1-s2.0-s0957582014000706-main

Please citeindustry. P

ARTICLE IN PRESSPSEP-439; No. of Pages 14Process Safety and Environmental Protection x x x ( 2 0 1 4 ) xxxxxx

Contents lists available at ScienceDirect

Process Safety and Environmental Protection

journa l h om ep age: www.elsev ier .com/ locate /ps ep

An ex aapplic s i

Seyed M in Ca Sciences & esarb Departmen 0 Ista

a

Fa men

to lysis

h entia

fa be a

ro ch ex

pr recog

case study focuses on Deethanizer failure in petrochemical plant operations to demonstrate the proposed methodol-

ogy. Consequently, the study has provided theoretical and practical values to challenge with operational data shortage

in risk assessment.

2014 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers.

Ke

m

1. Int

In conventcomponentues. Howevthe precisenents or fatree structuculty in conmodeling (L

To remeconventionusing fuzzyto Tanaka trapezoidalprinciple toand Wang (taneously dFTA. Sawerof the TE in

CorresponE-mail a

http://dx.do0957-5820/ this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Tree Analysis (FFTA) application in petrochemical process

ywords: Risk assessment; Fault tree analysis; Fuzzy sets; Petrochemical industry; Safety management; Operations

odelling

roduction

ional FTA, the Failure Probabilities (FP) of systems (i.e. Basic Events (BEs)) are treated as exact val-er, for many systems, it is very difcult to estimate

failure rate or probabilities of individual compo-ilure events in the quantitative analysis of faultres. In other word, the crisp approach has dif-veying imprecision or vagueness nature in systemiang and Wang, 1993; Lavasani et al., 2012).dy the gap about the mentioned inadequacy of theal FTA, extensive research has been performed by

set theory. The pioneering work on this belongset al. (1983), which treated probabilities of BEs as

fuzzy numbers, and applied the fuzzy extension determine the probability of Top Event (TE). Lin1997) developed a hybrid method which can simul-eal with probability and possibility measures in a

and Rao (1994) applied -cuts to determine the FP mechanical systems modeling with Fuzzy Fault

ding author. Tel.: +98 912 3585034.ddress: [email protected] (S.M. Lavasani).

Trees (FFTs). Cai et al. (1991) and Huang et al. (2004) adoptedpossibility theory to analyze FFTs. Dong and Yu (2005) appliedthe hybrid method to analyze FP of oil and gas transmissionpipeline. As another approach, Shu et al. (2006) used intuition-ist fuzzy methods to analyze FT on a printed circuit boardassembly.

Furthermore, Ping et al. (2007) used FFTA for assessing fail-ure of bridge construction. Toward marine accident analysisand prevention, Celik et al. (2010) proposed an investigationmodel based on FTA supported with fuzzy sets. Wang et al.(2013) employed FFTA for re and explosion of crude oil tanks.Recently, Liu et al. (2014) used FTA in emergency responseplanning.

The main aim of this research is to extend FFTA methodol-ogy to petrochemical process industry. This section introducesthe existing applications of FFTA throughout the variousindustries. The steps of research methodology including iden-tifying BEs, obtaining FP of BEs with known failure rate, ratingstate, aggregating stage, defuzzication process, transformingCrisp Failure Possibility (CFP) of BEs into FP, calculating all

i.org/10.1016/j.psep.2014.05.001 2014 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers.tension to Fuzzy Fault Tree Anation in petrochemical proces

iri Lavasania,, Anousheh Zendegania, Met Research Branch, Tehran Science and Research Branch University, Ht of Marine Engineering, Istanbul Technical University, Tuzla, 3494

b s t r a c t

ult Tree Analysis (FTA) is an established technique in risk manage

focused elds. It is a comprehensive, structured and logical ana

azards of complex systems. To conduct a quantitative FTA, it is ess

ct that sufcient data is not always available, the FTA method can

nment, so called as Fuzzy Fault Tree Analysis (FFTA). This resear

ocess industry in which re, explosion and toxic gas releases are rocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016lysis (FFTA)ndustry

elikb

ak, Tehran, Irannbul, Turkey

t associated with identied hazards specic

method aimed at identifying and assessing

l to have sufcient data. By considering the

dopted into the problems under fuzzy envi-

tends FFTA methodology to petrochemical

nized as potential hazards. Specically, the/j.psep.2014.05.001


ARTICLE IN PRESSPSEP-439; No. of Pages 142 Process Safety and Environmental Protection x x x ( 2 0 1 4 ) xxxxxx

eth

Minimal Cuprovided intant sectionsection em

2. Re

In circumsexists, therthe FTA stutheory witjudgment fThe new pstages. In separated second starates. In tto the vagfourth stagaggregatingwill then b(fuzzy possby employiconvert crisand quantiof all MCs structure o

2.1. Ide

As mentiontify hazardOccurrence(2010).

