A state of the art review of fuzzy approaches used in the failure modes and effects analysis a call for resear

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 En

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

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

1 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)

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 2 explains the traditional FMEA Section 3 explains the basic fuzzy approach Section 4 contains the reviews of various papers Finally, Section 5 concludes the paper with the new method that the authors wish to propose based on the findings from the review

2 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

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 1 to 10, as described in Tables 1 to 3 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

Table 1 Suggested ratings for occurrence of a failure mode

Rank Probability of occurrence Possible failure rate

10 Extremely high, failure inevitable ≥ in 2

Source: Chang (2009), Chang and Cheng (2010), Chang and Sun (2009),

Chang and Wen (2010) and Chang et al (2010)

Table 2 Suggested ratings for the severity of a failure mode

Rank Effect Severity of effect

2 Very minor Very minor effect on product or system performance

3 Minor Minor effect on product or system performance

4 Low Small effect on product performance The product does not require

repair

5 Moderate Moderate effect on product performance The product requires repair

6 Significant Product performance is degraded Comfort or convince

functions may not operate

7 Major Product performance is severely affected but functions

System is inoperable

8 Extreme Product is inoperable with loss of primary function

The system is inoperable

9 Serious Failure involves hazardous outcomes and/or non-compliance with

government regulations or standards

10 Hazardous 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)

Table 3 Suggested ratings for the detection of a failure mode

certain Design control will almost certainly detect a potential cause of failure or subsequent failure mode

2

Very high Very high chance the design control will detect a potential cause of failure or subsequent failure mode

3

High High chance the design control will detect a potential cause of failure or subsequent failure mode

4 Moderately

high Moderately high chance the design control will detect a potential cause of failure or subsequent failure mode

5

Moderate Moderate chance the design control will detect a potential cause of failure or subsequent failure mode

6

Low Low chance the design control will detect a potential cause of failure or subsequent failure mode

7

Very low Very low chance the design control will detect a potential cause of failure or subsequent failure mode

8

Remote Remote chance the design control will detect a potential cause of failure or subsequent failure mode

9

Very remote Very remote chance the design control will detect a potential cause of failure or subsequent failure mode

10 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)

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:

1 Develop a good understanding of what the system is supposed to do when it is operating properly

2 Divide the system into sub-systems and/or assemblies in order to localise the search for components

3 Use blue prints, schematics and flow charts to identify components and relations among components

4 Develop a complete component list for each assembly

5 Identify operational and environmental stresses that can affect the system Consider how these stresses might affect the performance of individual components

6 Determine failure modes of each component and the effects of failure modes on assemblies, sub-systems, and the entire system

7 Categorise the hazard level (severity) of each failure mode (several qualitative systems have been developed for this purpose)

8 Estimate the probability In the absence of solid quantitative statistical information, this can also be done using qualitative estimates

9 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 1

Figure 1 The FMEA process

Source: Pillay and Wang (2003)

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, 2 and 4, 1, 3 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

3 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

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

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)

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) = 1 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:

1 1

2 1 Ã

3

3 2

3

x a

μ (x)

<

⎧

⎪ −

⎪ −

⎩

(2)

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

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)

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)

4 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 4

Figure 2 Popularity of approaches used in FMEA (see online version for colours)

Table 4 The various approaches used for failure modes and effects analysis

Sl no Categories Approaches

Evidence theory AHP/ANP Fuzzy TOPSIS Grey theory

2 Mathematical

programming Linear programming Fuzzy DEA

intelligence Fuzzy rule base system Rule base system

Fuzzy cognitive mapping

approaches WLSM MOI partial ranking method Fuzzy AHP fuzzy rule system

OWGA operator DEMATEL FER grey theory Fuzzy AHP fuzzy TOPSIS ISM-ANP-UPN

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