Design Software Failure Mode and Effect Analysis using Fuzzy TOPSIS Based on Fuzzy Entropy
الموضوعات :
shahrzad Oveisi
1
,
Mohammad Nadjafi
2
,
Mohammad Ali Farsi
3
,
Ali moeini
4
,
Mahmood Shabankhah
5
1 - Department of Algorithms and Computation, College of Engineering Sciences, University of Tehran, Tehran, Iran
2 - Aerospace Research Institute (Ministry of Science, Research and Technology), Tehran, P.O.B. 14665-834, Iran
3 - Aerospace Research Institute (Ministry of Science, Research and Technology), Tehran, P.O.B. 14665-834, Iran
4 - Department of Algorithms and Computation, College of Engineering Sciences, University of Tehran, Tehran, Iran
5 - Department of Algorithms and Computation, College of Engineering Sciences, University of Tehran, Tehran, Iran
الکلمات المفتاحية: Risk Assessment, Fuzzy TOPSIS, Software FMEA, Requirement analysis, Fuzzy Entropy, Expert Opinion,
ملخص المقالة :
One of the key pillars of any operating system is its proper software performance. Software failure can have dangerous effects and consequences and can lead to adverse and undesirable events in the design or use phases. The goal of this study is to identify and evaluate the most significant software risks based on the FMEA indices with respect to reduce the risk level by means of experts’ opinions. To this end, TOPSIS as one of the most applicable methods of prioritizing and ordering the significance of events has been used. Since uncertainty in the data is inevitable, the entropy principle has been applied with the help of fuzzy theory to overcome this problem to weigh the specified indices.The applicability and effectiveness of the proposed approach is validated through a real case study risk analysis of an Air/Space software system. The results show that the proposed approach is valid and can provide valuable and effective information in assisting risk management decision making of our software system that is in the early stages of software life cycle. After obtaining the events and assessing their risk using the existing method, finally, suggestions are given to reduce the risk of the event with a higher risk rating.
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Design Software Failure Mode and Effect Analysis using Fuzzy TOPSIS Based on Fuzzy Entropy
Sh. Oveisi2,2*, M. Nadjafi1, M.A. Farsi1, A. Moeini2
1Aerospace Research Institute (Ministry of Science, Research and Technology), Tehran, P.O.B. 14665-834, Iran
2Department of Algorithms and Computation, College of Engineering Sciences, University of Tehran, Tehran, Iran
Abstract— One of the key pillars of any operating system is its proper software performance. Software failure can have dangerous effects and consequences and can lead to adverse and undesirable events in the design or use phases. The goal of this study is to identify and evaluate the most significant software risks based on the FMEA indices with respect to reduce the risk level by means of experts’ opinions. To this end, TOPSIS as one of the most applicable methods of prioritizing and ordering the significance of events has been used. Since uncertainty in the data is inevitable, the entropy principle has been applied with the help of fuzzy theory to overcome this problem to weigh the specified indices.The applicability and effectiveness of the proposed approach is validated through a real case study risk analysis of an Air/Space software system. The results show that the proposed approach is valid and can provide valuable and effective information in assisting risk management decision makingof our software system that is in the early stages of software life cycle. After obtaining the events and assessing their risk using the existing method, finally, suggestions are given to reduce the risk of the event with a higher risk rating.
Index Terms—Expert Opinion; Fuzzy TOPSIS;Fuzzy Entropy; Risk Assessment;Software FMEA.
I. Introduction
Design and produce a reliable and safe system is one of the essential characters in the aerospace industry and other
advanced systems[1]. System engineers define reliability and safety requirements to achieve a system at a world-class level[2]. This system should work in various conditions and keeps its performance at an acceptable level. With the ever-increased high requirement of reliability and safety for critical and essential systems, accurately assessing the pending failure of a system has become an active research area over the past decades. Several techniques and tools have been developed to achieve a reliable system[3]. Some techniques focus on design steps; some work on manufacturing, and many tools have been developed for maintenance management. A few techniques have been emerged to handle the system life cycle.
FMEA is a technique that can be used throughout the software life cycle is FMEA. Failure mode and effects analysis (FMEA) is an accessible and useful approach applied to Identify potential failure modes of system components means determining the causes of their impact assessment on system performance and eventually specifying the approaches reducing the chances of occurrence and outcomes as well as increasing the ability to detect failure modes[4, 5]. The FMEA widely used early in the design process of products is usually known as the Design- FMEA (DFMEA), which is implemented by using various approaches. Design-FMEA can help the designers to know the effects of the failure mode of product reliability and to determine the priority of design improvement [6].
