Int J Industrial and Systems Engineering, Vol 23, No 3, 2016 A state of the art review of fuzzy approaches used in the failure modes and effects analysis: a call for research Samuel Chrysostom* and Ravi Kumar Dwivedi Department of Mechanical Engineering, MANIT, Bhopal, India Email: samchrysostom@gmail.com Email: nitb.ravi@gmail.com *Corresponding author Abstract: Failure mode and effects analysis (FMEA) is a methodology to evaluate a system, design or process or service for possible ways in which failures can occur The conventional risk priority number (RPN) method has been criticised to have many deficiencies and many researchers have proposed many methods to overcome this problem Various reviews have been done on the FMEA procedures and also the models proposed The extensive reviews have narrowed down to the fuzzy logic used in the FMEA process The reviews have finally concluded that fuzzy models are the most common methods that help in overcoming the drawbacks that are caused by traditional processes Hence in this paper only the fuzzy methods used in failure modes and effects analysis have been reviewed After this review the authors conclude that fuzzy TLBO can be used in decision making, which has previously not been used in this process Keywords: failure mode and effects analysis; FMEA; failure; decision making; TLBO; fuzzy methods Reference to this paper should be made as follows: Chrysostom, S and Dwivedi, R.K (2016) ‘A state of the art review of fuzzy approaches used in the failure modes and effects analysis: a call for research’, Int J Industrial and Systems Engineering, Vol 23, No 3, pp.351–369 Biographical notes: Samuel Chrysostom is a post graduate student in maintenance engineering and management, from MANIT, Bhopal, India He has just started his research in the maintenance field He has done research on the failure modes and effects analysis, and fuzzy logic applications to FMEA Till now, he has only one publication in an international journal Ravi Kumar Dwivedi has served for 15 years in the Indian Air Force (maintenance of aeronautical, automobile and power plant), after completion of the bond, he joined one of the leading sugar industry of India as a Dy Chief Engineer (Automobile) and served for 15 months Presently, he is working as an Associate Professor, Mechanical Engineering Department, MANIT Bhopal, India His area of interest comprises maintenance engineering and management, production and industrial engineering, rapid prototyping and its multidisciplinary applications He has published 30 research papers in journals and conferences of national-international level, and guided 23 PG dissertations Currently, he is supervising four PhD and three PG scholars Copyright © 2016 Inderscience Enterprises Ltd 351 352 S Chrysostom and R.K Dwivedi This paper is a revised and expanded version of a paper entitled ‘A review on the methodologies used in failure modes and effects analysis (FMEA)’ presented at the International Conference on Electrical, Electronics, Computer Science, Management and Mechanical Engineering, Hyderabad, India, 17 November 2013 Introduction Failure mode and effect analysis (FMEA) is an engineering approach used to identify, categorise and eradicate known potential failures from a system, design, process and service When the method is used for criticality analysis it is also known as failure modes effects and criticality analysis (FMECA) This method is widely used and has applications in various industries including aerospace, where it has originated, nuclear, chemical and manufacturing sectors (Linton, 2003) A superior FMEA helps analysts to identify the failure modes along with the causes of these failures and can also help them prioritise the identified failure modes and can also help to perform corrective actions for these failure modes The main purpose of the technique is to identify and prevent the failure modes and the known problems from reaching the customer (Chin et al., 2009) A system, design, process, or service may usually have multiple failure modes or causes and effects In this situation, each failure mode or cause needs to be assessed and prioritised in terms of their risks so that high risky (or most dangerous) failure modes can be corrected with top priority (Wang et al., 2009) To execute the corrective actions for different failure modes the risk of identified failure modes need to be evaluated and prioritised The major concern of FMEA is to accentuate the prevention of problems linked to the timely treatment of the system, rather than finding a solution after the failure happens, unlike many other risk assessment tools This helps decision makers adjust the existing programs, increase compensating provisions, employ the recommended actions to reduce the likelihood of failures, decrease the probability of failure rates and avoid hazardous accidents At present, FMEA has been extensively used in a number of industries, including aerospace, automotive, nuclear, electronics, chemical, mechanical and medical