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An extension to Fuzzy Developed Failure Mode and Effects Analysis (FDFMEA) application for aircraft landing system
Safety Science 98 (2017) 113–123
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Safety Science journal homepage: www.elsevier.com/locate/ssci
An extension to Fuzzy Developed Failure Mode and Effects Analysis (FDFMEA) application for aircraft landing system Mohammad Yazdi a, Sahand Daneshvar a,⇑, Hashem Setareh b a b
Eastern Mediterranean University, Department Industrial Engineering, Gazimagusa, TRNC, Mersin 10, Turkey Petroleum University of Technology, Abadan Institute of Technology, Department of Safety and Protection Engineering, Abadan, Iran
a r t i c l e
i n f o
Article history: Received 7 December 2016 Received in revised form 8 March 2017 Accepted 13 June 2017
Keywords: Group decision-making Risk assessment Fuzzy set theory Landing system FMEA
a b s t r a c t This is an obvious fact that a significant number of accidents happening each year are due to the failure of aircraft systems’ components. To manage this risk, Failure Mode and Effects Analysis (FMEA), a wellknown method, is employed for reliability analysis in the mentioned fields. Three elements; Severity (S), Detection (D) and Occurrence (O) are considered in typical FMEA to calculate the Risk Priority Number (RPN) for concentrating on the risks and taking corrective actions. The significant numbers of shortcoming which have mentioned in literature can be faced to crisp RPN computation. Therefore, the purpose of this study was to extend FMEA by considering a group decision-making under the fuzzy environment. In fact, the present study was designed to contribute both theoretically and practically contributes to aircraft landing system as one of the important potential failure mode in aerospace industry. In an engineer standpoint the comparison of results between the conventional FMEA and Fuzzy Developed FMEA (FDFMEA) suggests that the risky failure modes accompanied with FDFMEA yield a more reliable result. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Nowadays, reliability and safety guarantee have been of increasing concern in Iranian Airlines company (Mahan Airline, 2015). FMEA as an inductive technique in nature can be applied in all aspects of failure analysis and tends to prepare information for risk management procedure (Modarres, 1993). It has been used in many different kinds of industry such as nuclear, chemical, electronics, and mechanical (Liu et al., 2013). FMEA was initially introduced in the 1940s by the U.S military, which published ‘‘MIL–P–1629” as a safety standard in 1949 (US Department of Defence, 1980). This technique was first developed in 1960s contractors for the U.S. National Aeronautics and Space Administration (NASA) due to aerospace industry, then it used to tolerate risk for Apollo mission to analyze failures on mission success (Bowles and Peláez, 1995; Carlson, 2012). Over the years, many variations of the conventional FMEA have been carried out. A primary discussion of failure analysis which employs a single matrix to system modeling has been performed by Kara-Zaitri et al. (1992). Later that, Bell studied a stochastic model of FMEA (Bell et al., n.d.). Wang and Ruxton (1996) ⇑ Corresponding author. E-mail addresses: [email protected] (M. Yazdi), sahand.daneshvar@ emu.edu.tr (S. Daneshvar), [email protected] (H. Setareh). http://dx.doi.org/10.1016/j.ssci.2017.06.009 0925-7535/Ó 2017 Elsevier Ltd. All rights reserved.
represent an approach in order to combine the Boolean Representation Method (BRM) and FMEA. However, along all studies based on conventional FMEA technique, it still imposes many common shortages in order to compute Risk Priority Number (RPN ¼ S O D), which is the product of the Severity (S), Detection (D) and Occurrence (O). The different combination of S, O and D might be found out in the same value of RPN. As an example, three types of failure modes with value of (10, 3, 8); (6, 8, 5) and (4, 6, 10) for S, O and D, respectively, have the same RPN = 240. Different combination causes of the conventional FMEA technique cannot recognize the hidden risk implications. Also, conventional FMEA considers the importance of the elements S, O and D with the same weight which is not effective in practical FMEA study. Besides, RPN value can be generated just 120 of the 1000 numbers from the production of elements. It means that the crisp value of RPN is not continues and there are limited numbers to prioritize the failure modes. Moreover, it is possible the assessors face by many lack of data and ambiguous information in conventional FMEA. For this reason finding the exact value of RPN needs the linguistic expressions including High, Low and Medium (Liu, 2016; Wang et al., 2009). To eliminate the aforementioned limitations the fuzzy set theory as a computational intelligence has been proposed. The formal introduction of fuzzy set theory is formulized by Prof. Zadeh in the early 1960s. Fuzzy set is a class of objects with degree of
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membership which is in interval zero and one (Zadeh, 1965). The notable point of fuzzy set is that they are more close to ambiguity which is based on approximation rather than preciseness (Gul and Guneri, 2016; Hong et al., 2016; Markowski and Mannan, 2009; Rajakarunakaran et al., 2015). Over the years, many applications of Fuzzy Developed FMEA (FDFMEA) have been applied in a verity of engineering fields to eliminate the mentioned drawbacks. Wang et al. (2009) estimate the occurrence probability by using expert opinion based on trapezoidal set and they develop it to the other risk parameters. In parallel way a fuzzy expressions is used by Kahraman et al. (2013) in order to prioritize healthcare issues. Besides, a new model based on (a) level was introduced by Hadi-Vencheh and Aghajani (2013). In this study the failure elements are demonstrated by linguistic expressions. Mandal and Maiti (2014) applied fuzzy set theory for risk assessment with using similarity value and possibility approach. In another study, failure analysis is done by employing fuzzy membership function by Helvacioglu and Ozen (2014) to find out the critical failures during yacht design. Also, Dag˘suyu et al. (2016) clarified the utilization conventional and fuzzy FMEA in failure analysis in sterilization plant. Despite all researches, there are rare studies to compare the conventional model and new one as FDFMEA on aircraft landing system. The purpose of this research is reaching to proper comparison based on reliability analysis between classical FMEA and developed FMEA under the fuzzy environment in aircraft landing system. In order to rank the identified failure modes, four experts who have experience and technical knowledge in this field participated in the study. The rest of paper is ordered as follows. After reviewing the proposed model in details in Section 2, FDFMEA will be applied on air craft landing system as case of study in Section 3. Finally, conclusion part will be explained in Section 4.
recognize the priority of corrective actions for improving the safety performance of components or subsystems. The description of these elements is provided as follows: Severity is generally figured out due to the enthusiasm of failure mode effect toward level including user or system. The effects of a specified failure mode are commonly demonstrated by user when they can be found out by them. For instance, a few ordinary failure effects for special pump which is installed in high-tech industry are: excessive vibration, noise and periodic leakage. Occurrence as a second element is usually assessed pursuant to the failure probability, which illustrates the proper number of failure predicted in the entire life of a specified item. In other words, the rating is founded on the predicted failure frequency. Also the last one, detectability is an identifying method and amends preparation(s) for each failure rate. All in all, Tables 1–3 as a guide represent the ranking of severity, occurrence and decidability elements respectively and also provide the linguistic expression and corresponding Fuzzy membership function (Chen and Hwang, 1992a; Modarres et al., 1999). The membership function can be defined for both trapezoidal and triangular fuzzy numbers as follows (Ramzali et al., 2015): ~ = (a1, a2, a3) (a) In triangular form, A
8 0; > > < xa1 ; 1 V i ðxÞ ¼ aa23a x > ; > : a3 a2 0;
9 x < a1 > > a1 6 x 6 a2 = a2 6 x 6 a3 > > ; x > a3
2. Methodology 2.1. The proposed model The structure of the proposed model is arisen from the set of Fuzzy theory and also the qualitative opinions which are extracted by experts’ judgment for purpose of satisfy the FMEA quantifiable ability. The novel model framework is extended in various steps which are merged from conventional FMEA and new one. First of all, like as all FMEA studies the component and process information should be collected. Secondly, the potential failure modes should be determined. Thirdly, at the same time the effects and causes of each failure and also current control process should be found out. Fourthly, expert judgments opinion is considered in order to find detectability, probability and severity of failure mode. Also, their opinion should be transfer to Fuzzy membership function, and the set of Fuzzy numbers are used in order to rate the opinions. Fifthly, aggregation process is applied through which all detectability; occurrence probability and severity rate are collected using linguistic expressions by employing experts’ opinions. Sixthly, defuzzification procedure is done by using a proper algorithm in order to convert the experts’ judgments (Fuzzy Possibility) to corresponding crisp possibility (CCP). Seventhly, RPN should calculate in this step. Finally, in order to report FMEA, necessity of correction actions for high amount of RPN should be considered. The framework of proposed model is provided in Fig. 1. As outline with accordance to conventional FMEA method, each failure mode is computed by three elements including severity (S), probability of occurrence (O) and obstacle of detectability (D). The amounts of these elements are provided between 1 (being the best case) and 10 (being the worst case) similar to Likert’s scale (Liu et al., 2013). Additionally, the amount of RPN helps assessors to
~ = (a1, a2, a3, a4) (b) In trapezoidal form, A
8 0; > > xa > > < a2 a11 ; V i ðxÞ ¼ 1; > x > ; > aa44a > 3 : 0;
9 x < a1 > > > a1 6 x 6 a2 > = a2 6 x 6 a3 > a3 6 x 6 a4 > > > ; x > a4
Due to the transfer linguistic expression to their corresponding fuzzy numbers, Chen and Hwang (1992a) presented a numerical approximation. To achieve this criterion, there are common verbal expressions in the system. According to Miller (1956), Nicolis and Tsuda (1985) scale one includes 2 verbal expressions (linguistic expression) and also scales eight includes 13 verbal expressions (linguistic expression). Chen’s transformation scale is shown in Table 4. Additionally, Yazdi et al. (2017) discussed that the generic estimation of human memory aptitude is seven plus-minus two patches. This notice means that the proper number of linguistic expression for human character to make a suitable judgment is between five and nine.
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Collect component and process function information
Determine potential failure modes
List current control process
Determine the cause of each failure
Determine the effects of each failure
Find detectability ranking (D)
Find probability occurrence ranking (O)
Find severity ranking (S) Aggregating Data
Collecting expert opinions and transferring into Fuzzy membership function
Procedure of Defuzzfing for S,O,D
Calculate RPN
No Correction required?
Yes FMEA Report
Recommended corrective actions
Modification Data Modifications
Fig. 1. Framework of proposed Fuzzy FMEA model.
Table 1 Severity evaluation element. Rank
Effect
Criteria
Linguistic expression
Corresponding Fuzzy number
9, 7, 4, 2, 1
Very High High Moderate Low Minor
According to this failure mode, death or mission losses occur. Severe injury, damage or incompleteness on mission may occurred by effect of failure mode. Loss of function by system or component may occur. Minor injury or depreciation in system performance. Usually injury or depreciation in system performance does not occur.
Very High High Medium Low Very low
(0.8, 0.9, 1, 1) (0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0.1, 0.3, 0.5) (0, 0, 0.1, 0.2)
10 8 5, 6 3
Table 2 Probability of occurrence evaluation element. Rank
Likelihood
Criteria
Predicted failure frequency
Linguistic expression
Corresponding Fuzzy number
10 9 8 7 6 5 4 3 2 1
Very High
Failure is almost unavoidable
Very High
(0.8, 0.9, 1, 1)
High
Repeated failures
High
(0.6, 0.75, 0.9)
Moderate
Occasional failures
Medium
(0.3, 0.5, 0.7)
Low
Rare failures
Low
(0.1, 0.3, 0.5)
Remote
Failure is unlikely
>1 in 2 1 in 8 1 in 20 1 in 40 1 in 80 1 in 400 1 in 1000 1 in 4000 1 in 20000 <1 in 106
Very low
(0, 0, 0.1, 0.2)
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M. Yazdi et al. / Safety Science 98 (2017) 113–123
Table 3 Detectability evaluation element. Rank
Detectability
Criteria
10 9 7, 8 5, 6 3, 4 1, 2
Non-detection Very low Low Moderate High Very High
Program Program Program Program Program Program
control or any user cannot detect a potential cause or failure mode. control or user will not detect a potential cause or failure mode. control or user is not likely to detect a potential cause or failure mode. control or user may detect a potential cause or failure mode. control or user has a proper chance of detecting a potential cause or failure mode. control or user will almost certainly detect a potential cause or failure mode.
Linguistic expression
Corresponding Fuzzy number
None Very low Low Medium High Very High
(0.8, 0.9, 1) (0, 0.1, 0.2) (0.5, 0.7, 0.9) (0.3, 0.5, 0.7) (0.1,0.3,0.5) (0,0,0.1)
Table 4 Linguistic expressions and their corresponding fuzzy numbers (Chen and Hwang, 1992b). Linguistic expressions None Very low Low-Very Low Fairly low Mol. Low Medium Mol. High Fairly High High High-Very High Very High Excellent Mol.: More or less.