Ob fail

undaFig. 1 Structure of proposed m

t sets (MCs) and FP of TE, and ranking of MCs are Section 2. In Section 3, a case study on an impor-

of petrochemical plant is demonstrated. The lastphasis the highlights of the research.

2.2. known

The fo this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Trrocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016

search methodology

tances where the lack or incompleteness of datae is a need to incorporate expert judgment intody. A framework proposed based on the fuzzy seth the FTA method is capable of quantifying therom experts who express opinions qualitatively.roposed framework is developed in eight differentthe rst stage, BEs with known failure rates isfrom those BEs with a vague failure rate. Thege is to obtain the FPs of BEs with known failurehe third stage, expert judgments are assignedue BEs. These ratings are fuzzy numbers. Thee is an aggregation procedure. It is performed by

of experts opinions. A defuzzication processe adopted to transform the experts judgmentsibility) to corresponding crisp possibility valuesng an appropriate algorithm. The sixth stage is top possibilities values to the FPs. MCs are identieded in the seventh stage. In the last stage, rankingcan consequently be produced. Fig. 1 presents thef proposed methodology.

ntifying BEs

ed, the rst step of the methodology is to iden-s with known failure rates from vague hazards.

failure rate of some hazards are available from PDS

rate or evenpredominathe occurre

1. Statistic2. Extrapo3. Expert j

The statof experienextrapolatiand similarThe expertprobabilitie

A compoure may ocis only detis assumedfor many svalves. If athe compon(Spouge, 20

P(t) = 12

where is interval.odology.

taining Failure Probability (FP) of BEs withure rate

tion of a good analysis is the pedigree of failureee Analysis (FFTA) application in petrochemical process/j.psep.2014.05.001

t probability data that is assigned to BEs. There arently three methods that can be used to determinence probability of an event namely (Preyssl, 1995):

al method.lation method.udgment method.

istical method involves the treatment of direct testce data and the calculation of the probabilities. Theon method involves the use of model prediction

condition or using standard reliability handbook. judgment method involves direct estimation ofs by specialists.nent is tested periodically with test interval. A fail-cur at any time in the test interval, but the failureected in a test. After a test/repair, the component

to be as good as new. This is a typical situationafety-critical components, like sensors and safetyn event failure of a kind which can be inspected,ent failure probability can be obtained from Eq. (1)00; Rausand and Hoyland, 2004).

(1)

the component failure rate and is the inspection


ARTICLE IN PRESSPSEP-439; No. of Pages 14Process Safety and Environmental Protection x x x ( 2 0 1 4 ) xxxxxx 3

If a comThe compounreliabilit

P(t) = 1 e

where theinterval. BaP can be ob

P(t) = 1 (

2.3. Ra

In this stagrespect to synthesis ouncertaintystraints or a scienticerally quancontributedpsychologyand philoso

Quantinumber of

Evidenceobtained

Data existhe solubto infer t

There ar Scaling u

is not dirthan resc

Expert tives and goimpartialityimportant expert (e.g.of experts (sonal experin homogenheterogenehomogenou

In this sfor evaluatfactors of e

Rating oterms whicBE.

2.4. Ag

Since eachto his/her is necessarsensus. DifChen, 1994posed a neemploying

1

titut

e tim

tion

14) m Hsu pezoxturesu aper.

andguisterts. r opin

a pcan taile

culatRu, R

nd E (a1, ezoiction

, B) =

ere (Ailaritculate the Average Agreement (AA) degree AA(Eu) of theerts.

Eu) = 1M 1

4u /= vv = 1

S(Ru, Rv) (5)

culate the Relative Agreement (RA) degree, RA(Eu) of theerts.

= 1, 2, . . ., M) as RA(Eu) = AA(Eu)Mu=1AA(Eu)

(6)

mate the Consensus Coefcient (CC) degree, CC(Eu) ofert, Eu(u = 1, 2, . . ., M):

Eu) = W(Eu) + (1 ) RA(Eu) (7)ponent is of a kind which cannot be inspected.nent failure probability P, which is also called they, is determined from Eq. (2).

t (2)

component failure rate and t is the relevant timesed on the Maclaren series, the above equation fortained from Eq. (3) if t 0.1

1 + t1!

+ 2t2

2!+

3t3

3!+ +

ntn

n!