technologies industries (Chang and Cheng, 2011; Sharma et al., 2005; Liu et al., 2012) It is notable that the failure in any of these industries can cause a life threatening situation to both the people working in these industries and also the environment Thus this method of risk assessment is very crucial to the fail safe running if these industries Several variations of the traditional FMEA have been developed over the years The use of knowledge-based system for automation of FMEA has been discussed by Price et al (1992) Meanwhile, Bell et al (1992) proposed the use of casual reasoning model for FMEA An approach to model the entire system using fuzzy cognitive mapping was developed by Peláez and Bowles (1996) An improvised FMEA approach using a single matrix to model the entire system to reflect the importance of an event relating to indenture under consideration and to the entire system is presented by Kara-Zaitri et al (1992) A state of the art review of fuzzy approaches 353 The paper aims to review the fuzzy techniques used in FMEA Liu et al (2013) have done an extensive review and have documented the research possibilities of FMEA The authors feel that the research can be done on the multi criteria decision making (MCDM) approaches The fuzzy logic approach is one of the MCDM approach Many researchers have used this method to evaluate the FMEA and prioritise the failures (Liu et al., 2013) This paper reviews the various fuzzy logic approaches that have been proposed Generally the fuzzy approach then requires an additional method to finalise the prioritisation It is in this step that the fuzzy approach varies from one author to another The rest of the paper is organised as follows Section explains the traditional FMEA Section explains the basic fuzzy approach Section contains the reviews of various papers Finally, Section concludes the paper with the new method that the authors wish to propose based on the findings from the review FMEA FMEA is a significant technique used to identify and eradicate the various potential failures to enhance the reliability of the system, thus increasing the safety of any complex system The technique provides explicit information for making risk management decisions which might prove to be the crucial decision of the process In order to analyse a specific system, process or product, a cross functional team should be established to perform FMEA The initial step is to identify all the possible potential failure modes of the product or system through a session of brainstorming After that, the critical analysis is done on the taking into account the risk factors: severity (S), occurrence (O), and detection (D) Analysts can identify known and potential failure modes and their causes and effects using FMEA, it also helps them prioritise the identified failure modes and to work out corrective actions for the failure modes The primary objective of FMEA is to identify and prevent the potential problems from reaching the customer The prioritisation of failure modes, so that the corrective actions might be implemented, is determined through the risk priority number (RPN) The RPN is obtained through the multiplication of the O, S and D of a failure That is RPN = O × S × D, (1) where O is the probability of the failure, S is the severity of the failure, and D is the probability of not detecting the failure The three factors are evaluated using the ranking scores from to 10, as described in Tables to The failure modes with higher RPNs are to be considered more critical and are to be given higher priorities Based on the scores of RPNs, failure modes can be ranked and proper actions should be implemented on the high-risk failure modes RPNs should be recalculated after the corrective actions have been implemented to check if the risk has been reduced if not completely eliminated, and also to determine the extent to which the corrective action for each failure mode has been effective 354 Table Rank 10 S Chrysostom and R.K Dwivedi Suggested ratings for occurrence of a failure mode Probability of occurrence Nearly impossible Remote Low Relatively high Moderate Moderately high High Repeated failures Very high Extremely high, failure inevitable Possible failure rate ≤1 in 1,500,000 in 150,000 in 15,000 in 2000 in 400 in 80 in 20 in in ≥ in Source: Chang (2009), Chang and Cheng (2010), Chang and Sun (2009), Chang and Wen (2010) and Chang et al (2010) Table Suggested ratings for the severity of a failure mode Rank Effect Severity of effect None Very minor Minor Low Moderate Moderate effect on product performance The product requires repair Significant Product performance is degraded Comfort or convince functions may not operate Major Product performance is severely affected but functions System is inoperable Extreme Product is inoperable with loss of primary function The system is inoperable Serious Failure involves hazardous outcomes and/or non-compliance with government regulations or standards 10 Hazardous No effect Very minor effect on