Scale 1
Scale 2
Scale 3
Scale 4
Scale 5
(0, 0, 0.2) (0, 0, 0.2, 0.4)
(0.1, 0.2, 0.3)
(0, 0, 0.3) (0, 0.25, 0.5)
(0.4, 0.6, 0.8)
(0.2, 0.5, 0.8)
(0.3, 0.5, 0.7)
(0.3, 0.5, 0.7)
(0.6, 0.8, 1)
(0.6, 0.8, 1, 1)
(0.6, 0.8, 1)
(0.5, 0.75, 1) (0.7, 1, 1)
(0.8, 1, 1)
For this purpose, transferring scale of six which includes 5 verbal expressions is chosen to fulfilling the intellectual assessment for finding the severity and occurrence elements and also scale eight which includes 13 verbal expressions is used for detectability evaluation element. Table 4 presents completely the fuzzy membership numbers in the form of trapezoidal numbers. Moreover, Preyssl (1995) made clear that there are mainly three ways including: statistical, extrapolation and expert judgment method that could be engaged to compute the amount of S, O and D. The statistical method includes the conduct of shortest test of practical data and the estimating of aforementioned elements. The other method is extrapolation method which contains the usage of guessing model and equal circumstance, and the last one is expert judgment method in which direct estimated amount of S, O and D is implicated by specialists. Thus, in this study the expert judgment is employed in order to identify the estimated amount of S, O and D. Through expert judgment, specialists express their opinions about each S, O and D based on each intellectual characteristic. Expert elicitation is the combination of specialists’ opinions about a subject when there is a lack or limited resources due to physical limitations. Experts’ elicitation is, in fact, a fundamental scientific solidarity methodology. It is usually applied to the study when infrequent events exist. Besides, expert elicitation usually quantifies uncertainty by allowing specialists to parameterize an educated guess. Expert Judgment method has been applied according to much regularity. Some of the main important fields related to probability elicitation are risk analysis, psychology, philosophy, decision examination, mathematics and Bayesian statistics. Quantification of characteristic is engaged in different conditions: Evidence is unfinished because it could not be practically attained.
Scale 6
(0, 0, 0.1, 0.2)
(0, 0, 0.1, 0.2)
(0, 0.2, 0.4) (0.2, 0.4, 0.6)
(0.1, 0.25, 0.4)
(0.3, 0.5, 0.7) (0.4, 0.6, 0.8) (0.6, 0.75, 0.9)
(0.6, 0.75, 0.9)
(0.8, 0.9, 1, 1)
(0.8, 0.9, 1, 1)
Scale 7 (0, 0, 0.2) (0, 0, 0.1, 0.3) (0, 0.2, 0.4) (0.2, 0.35, 0.5) (0.3, 0.5, 0.7) (0.5, 0.65, 0.8) (0.6, 0.8, 1) (0.7, 0.9, 1, 1) (0.8, 1, 1)
Scale 8 (0, 0, 0.1) (0, 0.1, 0.2) (0.1, 0.2, 0.3) (0.1, 0.3, 0.5) (0.3, 0.4, 0.5) (0.4, 0.45, 0.5) (0.3, 0.5, 0.7) (0.5, 0.55, 0.6) (0.5, 0.6, 0.7) (0.5, 0.7, 0.9) (0.7, 0.8, 0.9) (0.8, 0.9, 1) (0.9, 1, 1)
Data could be found out just for analogous circumstances. There are contradictory models or data references. Scaling up from experimentations to physical objective procedures is not direct (scaling of mean values is usually simpler than rescaling the uncertainties). When the uncertainties are substantial comparative to the demonstration of obedience (Kotra et al., 1996). Expert knowledge is affected by individual visions and purposes (Ford and Sterman, 1998). Thus, it is very difficult to assess the complete impartiality of expert knowledge. The main challenge is the selection of heterogeneous specialists (e.g., either scientists or workers) and homogenous specialists (it just includes scientists). Individual experience on expert judgment is presumed to be smaller in the homogeneous group as compared to the heterogeneous one as a result of experience differences. Therefore, by considering all possible opinions, a group of heterogeneous specialists could have a privilege over the homogeneous group. Moreover, the weights of experts are different, so in real life, the heterogeneous group is more realistic (Helvacioglu and Ozen, 2014). The criteria to recognize experts are established as follows: First one is the period of learning and experience of the experts in their exact field that affects their judgmental and logical behavior. Second is the individual conditions in which the experience is obtained including practical and theoretical conditions. In this study, a heterogeneous group of experts is chosen for estimating the amount of S, O and D. Accordingly, for qualifying the measurements, the importance of experts was measured to deal with the uncertainty and lack of sufficient data. In order to the score quality of an expert, the following qualities were considered: professional position, job experience, education level and age (Miri Lavasani et al., 2011; Omidvari et al., 2014). The score rating of experts are examined according to Table 5. The rating of expert judgment can be done according to the weight given to each element. The concept of linguistic expressions
M. Yazdi et al. / Safety Science 98 (2017) 113–123
117
Item
Categorize
Score
of linguistic variables. The linguistic expressions can be transferred to the corresponding fuzzy numbers. The procedure is explained in detail in what follows:
Profession position
Higher-ranking academic Low-ranking academic Engineer Technician Worker
5 4 3 2 1
1. Computing the degree of similarity (degree of agreement). ~u; R ~ v Þ is defined as opinions between each pair of experts Suv ðR ~u; R ~ v Þ when Eu and Ev . According to this consideration for Suv ðR
Job Tenure
More than 30 years 20–29 10–19 6–9 5
5 4 3 2 1
Education
PhD Master Bachelor Higher National Diploma (HND) School level
5 4 3 2 1
More than 50 40–49 30–39 Less than 30
4 3 2 1
Table 5 Score rating according to expert’s traits.
Age
~ = (a1, a2, a3) and B e = (b1, b2, b3) are two standard triangular A fuzzy numbers, then the degree of agreement function of S is defined as:
~ BÞ ~ ¼1 SðA;
1 XJ jai bi j i¼1 J
ð1Þ
~ BÞ ~ BÞ ~ 2 [0, 1], the greater value of S (A, ~ is the best simWhen SðA; ~ and B. ~ Moreover, the ilarity between two fuzzy numbers of A amount of J is 3 and 4 for triangular and trapezoidal fuzzy number respectively. 2. Next it is computing the Average of Agreement (AA) degree AAðEu Þ of the expert’s opinions.
has a high value in dealing with any circumstances which are illdefined or complex to be described in the old model of quantitative expression (Zadeh, 1965).
AAðEu Þ ¼
1 XJ ~ ~ u–v SðRu; Rv Þ J1 v¼1
ð2Þ
3. Computing the Relative Agreement (RA) degree, RAðEu Þ of the experts.
2.2. Aggregating data It is vital to aggregate expert’s opinion to attain a deal because each expert might have a variety of opinions according to her/his knowledge and experiences in the pertinent scope. According to many studies, there are many methods available for aggregation of the expert opinions including max–min Delphi method, arithmetic averaging operation, voting, game theory, TOPSIS, fuzzy priority relations, fuzzy Delphi method, etc.; however, Liu et al. (2014) found that no stable and definite theoretical guidance could be employed to select the most appropriate opinion. In order to collect linguistic expressions, a novel procedure is offered for both homogenous and heterogeneous group of experts (Lee, 2001). Aqlan et al.’s model which is the use of triangle fuzzy numbers whereas Hsu et al.’s model is based on collecting triangle and trapezoidal fuzzy numbers (Similarity Aggregation Method – SAM) (Aqlan and Mustafa Ali, 2014). The linguistic expression of this study is a combination of both methods. Hence, Hsu et al.’s procedure is employed in this study in order to aggregate the expert opinions (Hsu and Chen, 1996) (see Fig. 2). Suppose that each expert, Ej (k = 1, 2, . . ., n) states his attitude about a certain feature in a specific context by a predefined set
1. Computing the degree of similarity between two kind of expert for each basic event
AAðEu Þ Eu ðu ¼ 1; 2; . . . ; JÞ as RAðEu Þ ¼ PJ u¼1 AAðEu Þ
ð3Þ
4. Estimate the Consensus Coefficient (CC) degree, CCðEu Þ of expert’s opinions, Eu ðu ¼ 1; 2; . . . ; JÞ:
CCðEu Þ ¼ b WðEu Þ þ ð1 bÞ RAðEu Þ
ð4Þ
where WðEu Þ is the weight of each expert and b is the weight of each term, nominated as a relaxation factor of the offered procedure due to b (0 b 1). It illustrates the importance of W (Eu ) over RA (Eu ). When b = 0, no weight has been given to it by experts and thereby a homogenous group of experts should be employed whereas when b = 1, signifies that the consensus degree of an expert is equal to its importance weight. The result of Hsu et al.’s study suggested that the consensus coefficient of each expert is better known when the comparative competency of each expert’s opinion is estimated. Therefore, it has an important part for the decision maker to allocate a proper amount of b (Hsu and Chen, 1996). However, the result Ölçer and Odabasßi (2005) represents that the b coefficient is not sensitive
2. Computing the degree of agreement between two kind of expert
4. Computing the consensus degree of coefficient
3. Computing the relative degree of agreement between two kind of expert
5. Computing the aggregation result base on expert opinion
Fig. 2. The steps of aggregating data.
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M. Yazdi et al. / Safety Science 98 (2017) 113–123
on fuzzy multiple attribute decision-making which is applied on propulsion system Turkish maritime. ~ AG , 5. Finally, the aggregated result of the experts’ judgment R could be found out as follows:
~ AG ¼ CCðE1 Þ R ~ 2 CCðE2 Þ R ~ 2 CCðEm Þ R ~M R
ð5Þ
Where sign is fuzzy addition and is fuzzy scalar multiplication operator. Additionally (Kaufmann and Gupta, 1985) represented that the fuzzy operations of trapezoidal fuzzy member are trapezoidal fuzzy member. 2.3. Defuzzification procedure Defuzzification procedure is a quantifiable outcome of Fuzzy theory according to process of making. Zhao and Govind (1991) mentioned that there are many defuzzification issues appearing by the application of fuzzy control into the industrial processes. Thus, Fuzzy numbers in defuzzification procedure has high significant role for decision making in Fuzzy area. Runkler and Glesner (1993) discussed about several procedures which have been developed in recent years including Center Algorithm and Weighted Mean of Maximum. Also they noticed that none of procedures are the proper for all applications. The gravity or center of defuzzification environment technique is employed in this study. Also, this is a common and accurate for our purpose. This method was extended by Sugeno et al. (1999). Eq. (6) mathematically represents this technique:
R ti ðxÞxdx X ¼ R ti ðxÞdx
ð6Þ
where X⁄ = Defuzzified output; ti ðxÞ ¼ Aggregated membership function; x = output variable. Eq. (6) could be engaged to both trapezoidal and triangular fuzzy numbers and it is shown as:
RPNT ¼
n X RPNTj ;
j ¼ 1; 2; . . . ; n
ð9Þ
j¼1
where RPNT is the total RPN score for Tth component or subsystem, RPNTj illustrates the RPN score which is jth failure in Tth component or subsystem, Also j means that the number of failure mode in specified component or subsystem. Thus, considering the RPN score, the importance of each failure mode can be found out in order to prioritize for corrective actions. Additionally, according to ‘‘MIL-STD1629A” as a standard safety, a rule of thumb for controlling or eliminating the specified failure mode is attending to RPNs > 125 (Ayyub, 2014). But this standard was canceled without replacement in 1998, nevertheless remains in wide use for industry applications today (Department of Defense of the USA, 1998). 3. Result In order to explain the proposed method clearly, the detail of one of the numeric failure mode (A simplest aircraft landing system) is chosen as a case of study, because in recent years many accidents related to landing systems are reported by Iranian airlines (Mahan Airline, 2015). As it shows in Fig. 3 with pressing GDnB and GupB the gear come down and rise respectively. Switch (S1) send a signal to computer (C) during raising the gear (otherwise a fault signal is sent). In opposite side, when the gear are coming down the switch (S2) sends a signal to the computer (otherwise a fault signal is sent). Task switches is finding information about the actual location of the landing gear and stopping inconsistent commands. Additionally, Sco is a switch for controlling the gear. The main performances of aircraft landing systems for both types of operation (hardware and software) are provided as follows: Raising gear Coming down gear
~ = (a1, a2, a3) is: Defuzzification of triangular fuzzy number A
R a2
X ¼
xa2 xdx a1 a2 a1 R a2 xa2 dx a1 a2 a1
þ þ
R a3 a
R a23 a2
a3 x a3 a2 a3 x a3 a2
xdx dx
¼
1 ða1 þ a2 þ a3 Þ 3
GDnB
ð7Þ Computer (C)
~ = (a1, a2, a3, a4) Defuzzification of trapezoidal fuzzy number A can be gained by Eq. (8).