FMEA is a risk assessment methodology that is not evaluated solely based on personal opinion. Therefore, it is difficult to extract the actual value of each of the risk factors according to group opinion [7]. To overcome the above limitations, various evaluation methods are used, including prioritization based on similarity to ideal solution (TOPSIS), analytic hierarchy process (AHP), data envelopment analysis (DEA), decision making trial and evaluation laboratory (DEMATEL), and hybrid methods.
FMEA applies the Risk Priority Number (RPN) to calculate the risk of different system failure modes. RPN is the multiplication product of three risk factors: occurrence probability (O), the severity of outcome (S), and detection capability (D). Evidently, the higher the RPN value, the higher the risk associated with relevant failure mode. Despite its widespread use, the FMEA method has significant flaws that restrict the use of this technique, mainly when it is used for criticality in the calculation of RPNs. Traditional FMEA restrictions can be summarized as follows:
The relative importance of S, O, and D parameters is not considered in RPN calculation, and they are assumed to have equal weights. However, this can cause limitations in real applications. While the nature of developed risks is different, combining different risk factors can lead to the same RPNs.Correct determination of risk factors (D, O, S) is often a problem. FMEA team members may have different assessments for similar risk factors, some of which could be inaccurate, insecure, and incomplete and be caused by time constraints, lack of experience, and inadequate data. The RPN calculation formula is uncertain and lacks a strong scientific foundation. In other words, there is no particular logic explaining the multiplication of O, S, and D for calculating RPN. S, D, and O risk factors are evaluated based on hybrid discrete scales. This is while using multiplication operations for sequential scales is meaningless. Therefore, the results are not only meaningless but also misleading [8].
This article provides a way to assess software risk in the early stages of software development (the conceptual phase and requirements analysis phase). For this purpose, The paper presents a multi-factor decision-making approach for prioritizing failure modes as an alternative to the traditional approach of failure mode and effect analysis (FMEA) [9]. The fuzzy approach based on the technique for order performance by similarity to ideal solution (TOPSIS) to choose an optimal information system in a fuzzy environment where the data are often incomplete or not so deterministic. The priority ranking is formulated based on six parameters (failure occurrence, non-detection, maintainability, spare parts, economical safety, and economic cost). The Shannon's entropy concept has been used for assigning actual weights to maintenance parameters [10-14].
To evaluate the proposed method, it was applied to the Launch Abort System (LAS). A space vehicle LAS with functional dependencies among the elements. This system consists of two main subsystems which include the Emergency Detection System (EDS) as a module of the air/space vehicle system and the Launch Escape System (LES). EDS is used for detecting the abnormal and emergency conditions in a flying vehicle that designed to treat mechanical and electrical failures in each of the propulsion, electrical, and a control portion.
In this paper, after identifying the software failure modes using DFMEA and system hierarchy, the risk priority Number (RPN) of these scenarios was calculated by Fuzzy TOPSIS based Fuzzy Entropy.The rest of this paper is organized as follows. After the introduction, research background is presented in section 2, the proposed approach in the part 3 is explained in detail and step by step. In section 4, the proposed fuzzy approach, which includes fuzzy RPN, fuzzy entropy, and the TOPSIS fuzzy method, is examined in detail. In the section 5, the proposed method is applied step by step on a real case study of the air/space system and the results are shown. Finally, the conclusion is made in the section 6.
II. Research Background
FMEA goes back to the late 1940s. A US military manual entitled ‘Procedure for performing a failure mode, effects, and analysis’ was first published in 1949. Then, it was adopted by NASA, especially during the Apollo mission project in the early 1960s. In 1974, the US DoD (Department of Defense) extensively promoted the use of FMEA and formalized the technique under the MIL-STD 1629. After that, the Ford Motor Company promoted the use of FMEA in 1977 [15].
In the past years, various methods have been used to handle the uncertainty of assessment information given by FMEA team members. For example, Ilangkumaran et al. An FMEA framework for group evaluation have been developed using fuzzy analytic hierarchy process (AHP) to assess the risk of recovering a boiler in a paper- manufacturing unit [10, 16, 17]. Liu et al. presented a fuzzy risk assessment model for deciding the risk orders of failure modes using the VIKOR method to address some of the traditional FMEA flaws[18]. Liu et al. use a hybrid risk assessment model that takes advantage of a mean weighted fuzzy DEMETEL to prioritize failure modes [19, 20].