product or system performance Minor effect on product or system performance Small effect on product performance The product does not require repair Failure is hazardous, and occurs without warning It suspends operation of the system and/or involves non-compliance with government regulations Source: Chang (2009), Chang and Cheng (2010), Chang and Sun (2009), Chang and Wen (2010) and Chang et al (2010) A state of the art review of fuzzy approaches Table Rank Suggested ratings for the detection of a failure mode Detection Criteria Almost certain Design control will almost certainly detect a potential cause of failure or subsequent failure mode Very high High Moderately high Moderate Low Very low Remote 10 355 Very high chance the design control will detect a potential cause of failure or subsequent failure mode High chance the design control will detect a potential cause of failure or subsequent failure mode Moderately high chance the design control will detect a potential cause of failure or subsequent failure mode Moderate chance the design control will detect a potential cause of failure or subsequent failure mode Low chance the design control will detect a potential cause of failure or subsequent failure mode Very low chance the design control will detect a potential cause of failure or subsequent failure mode Remote chance the design control will detect a potential cause of failure or subsequent failure mode Very remote Very remote chance the design control will detect a potential cause of failure or subsequent failure mode Absolute uncertainty Design control does not detect a potential cause of failure or subsequent failure mode; or there is no design control Source: Chang (2009), Chang and Cheng (2010), Chang and Sun (2009), Chang and Wen (2010) and Chang et al (2010) 2.1 FMEA procedure The detailed procedure for carrying out an FMEA can be divided into several steps as highlighted by Pillay and Wang (2003) The steps are enlisted here: Develop a good understanding of what the system is supposed to when it is operating properly Divide the system into sub-systems and/or assemblies in order to localise the search for components Use blue prints, schematics and flow charts to identify components and relations among components Develop a complete component list for each assembly Identify operational and environmental stresses that can affect the system Consider how these stresses might affect the performance of individual components Determine failure modes of each component and the effects of failure modes on assemblies, sub-systems, and the entire system Categorise the hazard level (severity) of each failure mode (several qualitative systems have been developed for this purpose) 356 S Chrysostom and R.K Dwivedi Estimate the probability In the absence of solid quantitative statistical information, this can also be done using qualitative estimates Calculate the RPN: the RPN is given as the multiplication of the index representing the probability, severity and detectability 10 Determine if action needs to be taken depending on the RPN 11 Develop recommendations to enhance the system performance These fall into two categories: • preventive actions: avoiding a failure situation • compensatory actions: minimising losses in the event that a failure occurs 12 Prepare FMEA report by summarising the analysis in tabular form The pictorial representation of the procedure is shown in Figure Figure The FMEA process Source: Pillay and Wang (2003) A state of the art review of fuzzy approaches 357 2.2 Disabilities in FMEA FMEA has been proven to be one of the most important early preventive initiatives during the design stage of a system, product, and process or service (Chin et al., 2009) But the RPN has been criticised for various reasons (Chin et al., 2009; Liu et al., 2013; Bowles, 2004; Sankar and Prabhu, 2001; Ben-Daya and Raouf, 1996; Braglia et al., 2003a; Chang et al., 2001; Gilchrist, 1993; Pillay and Wang, 2003): • Dissimilar sets for O, S and D could produce the same value of RPN, thus proving the assessment difficult to comprehend as the hidden risk implications may be totally different For example, two different events with values of 2, 3, and 4, 1, for O, S and D respectively, will have the same RPN value of 12 However, the hidden risks of the two events may be extremely different from each other because of the different variables or sets of failure consequence This may cause a waste of resources and may even lead to a high risk event • The relative importance among the three risk factors is not considered The risk factors are assumed to have same importance However, this may not be practical • The mathematical formulation for determining RPN is questionable as there is no evidential proof as to why only these three factors and not other factors should not be considered in calculating RPN • The conversion of the scores for the three risk factors is different But this forms the most crucial step as the entire calculation depends on this step The factors