R a2 X ¼ ¼
Ra Ra xa1 xdx þ a23 xdx þ a34 a1 a2 a1 R a2 xa1 R a3 R a4 dx þ a2 dx þ a3 a1 a2 a1
GUpB
a4 x xdx a4 a3 a4 x dx a4 a3
1 ða4 þ a3 Þ2 a4 a3 ða1 þ a2 Þ2 þ a1 a2 3 ða4 þ a3 a1 a2 Þ
S co
Gear up
ð8Þ
So, as aforementioned earlier in order to use intellectual assessment the linguistic expression transferred to corresponding fuzzy numbers which is between zero and one while each elements of conventional FMEA established in interval [1,10]. Therefore, the last step of defuzzification procedure is multiplying each element to 10.
S1
S2 Switch Button
2.4. Compute RPN score The score of RPN could be presented as a criterion assessment in order to prioritize the higher risk failure modes. Moreover, if any subsystem available the total RPN should be computed as follows:
Gear Down Fig. 3. Simplest aircraft landing system (Ericson, 2005).
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M. Yazdi et al. / Safety Science 98 (2017) 113–123 Table 6 FMEA of the aircraft landing system. Process step
Potential cause (s)/failure mechanism
Detection Current design practice or process control
Initial effort computation of RPN
Software fault, fault in in the wiring of computer Software fault
Sensor
None
48
Sensor
None
84
Software fault, fault in in the wiring of computer Unknown Damage caused by the pressure Software fault and tension
Sensor
None
84
Sensor
None
84
None
180
None
180
None
18
None
18
None
12
None
12
Potential failure modes Failure rate
Potential effect(s) of failure
Expert knowledge for Aircraft landing system (Naftair Airline, 2015) FM1A Raising Gear Fault in raising the Unknown Extension system damage of wheels aircraft, taking off with open wheels. FM1B Raising wheels earlier Unknown Aircraft damaged on landing. than specified time FM2A Coming down Gear Fault in coming down Unknown Landing with closed wheels, the wheels Aircraft damaged on landing FM2B
Coming down wheels earlier than specified time FM3A Automatically test Fault on the run
Unknown Possible unsafe conditions
FM3B
Wrong run
Unknown Possible unsafe conditions
FM4A Fault reporting system FM4B
Fault on the run
Unknown Fault information was not reported, Without risk Unknown Fault information was reported mistakenly, Without risk Unknown Failure to register unsafe situation, Without risk Unknown Register unsafe situation mistakenly, Without risk
Wrong run Fault on the run
FM5A Record the result of automatically FM5B test
Wrong run
Software and electronic None fault Software and electronic None fault Software fault Pilot Report Software fault Pilot Report Software fault Data analysis Software fault Data analysis
Table 7 Expert weighting of group decision-making. Expert Expert Expert Expert Expert
1: 2: 3: 4:
Total
Profession position
Job experience
Education
Age
Weighting score
Engineer (3) Low-ranking academic(4) Higher-ranking academic(5) Engineer (3)
5 (1) 10–19 (3) 10–19 (3) 20–29 (4)
Master (4) Master (4) PhD (5) Bachelor (3)
28 39 44 56
0.17 0.25 0.31 0.27
15
11
16
10
(1) (2) (3) (4)
52/52 = 1
Table 8 Corresponding fuzzy numbers for each expert opinion. FM1A
FM1B
FM2A
FM2B
FM3A
FM3B
FM4A
FM4B
FM5A
FM5B
Expert 1 Severity Occurrence Detection
(0.3, 0.5, 0.7) (0.3, 0.5, 0.7) (0, 0, 1)
(0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0, 0, 1)
(0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0, 0, 1)
(0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0.8, 0.9, 1, 1) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
Expert 2 Severity Occurrence Detection
(0.3, 0.5, 0.7) (0.3, 0.5, 0.7) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.3, 0.5, 0.7) (0, 0, 1)
(0.6, 0.75, 0.9) (0.6, 0.75, 0.9) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.3, 0.5, 0.7) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0.8, 0.9, 1, 1) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
Expert 3 Severity Occurrence Detection
(0.6, 0.75, 0.9) (0.1, 0.3, 0.5) (0, 0, 1)
(0.6, 0.75, 0.9) (0.6, 0.75, 0.9) (0, 0, 1)
(0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0, 0, 1)
(0.3, 0.5, 0.7) (0.6, 0.75, 0.9) (0, 0, 1)
(0.3, 0.5, 0.7) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0.8, 0.9, 1, 1) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0, 0, 1)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0, 0, 1)
(0, 0, 0.1, 0.2) (0.6, 0.75, 0.9) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
Expert 4 Severity Occurrence Detection
(0.6, 0.75, 0.9) (0.1, 0.3, 0.5) (0, 0, 1)
(0.3, 0.5, 0.7) (0.6, 0.75, 0.9) (0, 0, 1)
(0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.6, 0.75, 0.9) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.6, 0.75, 0.9) (0.8, 0.9, 1)
(0.8, 0.9, 1, 1) (0.3, 0.5, 0.7) (0.8, 0.9, 1)
(0.8, 0.9, 1, 1) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.6, 0.75, 0.9) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.6, 0.75, 0.9) (0, 0, 1)
(0, 0, 0.1, 0.2) (0.6, 0.75, 0.9) (0, 0, 1)
Automatically test Fault reporting system Record the result of automatically test According to Fig. 3, the traditional FMEA table of failure modes is provided in Table 6. Here, the process steps denoted as FM1A, FM1B etc. and also RPN scores are computed as the initial effort. FMEA sheet (Table 6) is completed by Naftair Airline’s experts
and five process steps is only chosen for applying the proposed model to find out the effectiveness of new approach. As it mentioned earlier, in order to accomplish judgment for each elements of FMEA, a heterogeneous group of experts is engaged. Due to Table 5, it is so clear that the weights of experts are not same. Table 7 shows the experts’ weights which are used. In this study, four experts are participating to accomplish the judgments. Two of them have master in safety engineering and have
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M. Yazdi et al. / Safety Science 98 (2017) 113–123
trainer for aerospace industries since 2006. The last one is an engineer who published several papers and books related to safety and reliability analysis and he has been working at reliability center more than 20 years. Additionally, according to Tables 1–3 the fuzzy corresponding numbers are illustrated in Table 8, which are based on the expert’s opinion. FM1B is taken as an example to detailed aggregation computations for element S. The details are provided in Table 9. To compute consensus coefficient (Eq. (4)), relaxation factor (b) is considered 0.5 according to the type of their work. Eqs. (7) and (8) are employed to defuzzify of each failure modes. The computation of FM1B for element S is done as an example and the results of other failure modes, having crisp values with three decimal places are provided in Table 10.
Table 9 Aggregation computations for the FM1B (Element S). Expert 1 Expert 2 Expert 3 Expert 4 S(E1&E2)
(0.6, 0.75, 0.75, 0.9) (0.8, 0.9, 1, 1) (0.6, 0.75, 0.75, 0.9) (0.3, 0.5, 0.5, 0.7) ~ BÞ ~ ¼ 1 1 PJ 0.85 SðA;
S(E1&E3) S(E1&E4) S(E2&E3) S(E2&E4) S(E3&E4) AA(E1)
1 SE1;E2 ¼ 1 1=4 ð0:2 þ 0:15 þ 0:25 þ 0Þ = 0.85 0.75 0.825 0.575 0.75 ~ R ~v Þ 0.86 AAðEu Þ ¼ 1 PJu–v SðRu; J1
AA(E2) AA(E3) AA(E4) RA(E1)
0.75 1=ð4 1Þ ð0:85 þ 1 þ 0:75Þ ¼ 0:858 0.858 0.69 uÞ 0.27 RAðEu Þ ¼ PAAðE J
J
i¼1
jai bi j
v ¼1
u¼1
RA(E2) RA(E3) RA(E4) CC(E1) CC(E2) CC(E3) CC(E4) Aggregation for FM1B
X ¼
AAðEu Þ
0.23 0:86=ð0:86 þ 0:75 þ 0:858 þ 0:69Þ ¼ 0:27 0.27 0.21 0.22 CCðEu Þ ¼ b WðEu Þ þ ð1 bÞ RAðEu Þb = 0.5 0.24 0.5 0.17 + 0.5 0.27 = 0.22 0.29 0.24 ~ AG ¼ CCðE1 Þ R ~ 1 CCðE2 Þ R ~ 2 CCðEm Þ R ~M R
1 ð0:875 þ 0:749Þ2 ð0:875 0:749Þ ð0:575 þ 0:725Þ2 þ ð0:575 0:725Þ 3 ð0:875 þ 0:749 0:575 0:725Þ
¼ 0:729
The last step of defuzzification is multiplying X to 10.
X 10 ¼ 7:29 As aforementioned earlier the purpose of this study is to develop FMEA technique for aircraft landing systems. In order to reach this aim, one of the simplified aircraft landing systems is chosen as an application. The limitations of conventional RPN score actuate to new ranking method for the failure modes, which is FDFMEA. The score of RPN ranking for both conventional and fuzzy developed FMEA are provided in Table 11. To make more comprehensi-
0.22 (0.6,0.75,0.75,0.9) 0.24 (0.8,0.9,1,1) 0.29 (0.6,0.75,0.75,0.9) 0.24 (0.3,0.5,0.5,0.7) = (0.575,0.725,0.749,0.875)
been working as a risk assessor and safety auditor in varieties of industry more than four years. The third expert has a PhD in aerospace engineering and also has been working as consultant and Table 10 Defuzzified failure mode elements for aircraft landing system.
Severity Occurrence Detection Developed RPN Developed RPNa a
FM1A
FM1B
FM2A
FM2B
FM3A
FM3B
FM4A
FM4B
FM5A
FM5B
6.35 3.92 3.33 83 84
7.30 6.66 3.33 162 163
7.50 6.10 3.33 152 154
7.74 6.35 3.33 164 165
8.17 4.01 9.00 295 298
9.22 3.49 9.00 290 293
2.20 5.00 4.59 50 51
0.78 5.61 4.62 20 20
0.78 6.35 0.462 23 23
0.78 4.05 3.97 13 13
With considering elements weight S, O and D according to 1.01, 1 and 1 respectively.
Table 11 Ranking of the alternative for aircraft landing system. FM1A
FM1B
FM2A
FM2B
FM3A
FM3B
FM4A
FM4B
FM5A
FM5B
48 3 83 6
84 2 162 4
84 2 152 5
84 2 164 3
180 1 295 1
180 1 290 2
18 4 50 7
18 4 20 9
12 5 23 8
12 5 13 10
RPN Score
Conventional RPN Priority Rank Developed RPN Priority Rank
500 450 400 350 300 250 200 150 100 50 0 FM5B
FM4B
FM5A
FM4A
FM1A
Conventional RPN
FM2A
FM1B
Developed RPN
Fig. 4. Ranking of RPN score.
FM2B
FM3B
FM3A
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M. Yazdi et al. / Safety Science 98 (2017) 113–123
which is based on fuzzy method. However, FDFMEA ranks the high risky failure mode as ‘‘Fault on the run of automatically test (FM3A)”. Wrong run (FM3B) is ranked as second high RPN score whilst the element S in mentioned failure mode is more than specified element in FM3A (see Table 9). Therefore, considering the important weight of elements the FM3B has priority due to corrective actions. Additionally, it can find which sub-system has highest RPN score. Thus, the failure modes with higher RPN score are consid-
ble comparison as well as the most and least risky RPN score can be figured out from Fig. 4. According to results of RPN Ranking, all scores have been increased in FDFMEA technique in compression to conventional FMEA. Also, Developed RPN computation covers the different combination shortage of conventional RPN (FM2A, FM1B and FM2B in conventional RPN are same whereas in developed one are different). ‘‘Wrong run for registering the result of automatically test (FM5B)” is chosen as minor risky failure mode as ranked by RPN Table 12 RPN scores according to beta values. Beta coefficients
Failure modes
FM5B FM4B FM5A FM4A FM1A FM2A FM1B FM2B FM3B FM3A
0.1
0.3
0.5
0.7
0.9
23 26 26 38 83 139 153 162 280 283
26 26 29 49 83 139 153 162 281 304
13 20 23 50 83 152 162 164 290 295
22 26 25 47 83 140 154 162 284 291
21 22 25 57 83 140 155 161 286 293
350 300
Beta
RPN Scores
250
0.1
200
0.3 150
0.5 0.7
100
0.9 50 0 FM5B
FM4B
FM5A
FM4A
FM1A
FM2A
FM1B
FM2B
FM3B
FM3A
Filure modes Fig. 5. Sensitivity according to beta coefficient.
350 300
RPN Scores
250
Beta 0.1
200
0.3 150
0.5 0.7
100
0.9
50 0 FM5B
FM4B
FM5A
FM4A
FM1A
FM2A
FM1B
FM2B
FM3B
FM3A
Failure modes Fig. 6. Sensitivity according to beta coefficient for all identified failure modes.