Liu et al. developed a comprehensive, prioritized risk approach using fuzzy Mooltimorato decide how to rank the risk scenarios [19]. On the other hand, Braglia et al. suggested a new rational model based on fuzzy TOPSIS to offer correct prioritization of detected failure modes [21].
Kai et al. [6] proposed a perceptual computing model based on interval type-2 fuzzy group decision-making for FMEA. Wang et al. [23] proposed a hybrid interval-valued intuitionistic fuzzy (IVIF) MCDM approach that combines COPRAS (Complex Proportional Assessment) and ANP for FMEA.
EA. Zhao et al. [26] developed an integrated method based on IVIF continuous weighted entropy and IVIF MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full multiplicative) for FMEA. Moreover, Liu et al. [24] combined the IVIF MABAC (Multi Attributive Border Approximation area Comparison) and mathematical programming model to derive the risk priorities of failure modes with incomplete weight information of risk factors. Huang et al.[5]proposed a novel FMEA model based on linguistic distribution assessments and TODIM (an acronym in Portuguese of interactive and MCDM), in which a combination structure was established to consider the subjective and objective weights of risk factors. Tian et al.[29]developed a comprehensive fuzzy MCDM approach for FMEA by combining fuzzy best-worst method (BWM) and relative entropy (RE) to formulate a feasible and effective risk priority ranking of failure modes. Fattahi and Khalilzadeh[30] proposed a novel fuzzy hybrid method based on fuzzy FMEA, extended fuzzy MULTIMOORA, and fuzzy AHP methods, the weights of the three factors and the weight of each failure mode are computed by the extended fuzzy AHP and fuzzy MULTIMOORA methods, respectively. Deng and Jiang[31]studied the fuzzy risk evaluation in FMEA from a perspective of multi-sensor information fusion. By considering the non-exclusiveness between the evaluations of fuzzy linguistic variables to failure modes, a novel model called D numbers is used to model the non-exclusive fuzzy evaluations. A D numbers based multi-sensor information fusion method is proposed to establish a new model for fuzzy risk evaluation in FMEA.Selim et al[32]developed a fuzzy TOPSIS and FMEA-based dynamic maintenance planning framework. Barukab et al[33]described a novel enhanced TOPSIS-based procedure for tackling multi attribute group decision making (MAGDM) issues under spherical fuzzy setting, in which the weights of both decision-makers (DMs) and criteria are totally unknown.Mangeli et al. [34] utilized a hybrid approach based on support vector machine and fuzzy inference system to decrease the effect of personal's opinions in determining the factors of the severity and occurrence. In Table1, contributions of this papers, are reviewed.
Based on the above literature review, the current methods for dealing with risk assessment information in FMEA can be mainly classified into three types, i.e., the methods based on membership functions, the linguistic, symbolic methods based on ordinal scales, and those based on linguistic 2-tuples. However, the membership function method can describe fuzziness but not randomness; the latter two methods cannot produce a clear description of either fuzziness or randomness of qualitative information. Moreover, in these articles, the vacancy of software risk assessment is felt using these decision-making methods. For this reason, this article examines this topic.
Table 1
Review of related works
Authors | Contributions |
Kai et al. | A perceptual computing model based on interval type-2 fuzzy group decision-making for FMEA. |
Wang et al. | A hybrid interval-valued intuitionistic fuzzy (IVIF) MCDM approach that combines COPRAS (Complex Proportional Assessment) and ANP for FMEA. |
EA. Zhao et al. | Developing an integrated method based on IVIF continuous weighted entropy and IVIF MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full multiplicative) for FMEA. |
Moreover, Liu et al. | Combining the IVIF MABAC (Multi Attributive Border Approximation area Comparison) and mathematical programming model to derive the risk priorities of failure modes with incomplete weight information of risk factors. |
Huang et al. | Proposing a novel FMEA model based on linguistic distribution assessments and TODIM (an acronym in Portuguese of interactive and MCDM), in which a combination structure was established to consider the subjective and objective weights of risk factors. |
Tian et al. | developing a comprehensive fuzzy MCDM approach for FMEA by combining fuzzy best-worst method (BWM) and relative entropy (RE) to formulate a feasible and effective risk priority ranking of failure modes. |
Fattahi and Khalilzadeh | proposinga novel fuzzy hybrid method based on fuzzy FMEA, extended fuzzy MULTIMOORA, and fuzzy AHP methods, the weights of the three factors and the weight of each failure mode are computed by the extended fuzzy AHP and fuzzy MULTIMOORA methods, respectively. |