)= t (3)

ting state

e, experts express their opinions for each BE witheach subjective attribute. Expert elicitation is thef experts opinions of a subject where there is

due to insufcient data because of physical con-lack of resources. Experts elicitation is essentially

consensus methodology. Expert elicitation gen-ties uncertainty. Examples of elds that have

to probability elicitation are decision analysis,, risk analysis, Bayesian statistics, mathematicsphy.cation of subjective probabilities is employed in acircumstances (Korta et al., 1996):

is incomplete because it cannot be reasonably.ts only from analogous situations (one might knowility of one mineral and might use this informationhe solubility of another mineral).e conicting models or data sources.p from experiments to target physical processesect (scaling of mean values is often much simpleraling the uncertainties).

knowledge is inuenced by individual perspec-als (Ford and Sterman, 1998). Therefore, complete

of expert knowledge is difcult to achieve. Anconsideration is the selection of heterogeneous

both scientists and workers) or homogenous groupe.g. only scientists). The effect of difference in per-ience on expert judgment is assumed to be smallerous group compared to a heterogeneous group. Aous group of experts can have an advantage over as group through considering all possible opinions.tudy, a heterogeneous group of experts is selecteding the probability of vague events. The weightingxperts are determined according to Table 1.f expert judgment can be carried out by linguistich are used for soliciting expert opinions for each

gregating stage

expert may have a different opinion accordingexperiences and expertise in the relevant eld, ity to aggregate experts opinion to reach a con-ferent types of aggregation can be used (Hsu and; Aqlan and Ali, 2014). Aqlan and Ali (2014) pro-w method for aggregation of expert judgment bytriangle fuzzy numbers. As mentioned, Aqlan and

Table

Cons

Title

Servic

Educa

Ali (20whilstand traare mifore, Hthis pa

Hsuthe linof exphis/hetext byterms The de

1. CalSuv(Eu aA =trapfun

S(A

whsim

2. Calexp

AA(

3. Calexp

Eu(u

4. Estiexp

CC( this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Trrocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016Weighting score of different expert.

ion Classication Score

Senior academic 5Junior academic 4Engineer 3Technician 2Worker 1

e

30 years 52029 41019 369 25 1

time

PHD 5Master 4Bachelor 3HND 2School level 1

odel can just aggregate triangle fuzzy numbersand Chen (1994) model is able to aggregate triangleidal fuzzy numbers. Linguistic terms of this paper

of triangle and trapezoidal fuzzy numbers. There-nd Chen (1994) method of aggregation is used in

Chen (1994) presented an algorithm to aggregateic opinions of a homogenous/heterogeneous groupSuppose each expert, Ek (k = 1, 2, . . ., M) expressesion on a particular attribute against a specic con-

redened set of linguistic variables. The linguisticbe converted into corresponding fuzzy numbers.d algorithm is described as follows:

e the degree of agreement (degree of similarity)

v) of the opinions between each pair of experts

v, where Suv(Ru, Rv). According to this approach,a2, a3, a4) and B = (a1, a2, a3, a4) are two standarddal fuzzy numbers. Then the degree of similarity

of S, which is dened as:

1 14

4i=1

|ai bi| (4)

, B) [0, 1], the larger value of S(A, B), the greatery between two fuzzy numbers of A and B.ee Analysis (FFTA) application in petrochemical process/j.psep.2014.05.001



where method

= 0 noexpert aWhen as its imof each worthinthe deci

5. Finally, tcan be o

RAG = CC(E

2.5. De

Defuzzicaresult in futhe applica(Zhao and technique Sugeno in 1as:

X =

i(xi(x this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Trrocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016

Fig. 2 Process ow diagram of Dee

(0 1) is a relaxation factor of the proposed. It shows the importance W(Eu) over RA(Eu). When

importance has been given to the weight of annd hence a homogenous group of experts is used.

= 1, the consensus degree of an expert is the sameportance weight. The consensus degree coefcientexpert is good measure for evaluating the relativeess of each experts opinion. It is responsibility ofsion maker to assign an appropriate value to .he aggregated result of the experts judgment RAG,btained as follows:

1) R1 + CC(E2) R2 + + CC(EM) RM (8)

fuzzication process

tion is the process of producing a quantiablezzy logic. Defuzzication problems emerge fromtion of fuzzy control to the industrial processesGovind, 1991). The center of area defuzzicationis selected here. This technique was developed by985 (Sugeno, 1999). This method can be expressed

)xdx

)dx(9)

where X* imembershformula cazoidal fuzz(a1, a2, a3) i

X = a2

a1

xa2 a2

a1

Defuzzi(a1, a2, a3, a

X = a2

a1

xa a2

a1

= 13(a4

2.6. Tra

As aforemeof some evare vague. and CFPs ousing Eq. (1ee Analysis (FFTA) application in petrochemical process/j.psep.2014.05.001

thanizer.