cannot be precisely evaluated and it varies for each analyst as most of the information are linguistic and the conversion is required which varies from individual to individual • RPN considers only three factors and these relate only to safety, the other factors which relate to economics and productivity are ignored • Small changes in one rating can lead to huge differences and affect the RPN on a large scale, depending on other factors For instance, if O and D are both 10, then even a one point difference in severity will result in a 100 point difference, on the other hand if O and D are both 5, then a one point difference produces a 25-point difference in RPN Fuzzy set theory As the paper aims to review fuzzy logic in failure modes effects analysis, this section deals with some relative mathematical tools, which explain the fuzzy set theory 3.1 Fuzzy sets Fuzzy set theory was developed by Zadeh (1965) to solve fuzzy phenomenon problems present in the real world, such as uncertain, imprecise, unspecific, and fuzzy situations This theory, when measuring the ambiguity of concepts that are associated with human beings’ subjective judgments, has an advantage over the traditional set theory (Liu et al., 2012) Let X be the universe of discourse, X = {x1, x2, , xn}, a fuzzy set à of X is 358 S Chrysostom and R.K Dwivedi characterised by a membership function μÃ(ϰ), which associates with each element x in X a real number in the interval [0, 1] The function value μÃ(ϰ) is termed the grade of membership of ϰ in à (Zadeh, 1965) The larger μÃ(ϰ), the stronger the grade of membership for ϰ in à (Liu et al., 2012) 3.2 Fuzzy numbers A fuzzy set à of the universe of discourse ℵ is convex if and only if for all ϰ1, ϰ2 in ϰ, μÃ(λϰ1+(1 – λ) ϰ2) ≥ min(μÃ(ϰ1), μÃ(ϰ2), ;where λ [0, 1] A fuzzy set à of the universe of discourse ϰ is called a normal fuzzy set implying that ∃ϰiϰ, μÃ(ϰ1) = A fuzzy number is a fuzzy subset in the universe of discourse ϰ whose membership function is both convex and normal (Chen, 2001) Triangular and trapezoidal fuzzy numbers are the most common used fuzzy numbers both in theory and practice In fact, triangular fuzzy numbers are special cases of trapezoidal fuzzy numbers When the two most promising values are the same number, the trapezoidal fuzzy number becomes a triangular fuzzy number For sake of simplicity and without loss of generality, trapezoidal fuzzy numbers are preferred for representing the linguistic variables in this study A positive trapezoidal fuzzy number à can be denoted as (a1, a2, a3, a4) The membership function μÃ(ϰ) is defined as: ⎧ ⎪ x−a ⎪ ⎪ a − a1 μ à (x) = ⎨ ⎪ a3 − x ⎪ a3 − a2 ⎪ ⎩ for x < a1 for a1 ≤ x ≤ a (2) for a ≤ x ≤ a for x > a where [a2, a3] is called a mode interval of Ã, and a1 and a4 are called lower and upper limits of Ã, respectively Zadeh also provided the algebraic operations of the trapezoidal fuzzy numbers 3.3 Linguistic variables A linguistic variable is a variable whose values are expressed in linguistic terms The concept of linguistic variable is very useful in dealing with situations which are too complex or too ill-defined to be reasonably described by traditional quantitative expressions (Chen, 2001) These linguistic values can also be represented by fuzzy numbers In this paper, the importance weights of risk factors and the fuzzy ratings of failure modes with respect to each risk factor are considered as linguistic variables It should be noticed that the membership function values can be determined according to the historical data and the detailed questionnaire answered by all domain experts (Liu et al., 2011) A state of the art review of fuzzy approaches 359 3.4 Defuzzification An important step in fuzzy modelling and fuzzy multi-criteria decision-making is the defuzzification task which transforms a fuzzy number into a crisp value Many different techniques for this transformation can be utilised, but the most commonly used defuzzification method is the centroid defuzzification method, also known as the centre of gravity (COG) or centre of area (COA) defuzzification (Ebrahimnejad et al., 2012) Review of existing literature In this section, the literature review on risk evaluation in FMEA for priority ranking, using fuzzy logic, has been presented In this review we have considered the methods that use only fuzzy methods The fuzzy methods generally have a procedure as follows The initial step of the method is usually to identify the objectives of risk assessment and determine the analysis level Then the potential failure modes are described and sets of relevant factors are produced The risk factors are evaluated and the ratings of failure modes with respect to each other And the final step which is to optimise the selection of risk factors, which generally varies for each researcher The researchers have already done reviews on the techniques followed for various failure modes and effects analysis The data has been collected from various papers and has been given in a graphical form (Figure 2) as to