Deng and Jiang | The fuzzy risk evaluation in FMEA from a perspective of multi-sensor information fusion. By considering the non-exclusiveness between the evaluations of fuzzy linguistic variables to failure modes, a novel model called D numbers is used to model the non-exclusive fuzzy evaluations. A D numbers based multi-sensor information fusion method is proposed to establish a new model for fuzzy risk evaluation in FMEA. |
Selim et al. | A fuzzy TOPSIS and FMEA-based dynamic maintenance planning framework. |
Barukab et al. | A novel enhanced TOPSIS-based procedure for tackling multi attribute group decision making (MAGDM) issues under spherical fuzzy setting, in which the weights of both decision-makers (DMs) and criteria are totally unknown. |
Mangeli et al. | Utilizing a hybrid approach based on support vector machine and fuzzy inference system to decrease the effect of personal's opinions in determining the factors of the severity and occurrence. |
Ilangkumaran et al. | An FMEA framework for group evaluation have been developed using fuzzy analytic hierarchy process (AHP) to assess the risk of recovering a boiler in a paper- manufacturing unit |
Liu et al. | A fuzzy risk assessment model for deciding the risk orders of failure modes using the VIKOR method to address some of the traditional FMEA flaws |
Liu et al. | using a hybrid risk assessment model that takes advantage of a mean weighted fuzzy DEMETEL to prioritize failure modes |
Liu et al. | developing a comprehensive, prioritized risk approach using fuzzy Mooltimorato decide how to rank the risk scenarios |
Braglia et al. | A new rational model based on fuzzy TOPSIS to offer correct prioritization of detected failure modes |
III. Based on Proposed Approach
The present study is concerned with software risks in a space vehicle Launch Abort System (LAS). Design FMEA has been used to identify failures that may occur in this system through software.Afterward, to perform TOPSISand develop the decision matrix, the indicators used in the FMEA method were ranked by experts, and the decision matrix was presented based on them for identified risks. The entropy method was used to weigh indicators in this research. Finally, after performing the TOPSIS steps, the risks were prioritized, and the most important and most effective ones were identified. The workflow is shown in Fig. 1.
DFMEA is a methodical approach used for identifying potential risks introduced in a new or changed design of a product/service. The Design FMEA initially identifies design functions, failure modes, and their effects with corresponding severity ranking/danger of the effect. Then, causes and their mechanisms of the failure mode are identified.
Fig. 1 Proposed Fuzzy TOPSIS-Entropy Workflow
1. Software Design FMEA
High probability causes, indicated by the occurrence ranking, may drive action to prevent or reduce the cause’s impact on the failure mode.The detection ranking highlights the ability of specific tests to confirm the failure mode/causes are eliminated. The DFMEA also tracks improvements through Risk Priority Number (RPN) reductions. By comparing the before and after RPN, a history of improvement and risk mitigation can be chronicled [22]. SFMEA Design and SFMEA procedures are shown in Fig. 2 and Fig. 3.
2. FMEA Block Diagram
An FMEA Block Diagram is a graphical representation of the whole system or design that represents the limits of FMEA analysis. User interfaces between items and other information can help display the FMEA domain. FMEA Block Diagram identifies a representation of relationships and dependencies between components, including physical connection, material exchange, energy transfer, and data exchange.In systemic FMEA mode, FMEA Block Diagram should clearly show the interfaces between the system and users among various subsystems. For a sub-system FMEA, the FMEA Block Diagram should indicate the interfaces between several components [23].
3. FMEA Interface Matrix
FMEA Interface Matrix is a table representing subsystems or components on both dimensions of the graph. The table shows that user interfaces should be assessed in terms of interface type and analysis. There are four types of user interfaces: physical communication, material exchange, energy transfer, and data exchange. When failures comprise 50% or more of failure scenarios, it is imperative that each FMEA accurately examines the user interfaces between subsystems and components [6].
Fig. 2 Design SFMEA Overview
Fig. 3 SFMEA Process
4. Gathering Information of FMEA
Gathering all the documentation and event information is one of the essential steps in preparing FMEA. If this step is not appropriately performed, FMEA encounters a series of duties related to a lack of information and will cause a loss of time. Severalessential measures taken at this step are as follows: Bill of material (BOM), Legal and regulatory, Past FMEA, Field history, etc. BOM is known as the system history, which should be available to the FMEA team. Legal and regulatory cases related to all applicable laws as well as issues and documentation, should be accessible to the FMEA team. Field history also involves an attempt to prevent past failures [6].