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ered to be more important and will be given higher priorities for future corrective actions. Accordingly, as mentioned in methodology part, a common rule to control or eliminate the failure modes is attending to RPNs > 125. Therefore, in conventional FMEA, there are only two failure modes which need corrective actions whereas in new approach, five failure modes have been found out for further actions. From mentioned case of study for comparison two specified technique, it is clear that the ranking of FDFMEA is more perceptible in case of engineering purpose. Moreover, sensitivity analysis is applied to find out the beta effect on the RPN scores. Beta values are selected as a set of 0.1, 0.3, 0.5, 0,7 and 0.9 which is provided in Table 12. The result of sensitivity analysis represents that this case is not sensitive for beta coefficient. Fig. 5 illustrates that the RPN scores have not sensible change for all identified failure modes in different beta values. According to Fig. 6, it is obvious that while beta coefficient takes various ranges; the ranking of RPN scores remains the same. 4. Conclusion Failure mode and effects analysis (FMEA) is designed as a powerful tool to measure reliability analysis in widespread engineering fields. In FMEA technique, three elements which are called severity, occurrence and detection used to evaluate the potential failure modes. The risk priority number in classic model is equal to product of crisp value of the elements. However, the limitations of conventional FMEA are recognized during the study. Thus, this paper proposed to assess the risks with a conventional (FMEA) and fuzzy developed FMEA (FDFMEA) method for aircraft landing system. The FDFMEA technique which is used in this study seems to have many benefits because of its superiority over the conventional method. The FDFMEA technique which is applied for aircraft landing system handled the drawbacks of classic model and is sensitive to all inputs including linguistic variable, importance weigh of experts and etc. In comparison of the conventional with new ranking techniques, it is illustrated that the FDFMEA has better results due to the fuzzy set theory which is incorporated with reality. Accordingly, the limitations of this work are that FDFMEA is not so sensitive to relaxation factor in this case and also there is no way to ensure that the purposed aggregation procedure is more reliable. In addition, the complexity and time-consuming computation are reflected as the main limitation of FDFMEA in order to apply for whole of the specified system. Because of rare risk assessment which have been done for aircraft systems, it is recommended to develop these types of study for entire aircraft systems with considering the group decisionmaking methods such as fuzzy hybrid weighted, Grey relational projection, VIKOR, Fuzzy hybrid TOPSIS approach or combination of them. Moreover, it is recommended that the further studies should be done in order to indicate the importance of beta effect on RPN scores and also recognize the major and minor factors of specified case study. Additionally, as a direction for further studies, this approach can be applied for other types of industries such as oil & gas, marine & offshore, and railways. Acknowledgement In this study, authors would like to express their gratitude to the Iranian Naftair airline for supporting to represent failure modes which common occur in aircraft landing system with appoint of decision rules, and also to four experts participated in this study because of their invaluable insights and inputs.
References Aqlan, F., Mustafa Ali, E., 2014. Integrating lean principles and fuzzy bow-tie analysis for risk assessment in chemical industry. J. Loss Prev. Process Ind. 29, 39–48. http://dx.doi.org/10.1016/j.jlp.2014.01.006. Ayyub, B.M., 2014. Risk Analysis in Engineering and Economics, second ed. Bell, D., Cox, L., Jackson, S., Schaefer, P., n.d. Using causal reasoning for automated failure modes and effects analysis (FMEA). In: Annual Reliability and Maintainability Symposium 1992 Proceedings. IEEE, pp. 343–353. http:// dx.doi.org/10.1109/ARMS.1992.187847. Bowles, J.B., Peláez, C.E., 1995. Fuzzy logic prioritization of failures in a system failure mode, effects and criticality analysis. Reliab. Eng. Syst. Saf. 50, 203–213. http://dx.doi.org/10.1016/0951-8320(95)00068-D. Carlson, C. (Carl S.), 2012. Effective FMEAs Achieving Safe, Reliable, and Economical Products and Processes Using Failure Mode and Effects Analysis. John Wiley & Sons. Chen, S.-J., Hwang, C.-L., 1992a. Fuzzy Multiple Attribute Decision Making, Lecture Notes in Economics and Mathematical Systems. Springer, Berlin, Heidelberg. http://dx.doi.org/10.1007/978-3-642-46768-4. Chen, S.-J., Hwang, C.-L., 1992b. Fuzzy Sets and Their Operations. pp. 42–100. http:// dx.doi.org/10.1007/978-3-642-46768-4_3. Dag˘suyu, C., Göçmen, E., Narlı, M., Kokangül, A., 2016. Classical and fuzzy FMEA risk analysis in a sterilization unit. Comput. Ind. Eng. 101, 286–294. http://dx.doi. org/10.1016/j.cie.2016.09.015. Department of Defense of the USA, 1998. Electronic Reliability Design Handbook. Mil. Handb. MIL-HDBK-338B 1046. doi: MIL-HDBK-338B. Ericson, C.A., 2005. Hazard Analysis Techniques for System Safety. John Wiley & Sons Inc., Hoboken, NJ, USA. http://dx.doi.org/10.1002/0471739421. Ford, D.N., Sterman, J.D., 1998. Expert knowledge elicitation to improve formal and mental models. Syst. Dyn. Rev. 14, 309–340. http://dx.doi.org/10.1002/(SICI) 1099-1727(199824)14:4<309::AID-SDR154>3.0.CO;2-5. Gul, M., Guneri, A.F., 2016. A fuzzy multi criteria risk assessment based on decision matrix technique: a case study for aluminum industry. J. Loss Prev. Process Ind. 40, 89–100. http://dx.doi.org/10.1016/j.jlp.2015.11.023. Hadi-Vencheh, a., Aghajani, M., 2013. Failure mode and effects analysis A fuzzy group MCDM approach. J. Soft Comput. Appl. 2013, 1–14. http://dx.doi.org/ 10.5899/2013/jsca-00016. Helvacioglu, S., Ozen, E., 2014. Fuzzy based failure modes and effect analysis for yacht system design. Ocean Eng. 79, 131–141. http://dx.doi.org/10.1016/j. oceaneng.2013.12.015. Hong, Y., Pasman, H.J., Sachdeva, S., Markowski, A.S., Mannan, M.S., 2016. A fuzzy logic and probabilistic hybrid approach to quantify the uncertainty in layer of protection analysis. J. Loss Prev. Process Ind. 43, 10–17. http://dx.doi.org/ 10.1016/j.jlp.2016.04.006. Hsu, Hsi-Mei, Chen, Chen-Tung, 1996. Aggregation of fuzzy opinions under group decision making. Fuzzy Sets Syst. 79, 279–285. http://dx.doi.org/10.1016/01650114(95)00185-9. _ S Kahraman, C., Kaya, I., ß envar, Ö., 2013. Healthcare failure mode and effects analysis under fuzziness. Hum. Ecol. Risk Assess. An Int. J. 19, 538–552. http://dx.doi. org/10.1080/10807039.2012.737753. Kara-Zaitri, C., Keller, A.Z., Fleming, P.V., n.d. A smart failure mode and effect analysis package. In: Annual Reliability and Maintainability Symposium 1992 Proceedings. IEEE, pp. 414–421. http://dx.doi.org/10.1109/ARMS.1992.187857. Kaufmann, A. (Arnold), Gupta, M.M., 1985. Introduction to Fuzzy Arithmetic: Theory and Applications. Van Nostrand Reinhold Co.. Kotra, J.P., Lee, M.P., Eisenberg, N.A., DeWispelare, A.R., 1996. Branch Technical Position on the Use of Expert Elicitation in the High-Level Radioactive Waste Program. Nureg-1563. Lee, H.-S.L.H.-S., 2001. Aggregation of fuzzy opinions under group decision makingnnenvironment. In: 10th IEEE Int. Conf. Fuzzy Syst. (Cat. No.01CH37297) 1, pp. 279–285. http://dx.doi.org/10.1109/FUZZ.2001.1007275. Liu, H., 2016. FMEA Using Uncertainty Theories and MCDM Methods. http://dx.doi. org/10.1007/978-981-10-1466-6. Liu, H.-C., Liu, L., Liu, N., 2013. Risk evaluation approaches in failure mode and effects analysis: a literature review. Exp. Syst. Appl. 40, 828–838. http://dx.doi. org/10.1016/j.eswa.2012.08.010. Liu, Y., Fan, Z.P., Yuan, Y., Li, H., 2014. A FTA-based method for risk decision-making in emergency response. Comput. Oper. Res. 42, 49–57. http://dx.doi.org/ 10.1016/j.cor.2012.08.015. Mahan Airline, 2015. Annualy Report. Tehran. Mandal, S., Maiti, J., 2014. Risk analysis using FMEA: Fuzzy similarity value and possibility theory based approach. Expert Syst. Appl. 41, 3527–3537. http://dx. doi.org/10.1016/j.eswa.2013.10.058. Markowski, A.S., Mannan, M.S., 2009. Fuzzy logic for piping risk assessment (pfLOPA). J. Loss Prev. Process Ind. 22, 921–927. http://dx.doi.org/10.1016/j. jlp.2009.06.011. Miller, G., 1956. The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol. Rev. 101, 343–352. http://dx.doi. org/10.1037/h0043158. Miri Lavasani, M.R., Wang, J., Yang, Z., Finlay, J., 2011. Application of fuzzy fault tree analysis on oil and gas offshore pipelines. Int. J. Mar. Sci. Eng. 1, 29–42. Modarres, M., 1993. What Every Engineer Should Know About Reliability and Risk Analysis. M. Dekker. Modarres, M., Kaminskly, M., Krivtsov, V., 1999. Reliability Engineering and Risk Analysis.
M. Yazdi et al. / Safety Science 98 (2017) 113–123 Naftair Airline, 2015. Risk assessment study. Ahvaz. Nicolis, J.S., Tsuda, I., 1985. Chaotic dynamics of information processing: the ‘‘magic number seven plus-minus two” revisited. Bull. Math. Biol. 47, 343–365. http:// dx.doi.org/10.1007/BF02459921. Ölçer, A.I., Odabasßi, A.Y., 2005. A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem. Eur. J. Oper. Res. 166, 93–114. http://dx.doi.org/10.1016/j. ejor.2004.02.010. Omidvari, M., Lavasani, S.M.R., Mirza, S., 2014. Presenting of failure probability assessment pattern by FTA in Fuzzy logic (case study: Distillation tower unit of oil refinery process). J. Chem. Heal. Saf. 21, 14–22. http://dx.doi.org/10.1016/j. jchas.2014.06.003. Preyssl, C., 1995. Safety risk assessment and management-the ESA approach. Reliab. Eng. Syst. Saf. 49, 303–309. http://dx.doi.org/10.1016/0951-8320(95)00047-6. Rajakarunakaran, S., Maniram Kumar, A., Arumuga Prabhu, V., 2015. Applications of fuzzy faulty tree analysis and expert elicitation for evaluation of risks in LPG refuelling station. J. Loss Prev. Process Ind. 33, 109–123. http://dx.doi.org/ 10.1016/j.jlp.2014.11.016. Ramzali, N., Lavasani, M.R.M., Ghodousi, J., 2015. Safety barriers analysis of offshore drilling system by employing Fuzzy event tree analysis. Saf. Sci. 78, 49–59. http://dx.doi.org/10.1016/j.ssci.2015.04.004.
123
Runkler, T., Glesner, M., 1993. A set of axioms for defuzzification strategies towards a theory of rational defuzzification operators. In: Proc. Second IEEE Int. Conf. Fuzzy Set Syst., pp. 1161–1166. Sugeno, M., Nguyen, H.T., Prasad, N.R., 1999. Fuzzy Modeling and Control: Selected Works of M. Sugeno. CRC Press. US Department of Defence, 1980. Procedures for performing a failure mode, effects and criticality analysis. MIL-STD-1629, November, AMSC Number N3074 11, 149. http://dx.doi.org/10.1016/j.cardfail.2005.06.223. Wang, Y.-M., Chin, K.-S., Poon, G.K.K., Yang, J.-B., 2009. Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean. J. Expert Syst. Appl. 36, 1195–1207. http://dx.doi.org/10.1016/j.eswa.2007.11.028. Wang, J., Ruxton, T., Labrie, C.R., 1996. Design for safety of engineering systems with multiple failure state variables. Reliab. Eng. Syst. Saf. 50, 271–284. http://dx.doi. org/10.1016/0951-8320(95)00094-1. Yazdi, M., Nikfar, F., Nasrabadi, M., 2017. Failure probability analysis by employing fuzzy fault tree analysis. Int. J. Syst. Assur. Eng. Manage., 1–17 http://dx.doi.org/ 10.1007/s13198-017-0583-y. Zadeh, L., 1965. Fuzzy Sets. Inf. Control. http://dx.doi.org/10.1109/2.53. Zhao, R., Govind, R., 1991. Defuzzification of fuzzy intervals. Fuzzy Sets Syst. 43, 45– 55. http://dx.doi.org/10.1016/0165-0114(91)90020-Q.