s the defuzzied output, i(x) is the aggregatedip function and x is the output variable. The aboven be shown as follows for triangular and trape-y numbers. Defuzzication of fuzzy number A =s

a1a1 xdx +

a3a2

a3xa3a2 xdx

xa1a2a1 dx +

a3a2

a3xa3a2 dx

= 13(a1 + a2 + a3) (10)

cation of trapezoidal fuzzy number A =4) can be obtained by Eq. (11).

a12a1 xdx +

a3a2

xdx + a4

a3

a4xa4a3 xdx

xa1a2a1 dx +

a3a2

dx + a4

a3

a4xa4a3 dx

+ a3)2 a4a3 (a1 + a2)2 + a1a2(a4 + a3 a1 a2)

(11)

nsforming CFP of BEs into FP

ntioned, there are data available for failure ratesents whilst the data associated with the othersThere is inconsistency between FPs of certain BEsf vague events. This issue can be performed by2). Onisawa (1988) has proposed a function which

Please cite

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article in

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as: Lavasan

i, S.M

., et

al., A

n exten

sion to

Fuzzy

Fault

Tree A

nalysis

(FFTA)

application

in petroch

emical

process

industry.

Process Safety

and

Environ

men

tal Protection

(2014), h

ttp://d

x.doi.org/10.1016/j.p

sep.2014.05.001

ARTICLE IN PRESS

PSEP-439;

No.

of Pages

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Process

Safety

and

Enviro

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l Pro

tection

x

x x

(

2 0

1 4

)

xxxxxx

5

Table 2 BEs and failure states of Deethanizer.

1.Trip of P-401

1.1 Power Failure

1.1.1 Power failure from source(Mobin)

1.1.2 Trip from Sub Station1.1.2.1 Breaker Failure1.1.2.2 Transformer Failure1.1.2.3 Human error to stop thepump

1.2 Equipment Failure

1.2.1 Poor Maintenance

1.2.1.1 Poor PM (planning andcontrol)

1.2.1.2 Bad/wrong installation1.2.1.2.1 Lack of supervision1.2.1.2 .2 Lack of competency ofmaintenance workers

1.2.1.3 Poor quality of equipmentparts

1.2.1.3.1 Procurement inadequacy1.2.1.3.2 Lack of supervision andinspection by asset integrity dept.

1.2.2 Blockage in suction of P-4011.2.2.1 icing due to dryersdeciency1.2.2.2 Hydrate formation1.2.2.3 chocking of strainer

1.3 Human error to stop the pumpfrom DCS/Push bottom

1.3.1 Lack of knowledge (Training)1.3.2 Lack of skill (experience)1.3.3 Lack ofperception/carelessness

2. Failure FV 40071 A to close

2.1 Failure of Instrument Air (IA)2.1.1 Loss of IA from source(Mobin)2.1.2 Human error to close the IAvalves in plant/offsite battery limit

2.2. Failure/Error of FIC2.2.1 Equipment Failure2.2.2 Loose connections in IAnetwork

2.3 Human error in DCS to closethe FV

3. Failure of E-420

2.1 Failure of Instrument Air (IA)2.1.1 Loss of IA from source(Mobin)2.1.2 Human error to close the IAvalves in plant/offsite battery limit

3.1 Failure of C-501 due to poor PM

3.2 Equipment failure due tocorrosion

3.2.1 Internal (Inside erosion)3.2.2 External (Humidity)

4. Failure of TV-40075 to open 2.1 Failure of Instrument Air (IA)2.1.1 Loss of IA from source(Mobin)2.1.2 Human error to close the IAvalves in plant/offsite battery limit

Please cite

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i, S.M

., et

al., A

n exten

sion to

Fuzzy

Fault

Tree A

nalysis

(FFTA)

application

in petroch

emical

process

industry.