5. Risk Priority Number (RPN)
RPN calculation is required after identifying failure modes in a system and the need for their prioritization. RPN is a risk assessment method in FMEA. In this method, three factors of Occurrence (O), Severity (S), and Detection (D) are used, the product of which is equal to RPN given the independence of these factors. These three factors are traditionally divided into ten levels, which are detailed in some works, such as [24]. In this regard, the RPN value can be evaluated as:
| (1) |
IV. Proposed Fuzzy Approach
In order to express the fuzzy representation of the proposed method, the following subsections have been prepared.
1. Fuzzy RPN
Failure Mode and Effects Analysis (FMEA) is an analysis method of potential failure in products or processes, which is used in many quality management systems. FMEA is a crucial issue in determining the risk priorities of failure scenarios. In the classical FMEA method, the risk priorities of failure modes are determined by risk priority numbers (RPNs) through multiplying risk factors such as severity (S), occurrence (O), and theprobability of detection (D). However, definite RPNs have been criticized by many scholars and experts because of their shortcomings and disadvantages, so that significant efforts have been made in FMEA literature to address these shortcomings [20, 25].In this paper, we used FMEA,which is a powerful tool for risk evaluation. In traditional FMEA, risk priority number (RPN), has been calculated by multiplication of three criteria, theseverities of the traditional FMEA, in this paper, instead of calculating RPN-prioritizes risk factors with fuzzy TOPSIS.
2. Fuzzy Entropy
Shannon entropy is a measure of uncertainty in information formulated in terms of probability theory. It is well suited for measuring the relative contrast intensities of criteria to represent the average intrinsic information transmitted to the decision-maker. Therefore, this concept has been highlighted by many researchers for deciding the actual weights of criteria [20].In this study, the weight of criteria was determined based on Shannon entropy method following formulas (2) and (3):
Ej = - | (2) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| (3) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
dj=1-E | (4) |
Finally, the weights of indices were calculated using Eq. (5).
| (5) |
In this research, the weights of criteria were calculated based on the Shannon entropy method.
3. Fuzzy TOPSIS Method
TOPSIS is one of the developed classic multi-criteria decision-making methods[26, 27]. It is based on the concept that the chosen alternative should have the shortest distance from the positive ideal solution (PIS) and the farthest from the negative ideal solution (NIS). In the traditional formulation of the TOPSIS method, personal judges are represented with crisp values. Nevertheless, in reality,it is not always possible. A real lift Measurement by using crisp values is not always possible. A better approach may be to use linguistic value rather than a crisp value. Fuzzy Set theory can be used to present linguistic values for this reason; the fuzzy TOPSIS method is very suitable for salving real-life application problems under a fuzzy environment [10].
Step 1: Choose the linguistic rating values for the alternative concerning criteria.
Let us assume there are m possible alternatives called A= {
} which are to be evaluated against the criteria, C= {
) the criteria weights are denoted by 
(j=1,2….. n). The performance ratings of each expert 
(k = 1.2...K) for each alternative 
(i = 1, 2... m) concerning criteria,Cj(j= 1.2.... n) is denoted by
membership function µ
The scale used for solutions rating is given inTable 2.
Table 2
Linguistic variables for solutions ratings
Linguistic variables | Corresponding TFN |
Very poor Poor Medium Good Very good | (1,1,3) (1,3,5) (3, 5,7) (5,7,9) (7,9,11) |
Step2: Calculate fuzzy aggregate ratings for the alternatives
If the fuzzy ratings of all experts are described as TFN 
then the aggregated fuzzy rating is given by 
k where
a= | (6) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| (7) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| (8) |
Step 4: Construct the Normalize fuzzy decision matrix
The raw data are normalized using linear scale transformation to bring the various criteria scales into a comparable scale. The normalized fuzzy decision matrix 
is given by:
| (9) |
Where
| (10) | ||||||||||||||
| (11) |
Where, 
. Note that 
represented by 
Step 6: Determine the fuzzy ideal solution (FPIS) and fuzzy negative ideal solution (FNIS)
The FPIS and FNIS of the alternatives are computed as follow:
| (12) | ||||||||||||||
| (13) | ||||||||||||||
| (14) | ||||||||||||||
| (15) | ||||||||||||||
| (16) |
Step 9: Rank the alternatives
In step 9, the different alternatives are ranked according to the closeness coefficient (CCi) in decreasing order.