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An extension to Fuzzy Developed Failure Mode and Effects Analysis (FDFMEA) application for aircraft landing system Mohammad Yazdi a, Sahand Daneshvar a,⇑, Hashem Setareh b a b
Eastern Mediterranean University, Department Industrial Engineering, Gazimagusa, TRNC, Mersin 10, Turkey Petroleum University of Technology, Abadan Institute of Technology, Department of Safety and Protection Engineering, Abadan, Iran
a r t i c l e
i n f o
Article history: Received 7 December 2016 Received in revised form 8 March 2017 Accepted 13 June 2017
Keywords: Group decision-making Risk assessment Fuzzy set theory Landing system FMEA
a b s t r a c t This is an obvious fact that a significant number of accidents happening each year are due to the failure of aircraft systems’ components. To manage this risk, Failure Mode and Effects Analysis (FMEA), a wellknown method, is employed for reliability analysis in the mentioned fields. Three elements; Severity (S), Detection (D) and Occurrence (O) are considered in typical FMEA to calculate the Risk Priority Number (RPN) for concentrating on the risks and taking corrective actions. The significant numbers of shortcoming which have mentioned in literature can be faced to crisp RPN computation. Therefore, the purpose of this study was to extend FMEA by considering a group decision-making under the fuzzy environment. In fact, the present study was designed to contribute both theoretically and practically contributes to aircraft landing system as one of the important potential failure mode in aerospace industry. In an engineer standpoint the comparison of results between the conventional FMEA and Fuzzy Developed FMEA (FDFMEA) suggests that the risky failure modes accompanied with FDFMEA yield a more reliable result. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Nowadays, reliability and safety guarantee have been of increasing concern in Iranian Airlines company (Mahan Airline, 2015). FMEA as an inductive technique in nature can be applied in all aspects of failure analysis and tends to prepare information for risk management procedure (Modarres, 1993). It has been used in many different kinds of industry such as nuclear, chemical, electronics, and mechanical (Liu et al., 2013). FMEA was initially introduced in the 1940s by the U.S military, which published ‘‘MIL–P–1629” as a safety standard in 1949 (US Department of Defence, 1980). This technique was first developed in 1960s contractors for the U.S. National Aeronautics and Space Administration (NASA) due to aerospace industry, then it used to tolerate risk for Apollo mission to analyze failures on mission success (Bowles and Peláez, 1995; Carlson, 2012). Over the years, many variations of the conventional FMEA have been carried out. A primary discussion of failure analysis which employs a single matrix to system modeling has been performed by Kara-Zaitri et al. (1992). Later that, Bell studied a stochastic model of FMEA (Bell et al., n.d.). Wang and Ruxton (1996) ⇑ Corresponding author. E-mail addresses: [email protected] (M. Yazdi), sahand.daneshvar@ emu.edu.tr (S. Daneshvar), [email protected] (H. Setareh). http://dx.doi.org/10.1016/j.ssci.2017.06.009 0925-7535/Ó 2017 Elsevier Ltd. All rights reserved.
represent an approach in order to combine the Boolean Representation Method (BRM) and FMEA. However, along all studies based on conventional FMEA technique, it still imposes many common shortages in order to compute Risk Priority Number (RPN ¼ S O D), which is the product of the Severity (S), Detection (D) and Occurrence (O). The different combination of S, O and D might be found out in the same value of RPN. As an example, three types of failure modes with value of (10, 3, 8); (6, 8, 5) and (4, 6, 10) for S, O and D, respectively, have the same RPN = 240. Different combination causes of the conventional FMEA technique cannot recognize the hidden risk implications. Also, conventional FMEA considers the importance of the elements S, O and D with the same weight which is not effective in practical FMEA study. Besides, RPN value can be generated just 120 of the 1000 numbers from the production of elements. It means that the crisp value of RPN is not continues and there are limited numbers to prioritize the failure modes. Moreover, it is possible the assessors face by many lack of data and ambiguous information in conventional FMEA. For this reason finding the exact value of RPN needs the linguistic expressions including High, Low and Medium (Liu, 2016; Wang et al., 2009). To eliminate the aforementioned limitations the fuzzy set theory as a computational intelligence has been proposed. The formal introduction of fuzzy set theory is formulized by Prof. Zadeh in the early 1960s. Fuzzy set is a class of objects with degree of
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M. Yazdi et al. / Safety Science 98 (2017) 113–123
membership which is in interval zero and one (Zadeh, 1965). The notable point of fuzzy set is that they are more close to ambiguity which is based on approximation rather than preciseness (Gul and Guneri, 2016; Hong et al., 2016; Markowski and Mannan, 2009; Rajakarunakaran et al., 2015). Over the years, many applications of Fuzzy Developed FMEA (FDFMEA) have been applied in a verity of engineering fields to eliminate the mentioned drawbacks. Wang et al. (2009) estimate the occurrence probability by using expert opinion based on trapezoidal set and they develop it to the other risk parameters. In parallel way a fuzzy expressions is used by Kahraman et al. (2013) in order to prioritize healthcare issues. Besides, a new model based on (a) level was introduced by Hadi-Vencheh and Aghajani (2013). In this study the failure elements are demonstrated by linguistic expressions. Mandal and Maiti (2014) applied fuzzy set theory for risk assessment with using similarity value and possibility approach. In another study, failure analysis is done by employing fuzzy membership function by Helvacioglu and Ozen (2014) to find out the critical failures during yacht design. Also, Dag˘suyu et al. (2016) clarified the utilization conventional and fuzzy FMEA in failure analysis in sterilization plant. Despite all researches, there are rare studies to compare the conventional model and new one as FDFMEA on aircraft landing system. The purpose of this research is reaching to proper comparison based on reliability analysis between classical FMEA and developed FMEA under the fuzzy environment in aircraft landing system. In order to rank the identified failure modes, four experts who have experience and technical knowledge in this field participated in the study. The rest of paper is ordered as follows. After reviewing the proposed model in details in Section 2, FDFMEA will be applied on air craft landing system as case of study in Section 3. Finally, conclusion part will be explained in Section 4.
recognize the priority of corrective actions for improving the safety performance of components or subsystems. The description of these elements is provided as follows: Severity is generally figured out due to the enthusiasm of failure mode effect toward level including user or system. The effects of a specified failure mode are commonly demonstrated by user when they can be found out by them. For instance, a few ordinary failure effects for special pump which is installed in high-tech industry are: excessive vibration, noise and periodic leakage. Occurrence as a second element is usually assessed pursuant to the failure probability, which illustrates the proper number of failure predicted in the entire life of a specified item. In other words, the rating is founded on the predicted failure frequency. Also the last one, detectability is an identifying method and amends preparation(s) for each failure rate. All in all, Tables 1–3 as a guide represent the ranking of severity, occurrence and decidability elements respectively and also provide the linguistic expression and corresponding Fuzzy membership function (Chen and Hwang, 1992a; Modarres et al., 1999). The membership function can be defined for both trapezoidal and triangular fuzzy numbers as follows (Ramzali et al., 2015): ~ = (a1, a2, a3) (a) In triangular form, A
8 0; > > < xa1 ; 1 V i ðxÞ ¼ aa23a x > ; > : a3 a2 0;
9 x < a1 > > a1 6 x 6 a2 = a2 6 x 6 a3 > > ; x > a3
2. Methodology 2.1. The proposed model The structure of the proposed model is arisen from the set of Fuzzy theory and also the qualitative opinions which are extracted by experts’ judgment for purpose of satisfy the FMEA quantifiable ability. The novel model framework is extended in various steps which are merged from conventional FMEA and new one. First of all, like as all FMEA studies the component and process information should be collected. Secondly, the potential failure modes should be determined. Thirdly, at the same time the effects and causes of each failure and also current control process should be found out. Fourthly, expert judgments opinion is considered in order to find detectability, probability and severity of failure mode. Also, their opinion should be transfer to Fuzzy membership function, and the set of Fuzzy numbers are used in order to rate the opinions. Fifthly, aggregation process is applied through which all detectability; occurrence probability and severity rate are collected using linguistic expressions by employing experts’ opinions. Sixthly, defuzzification procedure is done by using a proper algorithm in order to convert the experts’ judgments (Fuzzy Possibility) to corresponding crisp possibility (CCP). Seventhly, RPN should calculate in this step. Finally, in order to report FMEA, necessity of correction actions for high amount of RPN should be considered. The framework of proposed model is provided in Fig. 1. As outline with accordance to conventional FMEA method, each failure mode is computed by three elements including severity (S), probability of occurrence (O) and obstacle of detectability (D). The amounts of these elements are provided between 1 (being the best case) and 10 (being the worst case) similar to Likert’s scale (Liu et al., 2013). Additionally, the amount of RPN helps assessors to
~ = (a1, a2, a3, a4) (b) In trapezoidal form, A
8 0; > > xa > > < a2 a11 ; V i ðxÞ ¼ 1; > x > ; > aa44a > 3 : 0;
9 x < a1 > > > a1 6 x 6 a2 > = a2 6 x 6 a3 > a3 6 x 6 a4 > > > ; x > a4
Due to the transfer linguistic expression to their corresponding fuzzy numbers, Chen and Hwang (1992a) presented a numerical approximation. To achieve this criterion, there are common verbal expressions in the system. According to Miller (1956), Nicolis and Tsuda (1985) scale one includes 2 verbal expressions (linguistic expression) and also scales eight includes 13 verbal expressions (linguistic expression). Chen’s transformation scale is shown in Table 4. Additionally, Yazdi et al. (2017) discussed that the generic estimation of human memory aptitude is seven plus-minus two patches. This notice means that the proper number of linguistic expression for human character to make a suitable judgment is between five and nine.
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Collect component and process function information
Determine potential failure modes
List current control process
Determine the cause of each failure
Determine the effects of each failure
Find detectability ranking (D)
Find probability occurrence ranking (O)
Find severity ranking (S) Aggregating Data
Collecting expert opinions and transferring into Fuzzy membership function
Procedure of Defuzzfing for S,O,D
Calculate RPN
No Correction required?
Yes FMEA Report
Recommended corrective actions
Modification Data Modifications
Fig. 1. Framework of proposed Fuzzy FMEA model.
Table 1 Severity evaluation element. Rank
Effect
Criteria
Linguistic expression
Corresponding Fuzzy number
9, 7, 4, 2, 1
Very High High Moderate Low Minor
According to this failure mode, death or mission losses occur. Severe injury, damage or incompleteness on mission may occurred by effect of failure mode. Loss of function by system or component may occur. Minor injury or depreciation in system performance. Usually injury or depreciation in system performance does not occur.
Very High High Medium Low Very low
(0.8, 0.9, 1, 1) (0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0.1, 0.3, 0.5) (0, 0, 0.1, 0.2)
10 8 5, 6 3
Table 2 Probability of occurrence evaluation element. Rank
Likelihood
Criteria
Predicted failure frequency
Linguistic expression
Corresponding Fuzzy number
10 9 8 7 6 5 4 3 2 1
Very High
Failure is almost unavoidable
Very High
(0.8, 0.9, 1, 1)
High
Repeated failures
High
(0.6, 0.75, 0.9)
Moderate
Occasional failures
Medium
(0.3, 0.5, 0.7)
Low
Rare failures
Low
(0.1, 0.3, 0.5)
Remote
Failure is unlikely
>1 in 2 1 in 8 1 in 20 1 in 40 1 in 80 1 in 400 1 in 1000 1 in 4000 1 in 20000 <1 in 106
Very low
(0, 0, 0.1, 0.2)
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M. Yazdi et al. / Safety Science 98 (2017) 113–123
Table 3 Detectability evaluation element. Rank
Detectability
Criteria
10 9 7, 8 5, 6 3, 4 1, 2
Non-detection Very low Low Moderate High Very High
Program Program Program Program Program Program
control or any user cannot detect a potential cause or failure mode. control or user will not detect a potential cause or failure mode. control or user is not likely to detect a potential cause or failure mode. control or user may detect a potential cause or failure mode. control or user has a proper chance of detecting a potential cause or failure mode. control or user will almost certainly detect a potential cause or failure mode.
Linguistic expression
Corresponding Fuzzy number
None Very low Low Medium High Very High
(0.8, 0.9, 1) (0, 0.1, 0.2) (0.5, 0.7, 0.9) (0.3, 0.5, 0.7) (0.1,0.3,0.5) (0,0,0.1)
Table 4 Linguistic expressions and their corresponding fuzzy numbers (Chen and Hwang, 1992b). Linguistic expressions None Very low Low-Very Low Fairly low Mol. Low Medium Mol. High Fairly High High High-Very High Very High Excellent Mol.: More or less.
