) to (15).
In the comparison of the connection number, $i$ is based on the “principle of ratio of $i$” [13]. The formula is shown as Equation (6).
$i=\frac{{{a}_{k}}}{{{a}_{k}}+{{b}_{k}}}$
Bringing the $i$ value into the top event with the connection number as the failure probability, we can calculate the top event failure probability value.Bringing the $i$ value into Equation (15), we can calculate the bottom event probability importance.Then, we can sort the risk of bottom event, find the key bottom event, and provide support for management decisions.
4. Case Study
4.1. Build the Fault Tree
This article takes a certain type of CNC machine tool spindle system as an example to verify the correctness of the proposed method.There is only one spindle in the headstock. Without the use of a transmission gear, only a set of triple V-belts is used to achieve stepless speed change through an AC continuously variable motor.The spindle drives the spindle encoder synchronously through a pair of pulleys and toothed belts.The tightness of the toothed belt is regulated by the screw.A hydraulic cylinder is mounted on the rear end of the spindle to control the clamping and release of the hydraulic chuck on the spindle.The main shaft system consists of a main shaft, bearings, spindle box, chuck, belt, and proximity switches.Through the analysis of fault records, the main faults of the spindle system are shown in Table 1.
The elements involved in the example system failure are ${{X}_{1}},\text{ }{{X}_{2}},\text{ }\cdots ,\text{ }{{X}_{15}}$,determined by designers, engineers, and maintenance staff to find the causality between the elements. The $(A+I)$ matrix is established as follows, and the reachable matrix M is calculated by using Equation(1).
Table 2 represents the row sum of each element in the reachable matrix M, and Table 3 shows the sort by row sum in ascending order.
The matrix is obtained by adjusting the rows and columns of the $M$ matrix. The relationship between the two elements can be transferred by other elements to delete the leapfrog binary relationship in the ${M}''$,and then the skeleton matrix ${M}''$ can be obtained.
In the skeleton matrix ${M}'',$ from the upper left corner to the lower right corner, a unit matrix decomposes the maximum order in turn. Elements in the same unit matrix belong to the same level. The remaining“1” indicates the causal relationship between the elements. According to the “1” element in the intersection of the two square boxes in ${M}'',$ draw an interpretative structural model that represents the causal relationship between elements at different levels in Figure 2.
The top event, the middle event, and the bottom event are all expressed in terms of elements when establishing the interpretive structure modeling. When the interpretative structure modeling is transformed into a fault tree, it transforms the elements into corresponding events according to the relationship between the levels, positions, and elements of the elements. The conversion rule states that only the elements pointed by the arrow are transformed into the top event, the elements not pointed by the arrow are transformed into bottom events, and the remaining elements are transformed into middle events. Translate the interpretive structure modeling into a fault tree as explained byFigure 2. The element ${{X}_{2}}$ is the top event denoted by T, the elements ${{X}_{1}},\text{ }{{X}_{6}},\text{ }{{X}_{7}},\text{ }{{X}_{10}},\text{ }{{X}_{9}},\text{ }{{X}_{12}},\text{ }{{X}_{14}},\text{ }{{X}_{8}},\text{ }{{X}_{15}}$, and ${{X}_{3}}$ are the bottom events, and ${{X}_{4}},\text{ }{{X}_{5}},\text{ }{{X}_{11}},\text{ }{{X}_{13}}$ are the middle eventsthat are represented by ${{M}_{1}},\text{ }{{M}_{2}},\text{ }{{M}_{3}}$,and${{M}_{4}}$. Logic gates between events are determined by designers, engineers, and maintenance personnel based on the actual situation. The fault tree is shown in Figure 3.
Once the fault tree is established, according to the logic gate operation rules, the minimum cut set can be found as:$\{{{X}_{1}}\},$$\{{{X}_{6}}\},$$\{{{X}_{7}}\},$$\{{{X}_{9}}\},$$\{{{X}_{10}}\},$$\{{{X}_{12}}\},$$\{{{X}_{15}}\},$$\{{{X}_{3}}\},$$\{{{X}_{14}}\},$$\{{{X}_{8}}\}.$.
4.2. Quantitative Calculation
The probabilities of each bottom event are estimated by the expert scoring method. The mean and variance of probability are calculated byEquations (2) and (3). The triangular fuzzy number of the bottom event probability is showninTable 4.