V. Implementation on Air/Space Application Example
We applied the results of our approach to a part of a real CPS known as Launch Abort System (LAS), the architecture of which is shown in Fig. 4. As shown, the tree construction of a space vehicle Launch Abort System (LAS) with functional dependencies among the elements. This system consists of two main subsystems which include the Emergency Detection System (EDS) as a module of the air/space vehicle system and the Launch Escape System (LES). EDS is used for detecting the abnormal and emergency conditions in flying vehicle that designed to treat mechanical and electrical failures in each of the propulsion, electrical and control portion. While the EDS system detects an unusual and faulty condition in one of the main parts of the LES system (i.e., electrical power failure, structural failure, guidance, and control faulty, etc.), it sensed and transmitted through a signal to trigger the FDEP gate of LES system. Generally, the launch escape system consists of: launch escape motor, pitch control motor, tower jettison motor, landing parachute, and the Master Event Sequencing Controller Subsystems(MESC). According to the launch and flight regimes and based on the flight altitude, the operation time of each motor-based subsystem is varied. A master event sequence controller on LES is an intelligent standalone microprocessor-based system, which monitors external inputs and controls the time and sequence of the event’s changes. MESCs are therefore utilized as a prioritizing tool to dictate the occurrence events. Fig. 5is a demonstration of system hierarchy for the all-terrain LAS (showing three of the subsystems down to components). Accordingly, Fig. 6is the example of system FMEA Block Diagrams from the all-space launch abort system FMEAs. In this kind of system FMEA demonstration, there are missing elements to the FMEA Block Diagram at the system level in comparison with the system hierarchy components. As shown, the system parts or subsystems can take various forms of interface. In the LAS system, there are four primary types of interfaces: a mechanical connection, a data exchange, energy transfer, and material exchange. Since the interface scan contains up to 50% or more of the total failure modes, it is essential that any FMEA carefully consider the interfaces between subsystems and components in addition to the content of the subsystems and components themselves. The interface matrix of the launch abort system FMEA block diagram based on the extracted system FMEA block diagram in Fig. 5 is tabulated.
After displaying the system hierarchy, the system FMEA block diagram, the LAS Interface Matrix, which was used to obtain Software DFMEA. Based on the type of connections between the elements of the system, we see the failure of our data study case study, which was obtained as a result of the FMEA design analysis(Table3).
Fig. 4 Tree construction with the dependency of LAS
Fig. 5Demonstration of system hierarchy for Launch Abort System
Fig. 6System FMEA block diagram all-space of LAS
The linguistic variables which are assigned for severity, occurrence,and detection by experts should be converted to a fuzzy format. Also, the weights of the criteria should change to the fuzzy format. The resulting fuzzy numbers act as data for entering the fuzzy TOPSIS technique.
Table 3
Failures of data exchange (software) inthe Launch Abort System
Event | Event name | |
Failure in sending data from the sensor to the processing unit | X1 | |
Failure in receiving data from the processing unit to sensor | X2 | |
Failure in sending data from the detector to processing unit | X3 | |
Failure in receiving data from processing unit to detector | X4 | |
Failure in sending data from Indication to processing unit | X5 | |
Failure in receiving data from processing unit to indication | X6 | |
Failure in sending data from parachute to processing unit | X7 | |
Failure in receiving data from processing unit to parachute | X8 | |
Failure in sending data from valve to processing unit | X9 | |
Failure in receiving data from processing unit to valve | X10 | |
Failure in sending data from management to processing unit | X11 | |
Failure in receiving data from processing to management unit | X12 | |
Failure in receiving data from the detector | X13 | |
Failure in receiving data from Airspace (sensor) | X14 | |
Failure in sending data from processing unit to Igniter | X15 | |
Failure in receiving data from Igniter to processing unit | X16 | |
Experts used ten-scale linguistic variables for evaluating the risk factors and their relative importance significances. They chose one linguistic variable based on their experience and insight; then, linguistic variables were converted into fuzzy triangular numbers, which are shown in Table 4.
According to the Table 4, linguistic terms converted and aggregated to the triangular fuzzy number and the decision matrix (Based on the evaluations of five FMEA team members about the importance of fuzzy aggregate ratings of 16 risk Factors)was constructed as Table 5. To obtain the weights of Occurrence, Severity, and Detection criteria, the entropy method described previously, and the results are presented in the following tables.