Process Safety

and

Environ

men

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(2014), h

ttp://d

x.doi.org/10.1016/j.p

sep.2014.05.001

ARTICLE IN PRESS

PSEP-439;

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6

Process

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tection

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(

2 0

1 4

)

xxxxxx

Table 2 (Continued)

5. Failure of PV-40102 to close4.1 Failure/Error of TICHuman error in DCS to open the FV2.1 Failure of Instrument Air (IA)Failure/Error of PIC2.3Human error in DCS to close theFVFailure of TV-40104

4.1.1 Equipment Failure2.1 Failure of Instrument Air (IA) 2.1.1 Loss of IA from source

(Mobin)2.1.1 Human error to close the IAvalves in plant/offsite battery limit

6.1.1 Failure/Error of TIC 6.1.1.1 Equipment Failure

6.2 Equipment Failure6.3 chocking due to polymerization

7.1 Failure of external body ofT-402

2.3 Human error in DCS to openthe FV6.2.1 Failure of FV 400916.2.2 6.2.3Failure of C-501Equipment failure due to corrosion

6.1.1.2 Loose connections in IAnetwork

6.2.3.1 Internal corrosion6.2.3.1 External corrosion

7.1.1 Bad manufacturing (Design)7.1.2 Poor welding

7.1.2.1 Poor Procedure7.1.2.2 Poor Supervision

7.1.3 Vibration7.1.4 corrosion 7.1.4.1 Internal

7.1.4.2 External7.2 Failure of supports 7.2.1 Bad manufacturing

7.2.2 Poor welding7.2.3 Vibration7.2.4 Lack of re proong in case ofre in adjacent area



eeth

can be usedby addressihuman sentity. The pras follows (1988; Lin an

FP ={

1/10

0,

2.7. Ca

By denitioing to the Tthat all failcan be obta

P(t) = P(MC+ P(M+ P(M

Where Pset i.

2.8. Ra

One of theimportanceimportancein the FT inSensitivity in the outp

erwiaintyd forrtainquesFig. 3 Fault tree representation of D

for converting CFP to FP. This function is derivedng some properties such as the proportionality ofsation to the logarithmic value of a physical quan-obability rate can be obtained from possibility rateOnisawa, 1988, 1990, 1996; Onisawa and Nishiwaki,

or othuncertmethoof uncetechni this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Trrocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016

d Wang, 1998):

K, CFP /= 0 CFP = 0

, K =[(

1 CFPCFP

)]1/3 2.301 (12)

lculating all MCs and FP of TE

n, a MC is a combination (intersection) of BEs lead-E. The combination is a minimal combination inures are needed for the TE to occur. TE probabilityined from Eq. (13).

1 MC2 . . . MCN) = P(MC1) + P(MC2) + CN) P(MC1 MC2) + P(MC1 MC3) + Ci MCj)) + (1)N1P(MC1 MC2 . . . MCN) (13)

(MCi) is the occurrence probability of minimal cut

nking of MCs

most important outputs of an FTA is the set of measures that are calculated for the TE. Such measures establish the signicance for all the MCs

terms of their contributions to the TE probability.Analysis (SA) is the study of how the uncertaintyut of a mathematical model or system (numerical

are current

Criticalit Risk Red

(TDS)

SA can b

Testing tin the pr

Increaseand outp

Uncertaisignican

Searchinpected re

Model sieffect onparts of t

Fussell-MC to the Tmodeled inall FT elemcalculated bthe particudetermine anizer failure.

se) can be apportioned to different sources of in its inputs. In other words, SA can be used as

testing robustness of a model results in presencety. SA of FTs is estimated by Importance measures

. The following probabilistic importance measuresee Analysis (FFTA) application in petrochemical process/j.psep.2014.05.001

ly in use for FTA:

y importanceuction Worth (RRW) or Top Decrease Sensitivity

e useful for a range of purposes, including:

he robustness of the results of a model or systemesence of uncertainty.d understanding of the relationships between inputut variables in a system or model.nty reduction: identifying model inputs that causet uncertainty in the output.g for errors in the model (by encountering unex-lationships between inputs and outputs).mplication xing model inputs that have no

the output, or identifying and removing redundanthe model structure.

Vesely Importance (F-VI) is the contribution of theE probability. F-VIs are determinable for every MC

the FT. This provides a numerical signicance ofents and allows them to be prioritized. The F-VI isy summing all the causes (MCs) of the TE involvinglar event. This measure has been applied to MCs tothe importance of individual MC. Where Qi(t) is the



Table 3 Deethanizer BEs.