Scale 1
Scale 2
Scale 3
Scale 4
Scale 5
(0, 0, 0.2) (0, 0, 0.2, 0.4)
(0.1, 0.2, 0.3)
(0, 0, 0.3) (0, 0.25, 0.5)
(0.4, 0.6, 0.8)
(0.2, 0.5, 0.8)
(0.3, 0.5, 0.7)
(0.3, 0.5, 0.7)
(0.6, 0.8, 1)
(0.6, 0.8, 1, 1)
(0.6, 0.8, 1)
(0.5, 0.75, 1) (0.7, 1, 1)
(0.8, 1, 1)
For this purpose, transferring scale of six which includes 5 verbal expressions is chosen to fulfilling the intellectual assessment for finding the severity and occurrence elements and also scale eight which includes 13 verbal expressions is used for detectability evaluation element. Table 4 presents completely the fuzzy membership numbers in the form of trapezoidal numbers. Moreover, Preyssl (1995) made clear that there are mainly three ways including: statistical, extrapolation and expert judgment method that could be engaged to compute the amount of S, O and D. The statistical method includes the conduct of shortest test of practical data and the estimating of aforementioned elements. The other method is extrapolation method which contains the usage of guessing model and equal circumstance, and the last one is expert judgment method in which direct estimated amount of S, O and D is implicated by specialists. Thus, in this study the expert judgment is employed in order to identify the estimated amount of S, O and D. Through expert judgment, specialists express their opinions about each S, O and D based on each intellectual characteristic. Expert elicitation is the combination of specialists’ opinions about a subject when there is a lack or limited resources due to physical limitations. Experts’ elicitation is, in fact, a fundamental scientific solidarity methodology. It is usually applied to the study when infrequent events exist. Besides, expert elicitation usually quantifies uncertainty by allowing specialists to parameterize an educated guess. Expert Judgment method has been applied according to much regularity. Some of the main important fields related to probability elicitation are risk analysis, psychology, philosophy, decision examination, mathematics and Bayesian statistics. Quantification of characteristic is engaged in different conditions: Evidence is unfinished because it could not be practically attained.
Scale 6
(0, 0, 0.1, 0.2)
(0, 0, 0.1, 0.2)
(0, 0.2, 0.4) (0.2, 0.4, 0.6)
(0.1, 0.25, 0.4)
(0.3, 0.5, 0.7) (0.4, 0.6, 0.8) (0.6, 0.75, 0.9)
(0.6, 0.75, 0.9)
(0.8, 0.9, 1, 1)
(0.8, 0.9, 1, 1)
Scale 7 (0, 0, 0.2) (0, 0, 0.1, 0.3) (0, 0.2, 0.4) (0.2, 0.35, 0.5) (0.3, 0.5, 0.7) (0.5, 0.65, 0.8) (0.6, 0.8, 1) (0.7, 0.9, 1, 1) (0.8, 1, 1)
Scale 8 (0, 0, 0.1) (0, 0.1, 0.2) (0.1, 0.2, 0.3) (0.1, 0.3, 0.5) (0.3, 0.4, 0.5) (0.4, 0.45, 0.5) (0.3, 0.5, 0.7) (0.5, 0.55, 0.6) (0.5, 0.6, 0.7) (0.5, 0.7, 0.9) (0.7, 0.8, 0.9) (0.8, 0.9, 1) (0.9, 1, 1)
Data could be found out just for analogous circumstances. There are contradictory models or data references. Scaling up from experimentations to physical objective procedures is not direct (scaling of mean values is usually simpler than rescaling the uncertainties). When the uncertainties are substantial comparative to the demonstration of obedience (Kotra et al., 1996). Expert knowledge is affected by individual visions and purposes (Ford and Sterman, 1998). Thus, it is very difficult to assess the complete impartiality of expert knowledge. The main challenge is the selection of heterogeneous specialists (e.g., either scientists or workers) and homogenous specialists (it just includes scientists). Individual experience on expert judgment is presumed to be smaller in the homogeneous group as compared to the heterogeneous one as a result of experience differences. Therefore, by considering all possible opinions, a group of heterogeneous specialists could have a privilege over the homogeneous group. Moreover, the weights of experts are different, so in real life, the heterogeneous group is more realistic (Helvacioglu and Ozen, 2014). The criteria to recognize experts are established as follows: First one is the period of learning and experience of the experts in their exact field that affects their judgmental and logical behavior. Second is the individual conditions in which the experience is obtained including practical and theoretical conditions. In this study, a heterogeneous group of experts is chosen for estimating the amount of S, O and D. Accordingly, for qualifying the measurements, the importance of experts was measured to deal with the uncertainty and lack of sufficient data. In order to the score quality of an expert, the following qualities were considered: professional position, job experience, education level and age (Miri Lavasani et al., 2011; Omidvari et al., 2014). The score rating of experts are examined according to Table 5. The rating of expert judgment can be done according to the weight given to each element. The concept of linguistic expressions
M. Yazdi et al. / Safety Science 98 (2017) 113–123
117
Item
Categorize
Score
of linguistic variables. The linguistic expressions can be transferred to the corresponding fuzzy numbers. The procedure is explained in detail in what follows:
Profession position
Higher-ranking academic Low-ranking academic Engineer Technician Worker
5 4 3 2 1
1. Computing the degree of similarity (degree of agreement). ~u; R ~ v Þ is defined as opinions between each pair of experts Suv ðR ~u; R ~ v Þ when Eu and Ev . According to this consideration for Suv ðR
Job Tenure
More than 30 years 20–29 10–19 6–9 5
5 4 3 2 1
Education
PhD Master Bachelor Higher National Diploma (HND) School level
5 4 3 2 1
More than 50 40–49 30–39 Less than 30
4 3 2 1
Table 5 Score rating according to expert’s traits.
Age
~ = (a1, a2, a3) and B e = (b1, b2, b3) are two standard triangular A fuzzy numbers, then the degree of agreement function of S is defined as:
~ BÞ ~ ¼1 SðA;
1 XJ jai bi j i¼1 J
ð1Þ
~ BÞ ~ BÞ ~ 2 [0, 1], the greater value of S (A, ~ is the best simWhen SðA; ~ and B. ~ Moreover, the ilarity between two fuzzy numbers of A amount of J is 3 and 4 for triangular and trapezoidal fuzzy number respectively. 2. Next it is computing the Average of Agreement (AA) degree AAðEu Þ of the expert’s opinions.
has a high value in dealing with any circumstances which are illdefined or complex to be described in the old model of quantitative expression (Zadeh, 1965).
AAðEu Þ ¼
1 XJ ~ ~ u–v SðRu; Rv Þ J1 v¼1
ð2Þ
3. Computing the Relative Agreement (RA) degree, RAðEu Þ of the experts.
2.2. Aggregating data It is vital to aggregate expert’s opinion to attain a deal because each expert might have a variety of opinions according to her/his knowledge and experiences in the pertinent scope. According to many studies, there are many methods available for aggregation of the expert opinions including max–min Delphi method, arithmetic averaging operation, voting, game theory, TOPSIS, fuzzy priority relations, fuzzy Delphi method, etc.; however, Liu et al. (2014) found that no stable and definite theoretical guidance could be employed to select the most appropriate opinion. In order to collect linguistic expressions, a novel procedure is offered for both homogenous and heterogeneous group of experts (Lee, 2001). Aqlan et al.’s model which is the use of triangle fuzzy numbers whereas Hsu et al.’s model is based on collecting triangle and trapezoidal fuzzy numbers (Similarity Aggregation Method – SAM) (Aqlan and Mustafa Ali, 2014). The linguistic expression of this study is a combination of both methods. Hence, Hsu et al.’s procedure is employed in this study in order to aggregate the expert opinions (Hsu and Chen, 1996) (see Fig. 2). Suppose that each expert, Ej (k = 1, 2, . . ., n) states his attitude about a certain feature in a specific context by a predefined set
1. Computing the degree of similarity between two kind of expert for each basic event
AAðEu Þ Eu ðu ¼ 1; 2; . . . ; JÞ as RAðEu Þ ¼ PJ u¼1 AAðEu Þ
ð3Þ
4. Estimate the Consensus Coefficient (CC) degree, CCðEu Þ of expert’s opinions, Eu ðu ¼ 1; 2; . . . ; JÞ:
CCðEu Þ ¼ b WðEu Þ þ ð1 bÞ RAðEu Þ
ð4Þ
where WðEu Þ is the weight of each expert and b is the weight of each term, nominated as a relaxation factor of the offered procedure due to b (0 b 1). It illustrates the importance of W (Eu ) over RA (Eu ). When b = 0, no weight has been given to it by experts and thereby a homogenous group of experts should be employed whereas when b = 1, signifies that the consensus degree of an expert is equal to its importance weight. The result of Hsu et al.’s study suggested that the consensus coefficient of each expert is better known when the comparative competency of each expert’s opinion is estimated. Therefore, it has an important part for the decision maker to allocate a proper amount of b (Hsu and Chen, 1996). However, the result Ölçer and Odabasßi (2005) represents that the b coefficient is not sensitive
2. Computing the degree of agreement between two kind of expert
4. Computing the consensus degree of coefficient
3. Computing the relative degree of agreement between two kind of expert
5. Computing the aggregation result base on expert opinion
Fig. 2. The steps of aggregating data.
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M. Yazdi et al. / Safety Science 98 (2017) 113–123
on fuzzy multiple attribute decision-making which is applied on propulsion system Turkish maritime. ~ AG , 5. Finally, the aggregated result of the experts’ judgment R could be found out as follows:
~ AG ¼ CCðE1 Þ R ~ 2 CCðE2 Þ R ~ 2 CCðEm Þ R ~M R
ð5Þ
Where sign is fuzzy addition and is fuzzy scalar multiplication operator. Additionally (Kaufmann and Gupta, 1985) represented that the fuzzy operations of trapezoidal fuzzy member are trapezoidal fuzzy member. 2.3. Defuzzification procedure Defuzzification procedure is a quantifiable outcome of Fuzzy theory according to process of making. Zhao and Govind (1991) mentioned that there are many defuzzification issues appearing by the application of fuzzy control into the industrial processes. Thus, Fuzzy numbers in defuzzification procedure has high significant role for decision making in Fuzzy area. Runkler and Glesner (1993) discussed about several procedures which have been developed in recent years including Center Algorithm and Weighted Mean of Maximum. Also they noticed that none of procedures are the proper for all applications. The gravity or center of defuzzification environment technique is employed in this study. Also, this is a common and accurate for our purpose. This method was extended by Sugeno et al. (1999). Eq. (6) mathematically represents this technique:
R ti ðxÞxdx X ¼ R ti ðxÞdx
ð6Þ
where X⁄ = Defuzzified output; ti ðxÞ ¼ Aggregated membership function; x = output variable. Eq. (6) could be engaged to both trapezoidal and triangular fuzzy numbers and it is shown as:
RPNT ¼
n X RPNTj ;
j ¼ 1; 2; . . . ; n
ð9Þ
j¼1
where RPNT is the total RPN score for Tth component or subsystem, RPNTj illustrates the RPN score which is jth failure in Tth component or subsystem, Also j means that the number of failure mode in specified component or subsystem. Thus, considering the RPN score, the importance of each failure mode can be found out in order to prioritize for corrective actions. Additionally, according to ‘‘MIL-STD1629A” as a standard safety, a rule of thumb for controlling or eliminating the specified failure mode is attending to RPNs > 125 (Ayyub, 2014). But this standard was canceled without replacement in 1998, nevertheless remains in wide use for industry applications today (Department of Defense of the USA, 1998). 3. Result In order to explain the proposed method clearly, the detail of one of the numeric failure mode (A simplest aircraft landing system) is chosen as a case of study, because in recent years many accidents related to landing systems are reported by Iranian airlines (Mahan Airline, 2015). As it shows in Fig. 3 with pressing GDnB and GupB the gear come down and rise respectively. Switch (S1) send a signal to computer (C) during raising the gear (otherwise a fault signal is sent). In opposite side, when the gear are coming down the switch (S2) sends a signal to the computer (otherwise a fault signal is sent). Task switches is finding information about the actual location of the landing gear and stopping inconsistent commands. Additionally, Sco is a switch for controlling the gear. The main performances of aircraft landing systems for both types of operation (hardware and software) are provided as follows: Raising gear Coming down gear
~ = (a1, a2, a3) is: Defuzzification of triangular fuzzy number A
R a2
X ¼
xa2 xdx a1 a2 a1 R a2 xa2 dx a1 a2 a1
þ þ
R a3 a
R a23 a2
a3 x a3 a2 a3 x a3 a2
xdx dx
¼
1 ða1 þ a2 þ a3 Þ 3
GDnB
ð7Þ Computer (C)
~ = (a1, a2, a3, a4) Defuzzification of trapezoidal fuzzy number A can be gained by Eq. (8).
R a2 X ¼ ¼
Ra Ra xa1 xdx þ a23 xdx þ a34 a1 a2 a1 R a2 xa1 R a3 R a4 dx þ a2 dx þ a3 a1 a2 a1
GUpB
a4 x xdx a4 a3 a4 x dx a4 a3
1 ða4 þ a3 Þ2 a4 a3 ða1 þ a2 Þ2 þ a1 a2 3 ða4 þ a3 a1 a2 Þ
S co
Gear up
ð8Þ
So, as aforementioned earlier in order to use intellectual assessment the linguistic expression transferred to corresponding fuzzy numbers which is between zero and one while each elements of conventional FMEA established in interval [1,10]. Therefore, the last step of defuzzification procedure is multiplying each element to 10.