4.3. Calculation of Top and Bottom Event Failure Probability
The fuzzy failure probability of the top event is calculated by Equation (9), $LT=0.2537+0.0882i$, the exact failure probability of the top event is calculated by Equation (14), and the result is 0.3194. The probability importance of the bottom event is calculated by Equation (13) and shown in Table 6.The exact probability value of the base event is calculated by Equation (14) and shown in Table 7.Bottom event exact values aresorted, and the sort result is ${{X}_{10}},\text{ }{{X}_{15}},\text{ }{{X}_{9}},\text{ }{{X}_{8}},\text{ }{{X}_{12}},\text{ }{{X}_{6}},\text{ }{{X}_{3}},\text{ }{{X}_{1}},\text{ }{{X}_{7}},\text{ }{{X}_{14}}$.Find and control the major events of system failure.
In this paper, interpretive structure modelingcombined with a hierarchical structure digraph method was investigated to build a fault tree. This paper proved that triangular fuzzy numbers can also be converted into binary connection numbers. This not only simplifies the calculation process, but also explorea new way of triangular fuzzy numbers usage.In future works, the reliability based topology for the motor will be investigated and applied when the constant force is observed. The determination of the “i” value in the binary connection number will also be a focus of future research.
Acknowledgements
This work was partially supported by the National Natural Science Foundation of China (No. 71761030).
After analyzing the shortcomings of traditional FTA and FMECA used in mechanism products, thought of integrated FTA and FMECA was brought out, and a corresponding FTAMCA system was built up based on VB and ACCESS which have more practical analyzing functions comparing to traditional FTA and FMECA.
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“Fault Diagnosis for Clutch and Brake based on Expert System, ”
Journal of Beijing University of Aeronautics and Astronautics, Vol. 26, No. 6, pp. 663-665, December 2000
In order to improve the efficiency of fault diagnosis for clutch and brake and aiming at the characteristics of clutch and brake failure, an expert system structure was designed based on fault tree analysis and binary decision diagrams, and a fault diagnosis method for clutch and brake based on expert system was proposed. Firstly, the fault tree was established by analyzing the fault cause of the clutch and brake through fishbone diagram. Secondly, the fault tree was analyzed qualitatively by binary decision diagrams to obtain the knowledge of diagnostic experts, and the fault diagnosis knowledge base was established by production rules. Then, the fault tree was analyzed quantitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, and the problem of rule conflict was solved and the efficiency of fault diagnosis was improved. Finally, the prototype system of the fault diagnosis expert system of clutch and brake was developed. The results show the effectiveness and feasibility of the proposed method.
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“A FaultTree Auto-Modeling Method based on Avionics System Architecture Model, ”
Computer Engineering& Science, Vol. 39, No. 12, pp. 2269-2277, December 2017
Based on FMECA(failure mode effect and criticality analysis) generated in the design phase of product, through more in-depth, systematic study of the fault diagnosis model, a new algorithm is proposed that can automatically construct fault tree based on FMECA.Research on fault diagnosis knowledge generated by product design knowledge is very significant, which can relieve predicament caused by the lack of diagnosis knowledge.Compared with fault tree structured by hand, the method can acquire fault tree with complete diagnosis knowledge efficiently and exactly.
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“Fault Tree Generation based on Fault Configuration, ”
Computer Science, Vol. 44, No. 2, pp. 182-191, February 2017
Fault tree analysis is an effective method to improve system safety and reliability.However, traditional manual fault tree generation is difficult to solve the problem of large scale and complexity of system and error-prone.In order to systematically support system faults modeling and formal analysis, a fault tree generation method based on fault configuration was proposed in this paper by introducing variability management form software product line into system faults modeling.Firstly, we defined fault feature diagram for describing the constraints among faults and proposed fault labeled transition system based on Kripke structure to describe system behavior.Secondly, a model checking procedure of generating fault tree was established based on the model semantics.Finally, using model checker SNIP, the safety properties specified with temporal logic were verified and fault tree was generated based on the result.Case study shows the effectiveness of the proposed approach.
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Forging＆StampingTechnology, Vol. 42, No. 12, pp. 163-169, December 2017
In order to improve the efficiency of fault diagnosis for clutch and brake and aiming at the characteristics of clutch and brake failure, an expert system structure was designed based on fault tree analysis and binary decision diagrams, and a fault diagnosis method for clutch and brake based on expert system was proposed. Firstly, the fault tree was established by analyzing the fault cause of the clutch and brake through fishbone diagram. Secondly, the fault tree was analyzed qualitatively by binary decision diagrams to obtain the knowledge of diagnostic experts, and the fault diagnosis knowledge base was established by production rules. Then, the fault tree was analyzed quantitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, and the problem of rule conflict was solved and the efficiency of fault diagnosis was improved. Finally, the prototype system of the fault diagnosis expert system of clutch and brake was developed. The results show the effectiveness and feasibility of the proposed method.