the type of approaches that have been used and their usage or popularity percentage The various techniques that fall under these categories are given in Table Figure Popularity of approaches used in FMEA (see online version for colours) 360 S Chrysostom and R.K Dwivedi Table Sl no The various approaches used for failure modes and effects analysis Categories Approaches MCDM ME-MCDM Evidence theory AHP/ANP Fuzzy TOPSIS Grey theory Mathematical programming Artificial intelligence Linear programming Fuzzy DEA Rule base system Fuzzy rule base system Fuzzy cognitive mapping Integrated approaches Fuzzy AHP fuzzy rule system WLSM MOI partial ranking method OWGA operator DEMATEL FER grey theory Fuzzy AHP fuzzy TOPSIS ISM-ANP-UPN Other approaches Cost-based model Monte Carlo simulation Minimum cut sets theory Source: Liu et al (2011) 4.1 Boolean representation method Fuzzy logic is one of the multi criteria decision making method, though there are many other methods to evaluate multi criteria decision making problems this method has been found to be used more than any other method based on the review by Liu et al (2013) Fuzzy logic is extensively useful because of the ease of conversion of the linguistic data into crisp scores This is an essential requirement for the FMEA process According to Liu et al (2013) the category of method most frequently applied to FMEA was found to be AI with 40.0% of all the reviewed papers MCDM approaches were the next most applied methods with 18 papers or 22.5% The most popular approach is fuzzy rule base system, followed by grey theory, cost-based model, AHP/ANP and linear programming The wide applicability of fuzzy rule-base system is because fuzzy logic and knowledge-based approach possess unique advantages Compared to the conventional FMEA methodology, the fuzzy expert system provides the following advantages: • Ambiguous, qualitative or imprecise information, as well as quantitative data can be used in criticality/risk assessment and they are handled in a consistent manner • It permits to combine the occurrence, severity and detectability of failure modes in a more flexible and realistic manner A state of the art review of fuzzy approaches 361 • It allows the failure risk evaluation function to be customised based on the nature of a process or a product • The fuzzy knowledge-based system can fully incorporate engineers’ knowledge and expertise in the FMEA analysis and substantial cost savings can thus be realised (Liu et al., 2013; Bowles and Peláez, 1995; Braglia et al., 2003a; Sharma et al., 2005; Tay and Lim, 2006a, 2006b, 2010; Xu et al., 2002) A multi expert MCDM technique for carrying out the calculation of the risk priority of failures in FMEA, without necessitating an arbitrary and artificial numerical conversion has been discussed by Franceschini and Galetto (2001) In this method risk factors were the evaluation criteria, while the failure modes had been considered as alternatives to be selected Each decision criteria is considered as a fuzzy subset over the set of alternatives to be selected After the aggregation of evaluations expressed on each criterion for a given alternative, the failure mode was determined with the maximum risk priority code If two or more failure modes have the same risk priority a detailed section was discussed to differentiate the relative ranking While others had presented about priority-based cost model, Hu et al (2009) presented a green component RPN (GC-RPN) to analyse the risks of green components to hazardous substance Fuzzy AHP was applied to determine the relative weightings of risk factors Then the GCRPN was calculated for each one of the components to identify and manage the risks derived from them Braglia et al (2003b) proposed an MCDM approach called fuzzy technique for order preference by similarity to ideal solution (TOPSIS) approach for FMECA, which considered the failure causes as alternatives, and the risk factors O, S and D related to a failure mode as criteria The failures were prioritised based on the measurement of the Euclidean distance of an alternative from an ideal goal In the proposed fuzzy TOPSIS approach, the three risk factors and their corresponding weights of importance were allowed to be assessed using triangular fuzzy numbers rather than precise crisp numbers, giving a final ranking for failure causes that is easy to interpret (Liu et al., 2013) Liu et al have proposed an approach for risk evaluation in failure modes and effects analysis with extended VIKOR They had considered the risk factors and their relative importance weights as linguistic variables Because linguistic assessments merely approximate the subjective judgment of decision makers, they considered linear trapezoidal membership functions to be adequate for capturing the vagueness of these linguistic assessments A systematic approach to apply the VIKOR was proposed to determine risk priorities of failure modes under a fuzzy environment in this section Their methodology is shown in Figure A fuzzy