S1
S2 Switch Button
2.4. Compute RPN score The score of RPN could be presented as a criterion assessment in order to prioritize the higher risk failure modes. Moreover, if any subsystem available the total RPN should be computed as follows:
Gear Down Fig. 3. Simplest aircraft landing system (Ericson, 2005).
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M. Yazdi et al. / Safety Science 98 (2017) 113–123 Table 6 FMEA of the aircraft landing system. Process step
Potential cause (s)/failure mechanism
Detection Current design practice or process control
Initial effort computation of RPN
Software fault, fault in in the wiring of computer Software fault
Sensor
None
48
Sensor
None
84
Software fault, fault in in the wiring of computer Unknown Damage caused by the pressure Software fault and tension
Sensor
None
84
Sensor
None
84
None
180
None
180
None
18
None
18
None
12
None
12
Potential failure modes Failure rate
Potential effect(s) of failure
Expert knowledge for Aircraft landing system (Naftair Airline, 2015) FM1A Raising Gear Fault in raising the Unknown Extension system damage of wheels aircraft, taking off with open wheels. FM1B Raising wheels earlier Unknown Aircraft damaged on landing. than specified time FM2A Coming down Gear Fault in coming down Unknown Landing with closed wheels, the wheels Aircraft damaged on landing FM2B
Coming down wheels earlier than specified time FM3A Automatically test Fault on the run
Unknown Possible unsafe conditions
FM3B
Wrong run
Unknown Possible unsafe conditions
FM4A Fault reporting system FM4B
Fault on the run
Unknown Fault information was not reported, Without risk Unknown Fault information was reported mistakenly, Without risk Unknown Failure to register unsafe situation, Without risk Unknown Register unsafe situation mistakenly, Without risk
Wrong run Fault on the run
FM5A Record the result of automatically FM5B test
Wrong run
Software and electronic None fault Software and electronic None fault Software fault Pilot Report Software fault Pilot Report Software fault Data analysis Software fault Data analysis
Table 7 Expert weighting of group decision-making. Expert Expert Expert Expert Expert
1: 2: 3: 4:
Total
Profession position
Job experience
Education
Age
Weighting score
Engineer (3) Low-ranking academic(4) Higher-ranking academic(5) Engineer (3)
5 (1) 10–19 (3) 10–19 (3) 20–29 (4)
Master (4) Master (4) PhD (5) Bachelor (3)
28 39 44 56
0.17 0.25 0.31 0.27
15
11
16
10
(1) (2) (3) (4)
52/52 = 1
Table 8 Corresponding fuzzy numbers for each expert opinion. FM1A
FM1B
FM2A
FM2B
FM3A
FM3B
FM4A
FM4B
FM5A
FM5B
Expert 1 Severity Occurrence Detection
(0.3, 0.5, 0.7) (0.3, 0.5, 0.7) (0, 0, 1)
(0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0, 0, 1)
(0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0, 0, 1)
(0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0.8, 0.9, 1, 1) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
Expert 2 Severity Occurrence Detection
(0.3, 0.5, 0.7) (0.3, 0.5, 0.7) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.3, 0.5, 0.7) (0, 0, 1)
(0.6, 0.75, 0.9) (0.6, 0.75, 0.9) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.3, 0.5, 0.7) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0.8, 0.9, 1, 1) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
Expert 3 Severity Occurrence Detection
(0.6, 0.75, 0.9) (0.1, 0.3, 0.5) (0, 0, 1)
(0.6, 0.75, 0.9) (0.6, 0.75, 0.9) (0, 0, 1)
(0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0, 0, 1)
(0.3, 0.5, 0.7) (0.6, 0.75, 0.9) (0, 0, 1)
(0.3, 0.5, 0.7) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0.8, 0.9, 1, 1) (0.1, 0.3, 0.5) (0.8, 0.9, 1)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0, 0, 1)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0, 0, 1)
(0, 0, 0.1, 0.2) (0.6, 0.75, 0.9) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
Expert 4 Severity Occurrence Detection
(0.6, 0.75, 0.9) (0.1, 0.3, 0.5) (0, 0, 1)
(0.3, 0.5, 0.7) (0.6, 0.75, 0.9) (0, 0, 1)
(0.6, 0.75, 0.9) (0.3, 0.5, 0.7) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.6, 0.75, 0.9) (0, 0, 1)
(0.8, 0.9, 1, 1) (0.6, 0.75, 0.9) (0.8, 0.9, 1)
(0.8, 0.9, 1, 1) (0.3, 0.5, 0.7) (0.8, 0.9, 1)
(0.8, 0.9, 1, 1) (0.3, 0.5, 0.7) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.6, 0.75, 0.9) (0.3, 0.5, 0.7)
(0, 0, 0.1, 0.2) (0.6, 0.75, 0.9) (0, 0, 1)
(0, 0, 0.1, 0.2) (0.6, 0.75, 0.9) (0, 0, 1)
Automatically test Fault reporting system Record the result of automatically test According to Fig. 3, the traditional FMEA table of failure modes is provided in Table 6. Here, the process steps denoted as FM1A, FM1B etc. and also RPN scores are computed as the initial effort. FMEA sheet (Table 6) is completed by Naftair Airline’s experts
and five process steps is only chosen for applying the proposed model to find out the effectiveness of new approach. As it mentioned earlier, in order to accomplish judgment for each elements of FMEA, a heterogeneous group of experts is engaged. Due to Table 5, it is so clear that the weights of experts are not same. Table 7 shows the experts’ weights which are used. In this study, four experts are participating to accomplish the judgments. Two of them have master in safety engineering and have
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M. Yazdi et al. / Safety Science 98 (2017) 113–123
trainer for aerospace industries since 2006. The last one is an engineer who published several papers and books related to safety and reliability analysis and he has been working at reliability center more than 20 years. Additionally, according to Tables 1–3 the fuzzy corresponding numbers are illustrated in Table 8, which are based on the expert’s opinion. FM1B is taken as an example to detailed aggregation computations for element S. The details are provided in Table 9. To compute consensus coefficient (Eq. (4)), relaxation factor (b) is considered 0.5 according to the type of their work. Eqs. (7) and (8) are employed to defuzzify of each failure modes. The computation of FM1B for element S is done as an example and the results of other failure modes, having crisp values with three decimal places are provided in Table 10.
Table 9 Aggregation computations for the FM1B (Element S). Expert 1 Expert 2 Expert 3 Expert 4 S(E1&E2)
(0.6, 0.75, 0.75, 0.9) (0.8, 0.9, 1, 1) (0.6, 0.75, 0.75, 0.9) (0.3, 0.5, 0.5, 0.7) ~ BÞ ~ ¼ 1 1 PJ 0.85 SðA;
S(E1&E3) S(E1&E4) S(E2&E3) S(E2&E4) S(E3&E4) AA(E1)
1 SE1;E2 ¼ 1 1=4 ð0:2 þ 0:15 þ 0:25 þ 0Þ = 0.85 0.75 0.825 0.575 0.75 ~ R ~v Þ 0.86 AAðEu Þ ¼ 1 PJu–v SðRu; J1
AA(E2) AA(E3) AA(E4) RA(E1)
0.75 1=ð4 1Þ ð0:85 þ 1 þ 0:75Þ ¼ 0:858 0.858 0.69 uÞ 0.27 RAðEu Þ ¼ PAAðE J
J
i¼1
jai bi j
v ¼1
u¼1
RA(E2) RA(E3) RA(E4) CC(E1) CC(E2) CC(E3) CC(E4) Aggregation for FM1B
X ¼
AAðEu Þ
0.23 0:86=ð0:86 þ 0:75 þ 0:858 þ 0:69Þ ¼ 0:27 0.27 0.21 0.22 CCðEu Þ ¼ b WðEu Þ þ ð1 bÞ RAðEu Þb = 0.5 0.24 0.5 0.17 + 0.5 0.27 = 0.22 0.29 0.24 ~ AG ¼ CCðE1 Þ R ~ 1 CCðE2 Þ R ~ 2 CCðEm Þ R ~M R
1 ð0:875 þ 0:749Þ2 ð0:875 0:749Þ ð0:575 þ 0:725Þ2 þ ð0:575 0:725Þ 3 ð0:875 þ 0:749 0:575 0:725Þ
¼ 0:729
The last step of defuzzification is multiplying X to 10.
X 10 ¼ 7:29 As aforementioned earlier the purpose of this study is to develop FMEA technique for aircraft landing systems. In order to reach this aim, one of the simplified aircraft landing systems is chosen as an application. The limitations of conventional RPN score actuate to new ranking method for the failure modes, which is FDFMEA. The score of RPN ranking for both conventional and fuzzy developed FMEA are provided in Table 11. To make more comprehensi-
0.22 (0.6,0.75,0.75,0.9) 0.24 (0.8,0.9,1,1) 0.29 (0.6,0.75,0.75,0.9) 0.24 (0.3,0.5,0.5,0.7) = (0.575,0.725,0.749,0.875)
been working as a risk assessor and safety auditor in varieties of industry more than four years. The third expert has a PhD in aerospace engineering and also has been working as consultant and Table 10 Defuzzified failure mode elements for aircraft landing system.
Severity Occurrence Detection Developed RPN Developed RPNa a
FM1A
FM1B
FM2A
FM2B
FM3A
FM3B
FM4A
FM4B
FM5A
FM5B
6.35 3.92 3.33 83 84
7.30 6.66 3.33 162 163
7.50 6.10 3.33 152 154
7.74 6.35 3.33 164 165
8.17 4.01 9.00 295 298
9.22 3.49 9.00 290 293
2.20 5.00 4.59 50 51
0.78 5.61 4.62 20 20
0.78 6.35 0.462 23 23
0.78 4.05 3.97 13 13
With considering elements weight S, O and D according to 1.01, 1 and 1 respectively.
Table 11 Ranking of the alternative for aircraft landing system. FM1A
FM1B
FM2A
FM2B
FM3A
FM3B
FM4A
FM4B
FM5A
FM5B
48 3 83 6
84 2 162 4
84 2 152 5
84 2 164 3
180 1 295 1
180 1 290 2
18 4 50 7
18 4 20 9
12 5 23 8
12 5 13 10
RPN Score
Conventional RPN Priority Rank Developed RPN Priority Rank
500 450 400 350 300 250 200 150 100 50 0 FM5B
FM4B
FM5A
FM4A
FM1A
Conventional RPN
FM2A
FM1B
Developed RPN
Fig. 4. Ranking of RPN score.
FM2B
FM3B
FM3A
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which is based on fuzzy method. However, FDFMEA ranks the high risky failure mode as ‘‘Fault on the run of automatically test (FM3A)”. Wrong run (FM3B) is ranked as second high RPN score whilst the element S in mentioned failure mode is more than specified element in FM3A (see Table 9). Therefore, considering the important weight of elements the FM3B has priority due to corrective actions. Additionally, it can find which sub-system has highest RPN score. Thus, the failure modes with higher RPN score are consid-
ble comparison as well as the most and least risky RPN score can be figured out from Fig. 4. According to results of RPN Ranking, all scores have been increased in FDFMEA technique in compression to conventional FMEA. Also, Developed RPN computation covers the different combination shortage of conventional RPN (FM2A, FM1B and FM2B in conventional RPN are same whereas in developed one are different). ‘‘Wrong run for registering the result of automatically test (FM5B)” is chosen as minor risky failure mode as ranked by RPN Table 12 RPN scores according to beta values. Beta coefficients
Failure modes
FM5B FM4B FM5A FM4A FM1A FM2A FM1B FM2B FM3B FM3A
0.1
0.3
0.5
0.7
0.9
23 26 26 38 83 139 153 162 280 283
26 26 29 49 83 139 153 162 281 304
13 20 23 50 83 152 162 164 290 295
22 26 25 47 83 140 154 162 284 291
21 22 25 57 83 140 155 161 286 293
350 300
Beta
RPN Scores
250
0.1
200
0.3 150
0.5 0.7
100
0.9 50 0 FM5B
FM4B
FM5A
FM4A
FM1A
FM2A
FM1B
FM2B
FM3B
FM3A
Filure modes Fig. 5. Sensitivity according to beta coefficient.
350 300
RPN Scores
250
Beta 0.1
200
0.3 150
0.5 0.7
100
0.9
50 0 FM5B
FM4B
FM5A
FM4A
FM1A
FM2A
FM1B
FM2B
FM3B
FM3A
Failure modes Fig. 6. Sensitivity according to beta coefficient for all identified failure modes.