Deethanizer failure Fault tree ref BE failure rate

1 Power failure from source (Mobin) 1.1.1 Linguistic term2 Breaker failure 1.1.2.1 Failure rate3 Transformer failure 1.1.2.2 Failure rate4 Human error to stop the pump (P-401) 1.1.2.3 Linguistic term5 Poor PM (planning and control) (P-401) 1.2.1.1 Linguistic term6 Lack of supervision (P-401) 1.2.1.2.1 Linguistic term7 Lack of competency of maintenance workers 1.2.1.2.2 Linguistic term8 Procurement inadequacy 1.2.1.3.1 Linguistic term9 Lack of supervision and inspection by asset integrity dept. 1.2.1.3.2 Linguistic term

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

contributiomeasure ca

IFVi (t) =Qi(QS(

Qi(t) = probaof TE due todecrease innot to occuTop Decreashows the

Table 4

BEs

1.1.2.1 1.1.2.22.1.1 2.2.1 2.2.2 3.1 Icing due to dryers deciency (Suction P-401) Hydrate formation (Suction P-401) Chocking of strainer (Suction P-401) Lack of knowledge (Training) Lack of skill (experience) Lack of perception/carelessness Loss of IA from source (Mobin) Human error to close the IA valves in plant/offsite battery limitEquipment Failure (FIC of FV-40071A) Loose connections in IA network (FIC of FV-40071A) Human error in DCS to close the FV Failure of C-501 due to poor PM Internal (inside erosion) (E-420) this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Trrocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016

External (humidity) (E-420) Equipment failure (TIC of TV-40075)Loose connections in IA network (TIC of TV-40075)Failure/error of PIC (PV-40102) Equipment failure (TIC of TV-40104) Loose connections in IA network (TIC of TV-40104) Failure of FV-40091 Failure of C-501 Internal corrosion (E-422) External corrosion (E-422) Chocking due to polymerization (E-422) Bad manufacturing (design) (external body of T-402) Poor welding Procedure (external body of T-402) Poor welding Supervision (external body of T-402) Vibration (external body of T-402) Internal corrosion (external body of T-402) External corrosion (external body T-402) Bad manufacturing (supports) Poor welding (supports) Vibration (supports) Lack of re proong in case of re in adjacent area (supports)

n of MC i to failure of the system, the importancen be quantied as follows (Modarres, 2006):

t)t)

(14)

bility of failure of MCi, QS(t) = probability of failure all MCs.Risk Reduction Worth (RRW) measures the

the probability of the TE if a given MC is assuredr. This importance measure can also be called these Sensitivity (TDS) (Shu et al., 2006). RRW for a MCdecrease in the probability of the TE that would be

obtained ifcalculated probabilitymum reducmodel robu

3. Ca

A petrochePolyethylenthe plasticof 300,000 t

FP of the BEs with known failure rate.

FP of BEs BEs FP of BEs BEs

0.01 3.2.1 0.012 6.1.1.2 0.015 3.2.2 0.008 6.2.1 0.002 4.1.1 0.014 6.2.2 0.014 4.1.2 0.009 6.2.3.1 0.018 5.1 0.013 6.2.3.2 0.02 6.1.1.1 0.014 6.3 1.2.2.1 Linguistic term1.2.2.2 Linguistic term1.2.2.3 Linguistic term1.3.1 Linguistic term1.3.2 Linguistic term1.3.3 Linguistic term2.1.1 Failure rate2.1.2 Linguistic term2.2.1 Failure rate2.2.2 Failure rate2.3 Linguistic term3.1 Failure rate3.2.1 Failure rateee Analysis (FFTA) application in petrochemical process/j.psep.2014.05.001

3.2.2 Failure rate4.1.1 Failure rate4.1.2 Failure rate5.1 Failure rate6.1.1.1 Failure rate6.1.1.2 Failure rate6.2.1 Failure rate6.2.2 Failure rate6.2.3.1 Failure rate6.2.3.2 Failure rate6.3 Failure rate7.1.1 Failure rate7.1.2.1 Linguistic term7.1.2.2 Linguistic term7.1.3 Failure rate7.1.4.1 Failure rate7.1.4.2 Failure rate7.2.1 Failure rate7.2.2 Linguistic term7.2.3 Failure rate7.2.4 Linguistic term

the MC did not occur. Therefore, the RRW can beby re-quantifying the FT with considering of the

of the given MC to 0. It thus measures the maxi-tion in the TE probability. RRW can be used to teststness.

se study

mical plant is built to manufacture Medium Densitye (MDP) and High Density Polyethylene (HDP) fors processing industry. The facility has a capacity/a based on 7920 h/y. The products are marketed

FP of BEs BEs FP of BEs

0.009 7.1.1 0.0170.011 7.1.3 0.020.0085 7.1.4.1 0.0190.017 7.1.4.2 0.0060.005 7.2.1 0.0150.023 7.2.3 0.012



ersio

Table 5

Linguistic

Very low (VLow (L) Medium (MHigh (H) Very high (

under the bplant is div

Plant Sectistock (ArePlant Sectiling (AreaPlant SectiPlant sectio

AdditionSection 02 ianizer is onDeethanize

3.1. Ide

A vent sysprovided toin propylenDeethanizetoo high teto form gucolumn anprovided aning, operatospare one. Twhere it conture. Steamat Deethanon the stea