model for prioritising failure modes based on the degree of match and fuzzy rule base to overcome limitations of traditional FMEA were presented by Gargama and Chaturvedi (2011) The method used the belief structure for the assessment of risk factors, and converted randomness in the assessed information into a fuzzy number The degree of match was used thereafter to estimate the matching between the assessed information and the fuzzy sets of risk factors The computed degree of match was taken as the input to the fuzzy rule-based systems where rules were processed resulting in failure classification with degree of certainty 362 Figure S Chrysostom and R.K Dwivedi Procedure for FMEA with extended VIKOR Note: Risk evaluation in failure mode and effects analysis with extended VIKOR method under fuzzy environment Source: Liu et al (2012) Fuzzy method and grey theory was used by Chang et al (1999), where fuzzy linguistic variables were used to evaluate the risk factors O, S and D and grey relation analysis was used to determine the risk priority of potential causes To carry out the grey relational analysis (GRA), fuzzy linguistic variables were defuzzified as crisp values, the lowest levels of the three risk factors were defined as a standard series, and the assessment information of the three risk factors for each potential cause was viewed as a comparative series, whose grey relational coefficient and degree of relational with the standard series were computed in terms of the grey theory (Liu et al., 2013) Wang et al (2009b) and Liu et al (2013) proposed fuzzy risk priority numbers (FRPNs) for prioritisation of failure modes to deal with the problem that it is not be realistic in real applications to determine the risk priorities of failure modes using the RPNs because they require the risk factors of each failure mode to be precisely evaluated A state of the art review of fuzzy approaches 363 In the paper, the FRPNs were defined as fuzzy weighted geometric means of the fuzzy ratings for O, S and D, and can be computed using a-level sets and linear programming models Finally, the FRPNs were defuzzified using centroid defuzzification method for ranking purpose Meanwhile Chen and Ko (2009a, 2009b) and Liu et al (2013) defined the FRPNs as fuzzy ordered weighted geometric averaging (FOWGA) of the three risk factors Bowles and Peláez (1995) and Liu et al (2013) described a fuzzy logic-based approach for prioritising failures in a system FMECA, which uses linguistic variables to describe O, S, D and the riskiness of failure The relationships between the riskiness and O, S, D were characterised by a fuzzy if-then rule base which was developed from expert knowledge and expertise Crisp ratings for O, S and D were fuzzified to match the premise of each possible if-then rule All the rules that have any truth in their premises were fired to contribute to the fuzzy conclusion set The fuzzy conclusion was then defuzzified by the weighted mean of maximum method (WMoM) as the ranking value of the risk priority Moss and Woodhouse (1999 and Liu et al (2013) also suggested a similar fuzzy logic approach for criticality analysis Yang et al (2008) presented a fuzzy rule-based Bayesian reasoning (FuRBaR) approach for prioritising failures in FMEA The technique was specifically developed to deal with some of the drawbacks concerning the use of conventional fuzzy logic (i.e., rule-based) methods in FMEA In their approach, subjective belief degrees were assigned to the consequent part of the rules to model the incompleteness encountered in establishing the knowledgebase A Bayesian reasoning mechanism was then used to aggregate all relevant rules for assessing and prioritising potential failure modes (Liu et al., 2013) The fuzzy RPN mode typically requires a large number of rules, and it is a time-consuming and tedious process in acquiring rules from domain experts in building a fuzzy if-then rule base Therefore, Braglia and Bevilacqua (2000) and Liu et al (2013) proposed the use of AHP for obtaining the rules for a particular fuzzy criticality assessment model Rule reduction method has been applied by many other researches to reduce the size of a fuzzy if-then rule base (Liu et al., 2013) Sharma et al (2005) employed 27 fuzzy if-then rules in their fuzzy FMEA for the feeding system in a paper mill, and they reduced a total of 125 fuzzy if then rules to 30 rules in the applications to other systems of the paper mill, such as pulping system, forming and press systems, washing system, paper machine and dryer system (Liu et al., 2013) Peláez and Bowles (1996) and Liu et al (2013) applied fuzzy cognitive maps (FCMs) to model the behaviour of a system for FMEA The FCM was a diagram to represent the causality of failures with failure node and causal relation path The path was described by using linguistic variables such as ‘some, always, often’ and relative scales were assigned for each term Then min-max inference approach was used to evaluate the net causal effect on any given node and