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The purpose of this study is to make a comprehensive analysis of the underlying influential factors which may account for the railway loess-featured tunnel collapse and, in turn, to establish a model for identifying and forecasting the likely risks to take place in the construction practice of such railway tunnels. It is just for the aforementioned purpose that we have first of all managed to identify and determine the causes and mechanisms for such tunnel collapse and the principal risk-involving factors of the case study sample, that is, the loess tunnel in the LanzhouChongqing Railway. And, then, we have made detailed analyses for the mutual relations among the above said influential factors with an Interpretation Structure Model( ISM). In so doing, we have been trying to adopt an Interpretative Structural Chart for depicting the most closely linked influential factors that may lead to the likely collapses, such as the extremely strong construction shocks and disturbances; not timely providing badly-needed supports; too long the close-looped cycles; unreasonable stair-case elevations; unqualified construction labor force; inappropriate choice of the excavation methoad; the underground water drainage; unqualified or unsatisfactory geological engineering investigation and project inspection; inefficient or ineffective on-spot engineering monitoring and control; low-quality concrete or cement building, etc. Based on the above said analyses in combination with the application of the fuzzy mathematical theory and the Fault Tree Theory, we have developed a Fuzzy Fault Tree model, and made a series of quantitative and qualitative analyses of the actual necessary evaluation items in reference to the key fuzzy critical risk-involving factors of the sample project. The results of our investigation and analysis show that the risk probability of the above mentioned sampling project is quite high with the groundwater leakage likeliness, in addition to the inappropriate choice of excavation approaches and unreasonable stair-case lengths. And, finally, this paper has provided a new approach to managing the collapse risks in such tunnel construction projects both qualitatively and quantitatively. What is more, the Interpretation Structure Model we have built up helps to disclose the uncertainty of the cause-and-consequence relationship between the various risk factors, enabling the engineers of such lines on the spot to identify and determine all the influential factors that may account for the different sorts of likely collapse risks. Thus, what we have done in this paper can help to disclose the probability of risk events objectively and increase the reliability of the fault tree diagnosis.
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To scientifically reveal the inherent law of Controlled Flight Into Terrain(CFIT)inducement for preventing CFIT accident, the Interpretative Structural Model(ISM) is introduced to analyze the relationship of CFIT inducement.In the model, first the inducement of CFIT are linked according to the people's understanding, and then with the aid of matrix calculation and graphic analysis technology, the complicate and unordered CFIT inducement factors are analyzed and organized as the hierarchical structure model that is easy to understand.In the example, by analyzing the CFIT accidents, the main inducements of CFIT can be summarized, and based on it ISM is used to establish the inducement relationship analysis model.The result shows that the proposed model has the advantages such as simple steps, clear logic relations, scientific and reasonable process, objective hierarchical structure and so on, which provides an effective method for CFIT inducement relationship analysis.
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The ordering of basic events is critical to fault tree analysis on the basis of binary decision diagrams (BDDs). Many attempts have been made to seek an efficient ordering result with the aim of reducing the complexity of BDD. In this article, a new ordering method, namely, priority ordering method, is proposed. The new method takes into account not only the effects of the layers of fault tree but also the repeated events, the neighboring events, and the number of events under the same gate. According to these four effects, the priorities that sort the basic events of the fault tree are defined. The new method inherits the merits of structure-based and weight-based methods. It is able to evaluate the basic events on the basis of the structure-based method and the size of the subtree on the basis of the weighted-based method. Demonstrated by the examples, the proposed priority ordering method is superior to the existing ordering methods in terms of reducing the nodes in the BDD and improving the efficiency in transforming a fault tree to a BDD. Copyright 2011 John Wiley & Sons, Ltd.
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In order to solve the problem of fuzzy probability and uncertainty of basic event probability in the evaluation of Petrochemical device by accident tree analysis(FTA),this paper introduces the triangular fuzzy number theory to establish a quantitative analysis model of fuzzy fault tree.The paper applies the model to analyzing the hydrocracking unit, obtains the probability distribution of the fire and explosion accidents, and points out the range of probability fluctuations.Then the paper applies the fuzzy number median method to obtaining the fuzzy importance degree of each basic event, getting the events order, and obtaining the influence degree of each factor on the fire event of the top event.The paper also identifies the main causes of the accident and works out effective measures to fundamentally prevent the occurrence of top incidents from the critical point.It is important for the prevention of saftey accidents in petrochemical enterprises and for effective saftey management.