7

.1

.2

.1 L L M

.2 M M H M M M L L L M H H

M H MVL L ML VL LM L LL VL L

L L M M H M

L L VLL M L

Table 6

No of exp

1 2 3 Fig. 4 Chen and Hwang conv

Fuzzy number of conversion scale 6.

terms Fuzzy sets

L) (0,0,0.1,0.2)(0.1,0.25,0.25,0.4)

) (0.3,0.5,0.5,0.7)(0.6,0.75,0.75,0.9)

VH) (0.8,0.9,1,1)

rand name LUPOLEN. For easy comprehension, theided into four main sections:

on 01: Purication (Area 700) and dosing of feed-a 100)on 02: Polymerization (Area 200) and powder hand-

300 & 400)on 03: Extrusion and product handling (Area 500)n 04: Granulate handling and logistic

ally, plant facilities are provided in Area 600.s one of the most important plant sections. Deeth-e of the main equipment of this section. Therefore,r is selected as case study in this paper.

Table

BEs

1.1.1 1.1.2.31.2.1.11.2.1.21.2.1.21.2.1.31.2.1.31.2.2.11.2.2.21.2.2.31.3.1 1.3.2 1.3.3 2.1.2 2.3 7.1.2.17.1.2.27.2.2 7.2.4 this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Trrocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016

ntifying BEs of Deethanizer

tem on propylene side of the E-420 and E-422 is evacuate non-condensable components containede that could accumulate. Bottom temperature ofr T-402 must be controlled carefully because at amperature the heavier olens in the bottom tendms and polymers, thus fouling the bottom of thed the reboiler. For this reason, a spare reboiler isd when reboiling becomes inefcient due to foul-r has to switch from the operating reboiler to thehe reboiling control valve is on the steam inlet linetrols the condensing pressure and hence tempera-

is injected in order to get a maximum temperatureizer bottom of about 82 C. A piping pot is providedm condensate line to make hydraulic guard.

The ovepropylene c0.3 wt% (0.4by FV-4007inhibitor isPackage Worder to limDiagram (P

Considegram of Deidentied a

Fault tretrated in Fi

Considerelated failuthe BEs are

Experts proles and decision weights.

ert Title Servicetime (Year)

Educationallevel

Senior 1019 Master Senior



Table 8 Aggregation calculation for the BE of 1.1.1.

Expert 1 (E1) 0.1 0.25 0.25 0.4Expert 2 (E2) 0.3 0.5 0.5 0.7Expert 3 (E3) 0.3 0.5 0.5 0.7

S (E12) 0.75 AA (E1) 0.75S (E13) 0.75 AA (E2) 0.875S (E23) 1 AA (E3) 0.875RA (E1) 0.3 CC (E1) 0.3315RA (E2) 0.35 CC (E2) 0.3415RA (E3) 0.35 CC (E3) 0.327Weight of expert 1 (E 1) 0.363Weight of expert 2 (E 2) 0.333Weight of expert 3 (E 3) 0.304Aggregation for 1.1.1 0.2337 0.417125 0.417125 0.60055

3.2. Separating BEs with known failure rate from BEswith unknown failure rate

The elements of the FT are divided into failure probabilityanalysis of BEs with known probabilities of occurrence andsubjective linguistic evaluations of hazards with unknownprobability rate. 43 BEs are identied for Deethanizer failure.24 of them there are nTable 3 preFT.

3.3. Caprobabilitie

As aforemthe pedigreassigned toard with k(1)(3). For enizer is 2.4 mechanicaEq. (1) as fo

FPmechanical

Table 9

BEs

1.1.1 1.1.2.3 1.2.1.1 1.2.1.2.1 1.2.1.2.2 1.2.1.3.1 1.2.1.3.2 1.2.2.1 1.2.2.2 1.2.2.3 1.3.1 1.3.2 1.3.3 2.1.2 2.3 7.1.2.1 7.1.2.2 7.2.2 7.2.4

FP of the BEs with known failure rates are calculated andpresented in Table 4.

3.4. Rating state

In the proposed method, a numerical approximation proposedby Chen and Hwang (1992) is used to convert linguistic term to

orresin thstic ts). T

n pluumbe anicok

hich bjectig. 4 per ts wi

give trapummenyed

10

are BEs with known occurrence probabilities whilstot historical data available for the other 19 BEs.sents all of the BEs associated with the proposed

lculating FPs of BEs with known occurrences

entioned, the foundation of a good analysis ise of failure rate or event probability data that is

BEs. Therefore, occurrence probabilities of haz-nown failure rate can be estimated by using Eqs.xample, the rate of mechanical failure of homoge-

103 with 4 inspections in a year. Therefore, FP ofl failure of homogenizer can be obtained by usingllows:

failure ofhomogenizer =12

2.4 103 412

= 4 103

Aggregation calculation for each subjective BE.