weighted mean of maximum method was used as defuzzification technique to extract the resulting confidence values on linguistic variables A data envelopment analysis approach for determining ranking indices among failure modes in which the typical FMEA parameters are modelled as fuzzy sets has been researched upon and published by Garcia et al (2005) By this approach, inference rules of the IF THEN kind can be bypassed The approach was applied to a typical PWR 364 S Chrysostom and R.K Dwivedi auxiliary feed water system The results have been compared to those obtained by means of: the RPNs, pure fuzzy logic concepts, and finally the DEA-APGF (profiling of severity efficiency) approach The linguistic variables had been mapped according to the characteristics of the failure modes to be considered, and under various conditions which were decided by the researchers For each linguistic variable there is an associated membership function established with the help of expert opinion The results demonstrate the potential of the combination of fuzzy logic concepts and data envelopment analysis for this class of problems An et al (2011) have applied fuzzy analytical hierarchy to railway risk assessment In the system, fuzzy reasoning approach (FRA) was employed to estimate the risk level of each hazardous event in terms of failure frequency, consequence severity and consequence probability This allows imprecision or approximate information in the risk analysis process Fuzzy analytical hierarchy process (fuzzy-AHP) technique has then been incorporated into the risk model to use its advantage in determining the relative importance of the risk contributions so that the risk assessment can be progressed from hazardous event level to hazard group level and finally to railway system level This risk assessment system evaluated both qualitative and quantitative risk data and information associated with a railway system effectively and efficiently, which provides railway risk analysts, managers and engineers with a method and tool to improve their safety management of railway systems and set safety standards The first step that the authors followed was to determine the inputs for the fuzzy sets and convert them to into unique fuzzy numbers The UFNs were then aggregated and the fuzzy values were then calculated Fuzzy methods have been used by Purba et al (2014) to assess the basic events of fault trees through qualitative data processing The study developed a fuzzy reliability algorithm to effectively generate basic event failure probabilities without reliance on quantitative historical failure data through qualitative data processing The linguistic values were articulated in terms of component failure possibilities in order to qualitatively assess basic event failure possibilities treated as inputs of the proposed model and generate basic event failure probabilities as its outputs To demonstrate the feasibility and effectiveness of the proposed algorithm, actual basic event failure probabilities were collected from nuclear power plant operating experiences are had been compared with the failure probabilities generated by the algorithm The results demonstrated that the proposed fuzzy reliability algorithm arises as a suitable alternative for the probabilistic reliability approach when quantitative historical failure data are unavailable Liu and Tsai (2012) applied fuzzy logic to assess the risk for occupational hazards in the construction industry To reduce or prevent occupational hazards in the construction industry, a fuzzy risk assessment method was proposed to provide a prevention and improvement technique against occupational hazards This method used two-stage quality function deployment (QFD) tables to represent the relationships among construction items, hazard types and hazard causes A fuzzy analytic network process (ANP) method was developed to identify important hazard types and hazard causes Failure modes and effect analysis (FMEA) was performed to assess the risk value of hazard causes based on the fuzzy inference approach The method was applied to a telecom engineering company in southern Taiwan The fuzzy system reliability analysis using different types of intuitionistic fuzzy numbers has been studied by Kumar and Yadav (2011) Before their proposition, to A state of the art review of fuzzy approaches 365 analyse the fuzzy system reliability, it was assumed that the failure rates of all components of a system follow the same type of fuzzy set or intuitionistic fuzzy set However, in practical problems, such type of situation rarely occurs Therefore, in their research, they had introduced a new algorithm to construct the membership function and non-membership function of fuzzy reliability of a system having components following different types of intuitionistic fuzzy failure rates Functions of intuitionistic fuzzy numbers had been calculated to construct the membership function and non-membership function of fuzzy reliability via nonlinear programming techniques