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According to the mechanism of the mine gas explosion accident occurred, a fault tree of the mine gas explosion was established, the gas explosion accident chain was analyzed and a fuzzy fault tree was applied to the analysis on the uncertainty of each danger source in the accident chain and the inconsistency of the importance during the accident occurred process. In the analysis on the calculation method of the fuzzy importance, a median method was applied to obtain the importance of the base accident. Finally the case analysis was applied to verify the feasibility and science of the fuzzy fault tree to the risk control of the mine gas explosion accident and to provide a new idea to the on- time accurate early warning of the mine gas explosion.
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“A Group Decision Making Method with Interval-Valued Triangular Fuzzy Attribute and Weight, ”
Fuzzy Systems and Mathematics, Vol. 31, No. 1, pp. 179-186, February 2017
Formation and diagnosis of turbine vibration fault usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty set-pair analysis connection mathematical theory in the set-pair analysis is used for fault diagnosis of turbine. First, calculate the distance between all kinds of fault diagnosis samples and the equipment fault knowledge base. List the orders of primary fault, secondary fault, and tertiary fault from small to big according to the Euclidean distances, and then analyze the influence of the uncertainty of the original data on the fault diagnosis. The conclusion of fault diagnosis is obtained. The application example shows, under the uncertainty of power equipment fault diagnosis process, by using the system uncertainty set-pair analysis connection number theory for fault diagnosis of turbine, the order of faults obtained is reasonable and practical. The physical meaning of the method presented is clear. The method is simple and practical, which can be used for fault diagnosis of other power equipment or systems, as well as the diagnosis of turbine vibration fault.
Y. L.Wang, “Systems Engineering, ”China Machine Press, Beijing, 2008
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“Mechanism ProductIntegrated Study of FTA and FMECA based on VB and ACCESS, ”
1
2009
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“Fault Diagnosis for Clutch and Brake based on Expert System, ”
1
2000
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“A FaultTree Auto-Modeling Method based on Avionics System Architecture Model, ”
1
2017
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“Research on Method of Fault Tree Created Automatically based on FMECA, ”
1
2009
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“Fault Tree Generation based on Fault Configuration, ”
1
2017
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“Fault Diagnosis for Clutch and Brake based on Expert System, ”
1
2017
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“Collapse Risk Analysis for the Loess-featured Tunnels in Railway Construction based on ISM and Fuzzy Fault Tree Method, ”
1
2017
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“Analysis on Influence Factors of Controlled Flight into Terrain of General Aviation based on ISM-CRITIC Method, ”
1
2018
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“Inducement Relationship Analysis of Controlled Flight into Terrain based on ISM Model, ”
1
2018
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“Fault Cause Analysis of Complex Manufacturing System based on DEMATEL-ISM, ”
1
2018
... Failure Mode Effect and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA) are both ways to express fault causality and retrieve fault information. Hu et al.explored the correlation of information between FMECA and FTA and combined the two methods. C # language and SQL database were utilized to develop computer-aided software[1]. Duet al.integrated FTA and FMECA methods, and a corresponding FTAMCA system was built up based on VB and ACCESS[2]. Tao et al. combined the disadvantages of FMECA and FTA, presented the automatic transform algebra between the FMECA and FTA of sub fault tree, and then established the computer aided dynamic fault tree method [3].Xuet al.proposed the fault tree automatic modeling method based on the avionics system architecture model. The safety analysis model was constructed by adding safety properties to the system design model and embedding an assertion mechanism of the advanced formal language Al-taRica to describe the fault transition process[4]. Yang systematically studied the fault diagnosis and analysis model based on the FMECA generated in the design phase of product, and a new method of automatic generation of fault tree analysis system based on FMECA was proposed. Compared with manual construction, this method can obtain the fault tree with complete diagnosis knowledge[5]. In order to systematically support system faults modeling and formal analysis, Huang et al.proposed a fault tree generation method based on fault configuration. [6]. Li et al.established the fault tree by analyzing the fault cause of the clutch and brake through fishbone diagrams. The fault tree was analyzed qualitatively by binary decision diagrams to calculate the importance of the minimum cut set and determine the rule priority, andthe problem of rule conflict was solved[7]. Guet al.used the interpretive structure model (ISM) to analyze the interrelation between the risk factors of the project, and the direct causes affecting the collapse of the tunnel project were obtained, and then the fault tree model was established[8]. In order to study the influence factors of controlled flight on terrain of general aviation, Sunet al.proposed the targeted prevention measure, and 30 controlled flight into terrain events were analyzed by using the element event analysis method. The paired comparison analysis of the influence factors was carried out using the interpretation structure(ISM)[9]. To scientifically reveal the inherent law of Controlled Flight into Terrain (CFIT) inducement for preventing CFIT accidents, Mei et al.used the Interpretative Structural Model to analyze the relationship of CFIT inducement[10]. In view of the complex fault mechanism of complex manufacturing systems, which is hierarchical, latent, causal, and fragile, Xia et al.put forward the DEMATEL-ISM, a quantitative analysis method for critical fault factors of the processing workshop [11]. ...