Table 4
Relation between linguistic variables and fuzzy triangular numbers
Linguistic variables | Triangular fuzzy numbers | |
Nearly impossible | NI | (0,0,1) |
Remote | R | (0,1,2) |
Low | L | (1,2,3) |
Relatively low | RL | (2,3,4) |
Moderate | M | (3,4,5) |
Moderate high | MH | (4,5,6) |
High | H | (5,6,7) |
Major | MJ | (6,7,8) |
Very high | VH | (7,8,9) |
Extremely high | EH | (8,9,10) |
Table 5
Assessment information on four risk factor in three criteria by five experts
Risk factor | Occurrence | Severity | Detection |
X1 | (1.4 2.4 3.4) | (6 7 8) | (7 8 9) |
X2 | (1.2 2.2 3.2) | (5.4 6.4 7.4) | (3.4 4.4 5.4) |
X3 | (1.6 2.6 3.6) | (5.8 6.8 7.8) | (3.4 4.4 5.4) |
X4 | (0.4 1.2 2.2) | (5 6 7) | (2.6 3.6 4.6) |
X5 | (2.6 3.6 4.6) | (3.2 4.2 5.2) | (5.8 6.8 7.8) |
X6 | (0.6 1.6 2.6) | (5.6 6.6 7.6) | (6.4 7.4 8.4) |
X7 | (1.8 2.8 3.8) | (6.6 7.6 8.6) | (3 4 5) |
X8 | (0.6 1.6 2.6) | (5.8 6.8 7.8) | (6.8 7.8 8.8) |
X9 | (1.4 2.4 3.4) | (5.46.47.4) | (7 8 9) |
X10 | (2.6 3.6 4.6) | (4 5 6) | (5 6 7) |
X11 | (1.6 2.6 3.6) | (4.6 5.6 6.6) | (5.2 6.2 7.2) |
X12 | (0.8 1.8 2.8) | (4.2 5.2 6.2) | (4.2 5.2 6.2) |
X13 | (3.6 4.6 5.6) | (5.4 6.4 7.4) | (3.6 4.6 5.6) |
X14 | (1.2 2.2 3.2) | (4.8 5.8 6.8) | (7 8 9) |
X15 | (0.6 1.6 2.6) | (3.8 4.8 5.8) | (4.2 5.2 6.2) |
X16 | (1.8 2.8 3.8) | (5.4 6.4 7.4) | (3 4 5) |
Weights of Occurrence, Severity, and Detection were calculated using entropy, which is presented in Table 6.
Table 6
Weights of the Criteria
Fuzzy weights | Criteria |
(0.397, 0.397, 0.397) | Occurrence |
(0.33, 0.33, 0.33) | Severity |
(0.253, 0.253, 0.253) | Detection |
TOPSIS fuzzy based on the Expert’s values was performed, as shown in Tables 7-10, and the rankings are presented in Table 10.
.
[2] *Corresponding author
Table 7
Normalized fuzzy decision matrix
Criterion | |||||||||||||||
Risk factor | Expert#1 | Expert#2 | Expert#3 | Expert#4 | Expert#5 | ||||||||||
| Occur. | Severity | Detect | Occur. | Severity | Detect | Occur. | Severity | Detect | Occur. | Severity | Detect | Occur. | Severity | Detect |
X1 | RL | H | VH | RL | MJ | VH | L | MJ | VH | L | EH | VH | L | H | VH |
X2 | R | H | MH | L | MJ | M | RL | H | MH | L | H | MH | R | MJ | RL |
X3 | L | EH | VH | RL | H | MJ | RL | H | H | L | MJ | MH | RL | H | VH |
X4 | R | H | RL | L | MJ | MH | L | H | RL | NI | H | M | R | MH | RL |
X5 | M | M | MJ | RL | MH | VH | M | M | H | RL | M | MJ | M | M | H |
X6 | R | H | MJ | L | H | MJ | R | MJ | MJ | L | MJ | VH | L | MJ | VH |
X7 | M | VH | M | L | MJ | M | RL | VH | M | RL | MJ | M | L | VH | M |
X8 | R | H | VH | R | MJ | VH | L | VH | MJ | L | MJ | VH | L | H | VH |
X9 | L | H | VH | L | EH | VH | L | M | VH | RL | M | VH | RL | H | VH |
X10 X11 X12 X13 X14 | RL RL R H L | H H M H H | VH VH RL M VH | L L RL M RL | L M H VH M | H MH MH MH VH | VH RL L MH L | L H H H H | M H MH MH VH | RL RL L M L | H H M M EH | M M MH M VH | L L R M L | EH H H VH M | VH VH RL MH VH |