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ered to be more important and will be given higher priorities for future corrective actions. Accordingly, as mentioned in methodology part, a common rule to control or eliminate the failure modes is attending to RPNs > 125. Therefore, in conventional FMEA, there are only two failure modes which need corrective actions whereas in new approach, five failure modes have been found out for further actions. From mentioned case of study for comparison two specified technique, it is clear that the ranking of FDFMEA is more perceptible in case of engineering purpose. Moreover, sensitivity analysis is applied to find out the beta effect on the RPN scores. Beta values are selected as a set of 0.1, 0.3, 0.5, 0,7 and 0.9 which is provided in Table 12. The result of sensitivity analysis represents that this case is not sensitive for beta coefficient. Fig. 5 illustrates that the RPN scores have not sensible change for all identified failure modes in different beta values. According to Fig. 6, it is obvious that while beta coefficient takes various ranges; the ranking of RPN scores remains the same. 4. Conclusion Failure mode and effects analysis (FMEA) is designed as a powerful tool to measure reliability analysis in widespread engineering fields. In FMEA technique, three elements which are called severity, occurrence and detection used to evaluate the potential failure modes. The risk priority number in classic model is equal to product of crisp value of the elements. However, the limitations of conventional FMEA are recognized during the study. Thus, this paper proposed to assess the risks with a conventional (FMEA) and fuzzy developed FMEA (FDFMEA) method for aircraft landing system. The FDFMEA technique which is used in this study seems to have many benefits because of its superiority over the conventional method. The FDFMEA technique which is applied for aircraft landing system handled the drawbacks of classic model and is sensitive to all inputs including linguistic variable, importance weigh of experts and etc. In comparison of the conventional with new ranking techniques, it is illustrated that the FDFMEA has better results due to the fuzzy set theory which is incorporated with reality. Accordingly, the limitations of this work are that FDFMEA is not so sensitive to relaxation factor in this case and also there is no way to ensure that the purposed aggregation procedure is more reliable. In addition, the complexity and time-consuming computation are reflected as the main limitation of FDFMEA in order to apply for whole of the specified system. Because of rare risk assessment which have been done for aircraft systems, it is recommended to develop these types of study for entire aircraft systems with considering the group decisionmaking methods such as fuzzy hybrid weighted, Grey relational projection, VIKOR, Fuzzy hybrid TOPSIS approach or combination of them. Moreover, it is recommended that the further studies should be done in order to indicate the importance of beta effect on RPN scores and also recognize the major and minor factors of specified case study. Additionally, as a direction for further studies, this approach can be applied for other types of industries such as oil & gas, marine & offshore, and railways. Acknowledgement In this study, authors would like to express their gratitude to the Iranian Naftair airline for supporting to represent failure modes which common occur in aircraft landing system with appoint of decision rules, and also to four experts participated in this study because of their invaluable insights and inputs.
References Aqlan, F., Mustafa Ali, E., 2014. Integrating lean principles and fuzzy bow-tie analysis for risk assessment in chemical industry. J. Loss Prev. Process Ind. 29, 39–48. http://dx.doi.org/10.1016/j.jlp.2014.01.006. Ayyub, B.M., 2014. Risk Analysis in Engineering and Economics, second ed. Bell, D., Cox, L., Jackson, S., Schaefer, P., n.d. Using causal reasoning for automated failure modes and effects analysis (FMEA). In: Annual Reliability and Maintainability Symposium 1992 Proceedings. IEEE, pp. 343–353. http:// dx.doi.org/10.1109/ARMS.1992.187847. Bowles, J.B., Peláez, C.E., 1995. Fuzzy logic prioritization of failures in a system failure mode, effects and criticality analysis. Reliab. Eng. Syst. Saf. 50, 203–213. http://dx.doi.org/10.1016/0951-8320(95)00068-D. Carlson, C. (Carl S.), 2012. Effective FMEAs Achieving Safe, Reliable, and Economical Products and Processes Using Failure Mode and Effects Analysis. John Wiley & Sons. Chen, S.-J., Hwang, C.-L., 1992a. Fuzzy Multiple Attribute Decision Making, Lecture Notes in Economics and Mathematical Systems. Springer, Berlin, Heidelberg. http://dx.doi.org/10.1007/978-3-642-46768-4. Chen, S.-J., Hwang, C.-L., 1992b. Fuzzy Sets and Their Operations. pp. 42–100. http:// dx.doi.org/10.1007/978-3-642-46768-4_3. Dag˘suyu, C., Göçmen, E., Narlı, M., Kokangül, A., 2016. Classical and fuzzy FMEA risk analysis in a sterilization unit. Comput. Ind. Eng. 101, 286–294. http://dx.doi. org/10.1016/j.cie.2016.09.015. Department of Defense of the USA, 1998. Electronic Reliability Design Handbook. Mil. Handb. MIL-HDBK-338B 1046. doi: MIL-HDBK-338B. Ericson, C.A., 2005. Hazard Analysis Techniques for System Safety. John Wiley & Sons Inc., Hoboken, NJ, USA. http://dx.doi.org/10.1002/0471739421. Ford, D.N., Sterman, J.D., 1998. Expert knowledge elicitation to improve formal and mental models. Syst. Dyn. Rev. 14, 309–340. http://dx.doi.org/10.1002/(SICI) 1099-1727(199824)14:4<309::AID-SDR154>3.0.CO;2-5. Gul, M., Guneri, A.F., 2016. A fuzzy multi criteria risk assessment based on decision matrix technique: a case study for aluminum industry. J. Loss Prev. Process Ind. 40, 89–100. http://dx.doi.org/10.1016/j.jlp.2015.11.023. Hadi-Vencheh, a., Aghajani, M., 2013. Failure mode and effects analysis A fuzzy group MCDM approach. J. Soft Comput. Appl. 2013, 1–14. http://dx.doi.org/ 10.5899/2013/jsca-00016. Helvacioglu, S., Ozen, E., 2014. Fuzzy based failure modes and effect analysis for yacht system design. Ocean Eng. 79, 131–141. http://dx.doi.org/10.1016/j. oceaneng.2013.12.015. Hong, Y., Pasman, H.J., Sachdeva, S., Markowski, A.S., Mannan, M.S., 2016. A fuzzy logic and probabilistic hybrid approach to quantify the uncertainty in layer of protection analysis. J. Loss Prev. Process Ind. 43, 10–17. http://dx.doi.org/ 10.1016/j.jlp.2016.04.006. Hsu, Hsi-Mei, Chen, Chen-Tung, 1996. Aggregation of fuzzy opinions under group decision making. Fuzzy Sets Syst. 79, 279–285. http://dx.doi.org/10.1016/01650114(95)00185-9. _ S Kahraman, C., Kaya, I., ß envar, Ö., 2013. Healthcare failure mode and effects analysis under fuzziness. Hum. Ecol. Risk Assess. An Int. J. 19, 538–552. http://dx.doi. org/10.1080/10807039.2012.737753. Kara-Zaitri, C., Keller, A.Z., Fleming, P.V., n.d. A smart failure mode and effect analysis package. In: Annual Reliability and Maintainability Symposium 1992 Proceedings. IEEE, pp. 414–421. http://dx.doi.org/10.1109/ARMS.1992.187857. Kaufmann, A. (Arnold), Gupta, M.M., 1985. Introduction to Fuzzy Arithmetic: Theory and Applications. Van Nostrand Reinhold Co.. Kotra, J.P., Lee, M.P., Eisenberg, N.A., DeWispelare, A.R., 1996. Branch Technical Position on the Use of Expert Elicitation in the High-Level Radioactive Waste Program. Nureg-1563. Lee, H.-S.L.H.-S., 2001. Aggregation of fuzzy opinions under group decision makingnnenvironment. In: 10th IEEE Int. Conf. Fuzzy Syst. (Cat. No.01CH37297) 1, pp. 279–285. http://dx.doi.org/10.1109/FUZZ.2001.1007275. Liu, H., 2016. FMEA Using Uncertainty Theories and MCDM Methods. http://dx.doi. org/10.1007/978-981-10-1466-6. Liu, H.-C., Liu, L., Liu, N., 2013. Risk evaluation approaches in failure mode and effects analysis: a literature review. Exp. Syst. Appl. 40, 828–838. http://dx.doi. org/10.1016/j.eswa.2012.08.010. Liu, Y., Fan, Z.P., Yuan, Y., Li, H., 2014. A FTA-based method for risk decision-making in emergency response. Comput. Oper. Res. 42, 49–57. http://dx.doi.org/ 10.1016/j.cor.2012.08.015. Mahan Airline, 2015. Annualy Report. Tehran. Mandal, S., Maiti, J., 2014. Risk analysis using FMEA: Fuzzy similarity value and possibility theory based approach. Expert Syst. Appl. 41, 3527–3537. http://dx. doi.org/10.1016/j.eswa.2013.10.058. Markowski, A.S., Mannan, M.S., 2009. Fuzzy logic for piping risk assessment (pfLOPA). J. Loss Prev. Process Ind. 22, 921–927. http://dx.doi.org/10.1016/j. jlp.2009.06.011. Miller, G., 1956. The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol. Rev. 101, 343–352. http://dx.doi. org/10.1037/h0043158. Miri Lavasani, M.R., Wang, J., Yang, Z., Finlay, J., 2011. Application of fuzzy fault tree analysis on oil and gas offshore pipelines. Int. J. Mar. Sci. Eng. 1, 29–42. Modarres, M., 1993. What Every Engineer Should Know About Reliability and Risk Analysis. M. Dekker. Modarres, M., Kaminskly, M., Krivtsov, V., 1999. Reliability Engineering and Risk Analysis.
M. Yazdi et al. / Safety Science 98 (2017) 113–123 Naftair Airline, 2015. Risk assessment study. Ahvaz. Nicolis, J.S., Tsuda, I., 1985. Chaotic dynamics of information processing: the ‘‘magic number seven plus-minus two” revisited. Bull. Math. Biol. 47, 343–365. http:// dx.doi.org/10.1007/BF02459921. Ölçer, A.I., Odabasßi, A.Y., 2005. A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem. Eur. J. Oper. Res. 166, 93–114. http://dx.doi.org/10.1016/j. ejor.2004.02.010. Omidvari, M., Lavasani, S.M.R., Mirza, S., 2014. Presenting of failure probability assessment pattern by FTA in Fuzzy logic (case study: Distillation tower unit of oil refinery process). J. Chem. Heal. Saf. 21, 14–22. http://dx.doi.org/10.1016/j. jchas.2014.06.003. Preyssl, C., 1995. Safety risk assessment and management-the ESA approach. Reliab. Eng. Syst. Saf. 49, 303–309. http://dx.doi.org/10.1016/0951-8320(95)00047-6. Rajakarunakaran, S., Maniram Kumar, A., Arumuga Prabhu, V., 2015. Applications of fuzzy faulty tree analysis and expert elicitation for evaluation of risks in LPG refuelling station. J. Loss Prev. Process Ind. 33, 109–123. http://dx.doi.org/ 10.1016/j.jlp.2014.11.016. Ramzali, N., Lavasani, M.R.M., Ghodousi, J., 2015. Safety barriers analysis of offshore drilling system by employing Fuzzy event tree analysis. Saf. Sci. 78, 49–59. http://dx.doi.org/10.1016/j.ssci.2015.04.004.
123
Runkler, T., Glesner, M., 1993. A set of axioms for defuzzification strategies towards a theory of rational defuzzification operators. In: Proc. Second IEEE Int. Conf. Fuzzy Set Syst., pp. 1161–1166. Sugeno, M., Nguyen, H.T., Prasad, N.R., 1999. Fuzzy Modeling and Control: Selected Works of M. Sugeno. CRC Press. US Department of Defence, 1980. Procedures for performing a failure mode, effects and criticality analysis. MIL-STD-1629, November, AMSC Number N3074 11, 149. http://dx.doi.org/10.1016/j.cardfail.2005.06.223. Wang, Y.-M., Chin, K.-S., Poon, G.K.K., Yang, J.-B., 2009. Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean. J. Expert Syst. Appl. 36, 1195–1207. http://dx.doi.org/10.1016/j.eswa.2007.11.028. Wang, J., Ruxton, T., Labrie, C.R., 1996. Design for safety of engineering systems with multiple failure state variables. Reliab. Eng. Syst. Saf. 50, 271–284. http://dx.doi. org/10.1016/0951-8320(95)00094-1. Yazdi, M., Nikfar, F., Nasrabadi, M., 2017. Failure probability analysis by employing fuzzy fault tree analysis. Int. J. Syst. Assur. Eng. Manage., 1–17 http://dx.doi.org/ 10.1007/s13198-017-0583-y. Zadeh, L., 1965. Fuzzy Sets. Inf. Control. http://dx.doi.org/10.1109/2.53. Zhao, R., Govind, R., 1991. Defuzzification of fuzzy intervals. Fuzzy Sets Syst. 43, 45– 55. http://dx.doi.org/10.1016/0165-0114(91)90020-Q.