“A New Ordering Method of based Events in Fault Tree Analysis, ”
1
2012
... Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21]. ...
“Study on Method for Triangular Fuzzy NumberbasedMulti-attribute Decision Making with Preference Informationon Alternatives, ”
2
2002
... Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21]. ...
... In the comparison of the connection number, $i$ is based on the “principle of ratio of $i$” [13]. The formula is shown as Equation (6). ...
“Fuzzy Comprehensive Assessment of Power Enterprise R＆D Risk based on Triangular Fuzzy Number, ”
1
2017
... Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21]. ...
“Analysis and Application of Fire and Explosion Fault Tree in Hydrocracking Unit based on Triangular FuzzyNumber, ”
1
2017
... Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21]. ...
“Analysis on Danger Sources of Mine Gas Explosion based on Fuzzy Fault Tree, ”
1
2014
... Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21]. ...
“A Group Decision Making Method with Interval-Valued Triangular Fuzzy Attribute and Weight, ”
1
2017
... Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21]. ...
“New Multiple Attribute Decision-Making Model with Triangular Fuzzy Numbers based on Connection Numbers, ”
2
2009
... Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21]. ...
... SPA (set pair analysis) was put forward by Zhao in 1989 [18].SPA is a new theory of uncertainty. The core idea of SPA is to analyze the deterministic and uncertainty measures of objective things as a system, dealing with mixed uncertainty problems caused by fuzzy, random, unascertained, and mediating. The connection number is the main mathematical tool in the SPA. As a kind of connection number, the binary connection number is defined as follows: ...
“Triangular Fuzzy Number Multi-Attribute Decision-Making with the Attribute Weight Unknown based on Connection Number, ”
1
2017
... Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21]. ...
“Interval Number Multiple-Attribute Decision-Making based on Adjoint Functions of Connection Number, ”
1
2018
... Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21]. ...
“Fault Diagnosis of Turbine based on Multiple Dual Connection Number, ”
1
2016
... Huang et al.put forward a method of bottom event sorting based on BDD. In addition to considering the influence of the number of layers of events in the fault tree on sorting, the method also takes into account the factors such as repeated events, adjacent events, and the number of events contained in logic gates. The above four indicators jointly determine the priority of bottom event sequencing[12].Xuet al.and Li et al.thought that triangular fuzzy numbers are also commonly used mathematical tools in solving decision problems. Based on the possible degree formulas of the comparison of the triangular fuzzy numbers and the ranking formulas of the complementary judgment matrix, the decision plans are ranked and selected[13-14].Zhao et al.and Li et al.used the fuzzy number median method to obtain the fuzzy importance degree and order of each basic event [15-16].By utilizing the theories of set pair analysis and statistical, the interval fuzzy number is transformed into connection number in the form of “the mean and variance”, which retains the certainty and uncertainty in interval triangular fuzzy decision-making information[17]. By using the uncertainty systems theory in the set pair analysis, the median, and the interval of values prescribed by the upper andlower bounds of triangular fuzzy numbers, the triangular fuzzy numbersare transformed into connection numbers, and then the decision model is given. The attribute values with the triangular fuzzy number are converted into connection numbers with the form of “average+deviation”, andthe sort of uncertainty is analyzed by using the “i” different values of connection numbers [18-19].Lu et al.used the connection number in multi-attribute decision-making and proposed a new method of the “i” value. [20]. Formation and diagnosis ofturbine vibration usually is affected by many uncertain factors. Based on the uncertainty of power equipment fault diagnosis process, the uncertainty analysis connection mathematical theory was used for fault diagnosis of turbines by Zhao [21]. ...
1
2008
... The ISM is a determining technology of the whole structure of the system based on various creative techniques. By exploring the elements of the system and defining the significance of the correlation between the elements, the concrete relationship between the elements based on the binary relation is given. Moreover, the structure model of a complex system is established by digraph and matrix, which are easy to understand and easy to deal with. The technology of interpretive structure modeling was developed by Warfield in 1973 to analyze complex socio-economic problems [22]. The flow chart of the fault tree is set up by using ISM, as shown in Figure 1.The modeling steps are as follows. ...