X15 | L | M | MH | L | H | M | R | H | MH | L | M | VH | R | M | M |
X16 | M | VH | M | L | VH | M | RL | M | M | RL | VH | M | L | M | M |
Table 8
Weighted normalized fuzzy decision matrix
Risk factor | Occurrence | Occurrence | Occurrence | Severity | Severity | Severity | Detection | Detection | Detection |
X1 | 0.046706 | 0.066167 | 0.113429 | 0.132 | 0.150857 | 0.176 | 0.073089 | 0.082225 | 0.093971 |
X2 | 0.049625 | 0.072182 | 0.132333 | 0.142703 | 0.165 | 0.195556 | 0.121815 | 0.1495 | 0.193471 |
X3 | 0.044111 | 0.061077 | 0.09925 | 0.135385 | 0.155294 | 0.182069 | 0.121815 | 0.1495 | 0.193471 |
X4 | 0.072182 | 0.132333 | 0.397 | 0.150857 | 0.176 | 0.2112 | 0.143 | 0.182722 | 0.253 |
X5 | 0.034522 | 0.044111 | 0.061077 | 0.203077 | 0.251429 | 0.33 | 0.084333 | 0.096735 | 0.113414 |
X6 | 0.061077 | 0.09925 | 0.264667 | 0.138947 | 0.16 | 0.188571 | 0.07831 | 0.088892 | 0.102781 |
X7 | 0.041789 | 0.056714 | 0.088222 | 0.122791 | 0.138947 | 0.16 | 0.13156 | 0.16445 | 0.219267 |
X8 | 0.061077 | 0.09925 | 0.264667 | 0.135385 | 0.155294 | 0.182069 | 0.07475 | 0.084333 | 0.096735 |
X9 | 0.046706 | 0.066167 | 0.113429 | 0.142703 | 0.165 | 0.195556 | 0.073089 | 0.082225 | 0.093971 |
X10 | 0.034522 | 0.044111 | 0.061077 | 0.176 | 0.2112 | 0.264 | 0.093971 | 0.109633 | 0.13156 |
X11 | 0.044111 | 0.061077 | 0.09925 | 0.16 | 0.188571 | 0.229565 | 0.091361 | 0.106097 | 0.1265 |
X12 | 0.056714 | 0.088222 | 0.1985 | 0.170323 | 0.203077 | 0.251429 | 0.106097 | 0.1265 | 0.156619 |
X13 | 0.028357 | 0.034522 | 0.044111 | 0.142703 | 0.165 | 0.195556 | 0.117464 | 0.143 | 0.182722 |
X14 | 0.049625 | 0.072182 | 0.132333 | 0.155294 | 0.182069 | 0.22 | 0.073089 | 0.082225 | 0.093971 |
X15 | 0.061077 | 0.09925 | 0.264667 | 0.182069 | 0.22 | 0.277895 | 0.106097 | 0.1265 | 0.156619 |
X16 | 0.041789 | 0.056714 | 0.088222 | 0.142703 | 0.165 | 0.195556 | 0.13156 | 0.16445 | 0.219267 |
Table 9
Idele+ and Idele-
Idele+ | 0.397 | 0.33 | 0.253 |
Idele- | 0.028357 | 0.122791 | 0.073089 |
Table10
Closeness coefficient (CCi) and final ranking
Risk factor |
|
| (CCi) | Rank |
X1 | 0.670867 | 0.103079 | 0.033792 | 16 |
X2 | 0.580332 | 0.203197 | 0.065799 | 4 |
X3 | 0.60555 | 0.172686 | 0.056299 | 9 |
X4 | 0.469936 | 0.412482 | 0.1186 | 1 |
X5 | 0.592083 | 0.19727 | 0.063408 | 6 |
X6 | 0.60223 | 0.207959 | 0.065125 | 5 |
X7 | 0.614281 | 0.167537 | 0.05437 | 10 |
X8 | 0.611636 | 0.198538 | 0.062176 | 8 |
X9 | 0.656592 | 0.117852 | 0.03861 | 15 |
X10 | 0.611302 | 0.163836 | 0.053627 | 11 |
X11 | 0.615614 | 0.159268 | 0.052149 | 12 |
X12 | 0.540184 | 0.257493 | 0.081902 | 3 |
X13 | 0.633724 | 0.138999 | 0.04564 | 14 |
X14 | 0.630987 | 0.147814 | 0.048155 | 13 |
X15 | 0.505791 | 0.315106 | 0.097392 | 2 |
X16 | 0.587936 | 0.194025 | 0.062955 | 7 |
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