Using the proposed algorithm, membership functions and non-membership functions of fuzzy reliability of a series system and a parallel system were constructed Geum et al (2011) proposed a systematic approach for identifying and evaluating potential failures using a service-specific failure mode and effect analysis (service-specific FMEA) and GRA They proposed an approach consisting of two stages: construction of service-specific FMEA and application of GRA The first stage, construction of service-specific FMEA, was aimed at incorporating the service specific characteristics to the traditional FMEA, providing three dimensions and 19 sub-dimensions, encompassing the service characteristics At the second stage, GRA is applied to calculate the risk priority of each failure mode to deal with the necessities of a flexible evaluation framework under these interrelated multi-dimensions Chang et al (2013) proposed a novel approach, integrating GRA and the decision-making trial and evaluation laboratory (DEMATEL) method, to rank the risk of failure, wherein the GRA was used to modify RPN values to lower duplications and the ordered weighted rule had been followed; then, the DEMATEL method was applied to examine the direct and indirect relationships between FMs and CFs, giving higher priority when a single CF causes FMs to occur multiple times Oke et al (2009) have done research on the Application of neuro fuzzy framework to maintenance scheduling activity monitoring They have applied neuro fuzzy principles to a maintenance scheduling framework that involved selection of alternate preventive maintenance and operations such that the total preventive maintenance cost is minimised Fuzzy logic, which incorporates an alternative way of thinking that allows modelling complex systems using a higher level of abstraction originating from our knowledge and experience, is incorporated into the overall framework that has been presented This is achieved through the fusion of neural networks and fuzzy logic in neuro fuzzy models as applied here to allow uncertainty reasoning with linguistic inputs and interpretation of results in terms of natural language This paper has shown why neuro fuzzy models should be applied on the problem described, and how the neuro fuzzy principles are applied in a shipping organisation for preventive maintenance scheduling of a fleet of ships The work demonstrated how uncertainty representation and fuzzy inferences in relation to ship maintenance scheduling could be established Conclusions and suggestion for future work Because of the many disadvantages of the traditional FMEA many researchers have developed many methods to solve for the risk factors and calculate RPN The fuzzy methods are the most frequently used methods in this particular methodology for calculating RPN, as reported by Hu et al (Liu et al., 2013) Hence this paper has 366 S Chrysostom and R.K Dwivedi reviewed the papers employing fuzzy logic methods to solve for the risk analysis problems Some of the problems have been found with the traditional FMEA methods and these have been listed in the above sections It has been observed from the review that validation has not been done to optimise the fuzzy method that has been used The authors suggest that the optimisation technique based on teacher learner-based optimisation be done to validate the fuzzy methods The fuzzy TLBO method has been used by Ahmad Moghadam and Seifi (2014) for optimising the reactive power control variables for energy loss minimisation In this paper the researchers have used fuzzy TLBO method to overcome the problems that were occurring when the same problem was tried to solve using fuzzy linear programming The fuzzy TLBO can be used in decision making process and this will help in overcoming the problems encountered in traditional FMEA This process has been applied by the authors on a shot blasting machine to assess the risk values The outcomes are well aligned with the research review The methods of fuzzy logic give an improved ranking method and thereby make decisions based on the risk priority analysis The fuzzy analysis of shot blasting involved the calculation of the traditional RPN and then calculating the fuzzy RPN and comparing the results The results had shown that the fuzzy method had provided a better ranking method and the drawbacks in traditional method have been overcome References An, M., Chen, Y and Baker, C.J (2011) ‘A fuzzy reasoning and fuzzy-analytical hierarchy process based approach to the process of railway risk information: a railway risk 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(1992) ‘Using causal reasoning for automated failure and effects analysis (FMEA)’, Proceedings of Annual Reliability and Maintainability Symposium, pp.343–53 Ben-Daya, M and Raouf, A (1996) ? ?A revised... Chang, K-H., Chang, Y-C and Tsai, I-T (2013) ‘Enhancing FMEA assessment by integrating grey relational analysis and the decision making trial and evaluation laboratory approach’, Engineering Failure