Aggregation of eachsubjective BE

(0.23,0.42,0.42,0.6)(0.13,0.24,0.27,0.42)

their cterms (linguitic termis seveable nto mak1956; Nof 6 wthe surate. Fthis pahazard

Thelar andfuzzy n

As emplo

Table

BEs

1.1.1 1.1.2.3 this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Trrocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016

(0.16,0.33,0.33,0.49)(0.5,0.67,0.67,0.83)(0.3,0.5,0.5,0.7)(0.16,0.33,0.33,0.49)(0.39,0.58,0.58,0.76)(0.3,0.5,0.5,0.7)(0.1,0.25,0.25,0.4)(0.5,0.67,0.67,0.83)(0.39,0.58,0.58,0.76)(0.13,0.24,0.27,0.42)(0.07,0.17,0.2,0.34)(0.17,0.33,0.33,0.5)(0.07,0.17,0.2,0.34)(0.16,0.33,0.33,0.49)(0.39,0.58,0.58,0.76)(0.07,0.17,0.2,0.34)(0.16,0.33,0.33,0.49)

1.2.1.1 1.2.1.2.1 1.2.1.2.2 1.2.1.3.1 1.2.1.3.2 1.2.2.1 1.2.2.2 1.2.2.3 1.3.1 1.3.2 1.3.3 2.1.2 2.3 7.1.2.1 7.1.2.2 7.2.2 7.2.4 ponding fuzzy numbers. There are generic verbale system where scale 1 contains two verbal termserms) and scale 8 contains 13 verbal terms (linguis-he typical estimate of a human memory capacity,s-minus two chunks, which means that the suit-

er for linguistic term selection for human beings appropriate judgment is between 5 and 9 (Miller,is and Tsuda, 1985). Therefore, conversion scalecontains 5 verbal terms is selected for performingive assessment of hazards with unknown failurepresents the fuzzy linguistic scale that is used ino involve the judgments of experts with respect toth unknown failure rate.n linguistic terms are in the form of both triangu-ezoidal fuzzy numbers. Table 5 represents all the

bers in the form of trapezoidal numbers.tioned, a heterogeneous group of experts isto perform the judgment for the vague events.

Deffuzication process for all subjective BEs.

Aggregation ofsubjective basic events

Defuzzication ofsubjective BEs (CFP)

(0.23,0.42,0.42,0.6) 0.417(0.13,0.24,0.27,0.42) 0.269ee Analysis (FFTA) application in petrochemical process/j.psep.2014.05.001

(0.16,0.33,0.33,0.49) 0.326(0.5,0.67,0.67,0.83) 0.667(0.3,0.5,0.5,0.7) 0.5(0.16,0.33,0.33,0.49) 0.326(0.39,0.58,0.58,0.76) 0.576(0.3,0.5,0.5,0.7) 0.5(0.1,0.25,0.25,0.4) 0.250(0.5,0.67,0.67,0.83) 0.667(0.39,0.58,0.58,0.76) 0.579(0.13,0.24,0.27,0.42) 0.269(0.07,0.17,0.2,0.34) 0.196(0.17,0.33,0.33,0.5) 0.333(0.07,0.17,0.2,0.34) 0.196(0.16,0.33,0.33,0.49) 0.326(0.39,0.58,0.58,0.76) 0.579(0.07,0.17,0.2,0.34) 0.198(0.16,0.33,0.33,0.49) 0.329



Table 11 Converting CFP into FP.

BEs Defuzzication ofsubjective BEs (CFP)

FP ofsubjective BEs

1.1.1 0.417 0.00271.1.2.3 0.269 0.00061.2.1.1 0.326 0.00121.2.1.2.1 0.667 0.01491.2.1.2.2 0.5 0.0051.2.1.3.1 0.326 0.00121.2.1.3.2 0.576 0.00831.2.2.1 0.5 0.0051.2.2.2 0.250 0.00051.2.2.3 0.667 0.01491.3.1 0.579 0.00851.3.2 0.269 0.00061.3.3 0.196 0.00022.1.2 0.333 0.00132.3 0.196 0.00027.1.2.1 0.326 0.00127.1.2.2 0.579 0.00857.2.2 0.198 0.00027.2.4 0.329 0.0012

The weighbe obtainethis case, judgments.weights.

Expert juillustrated

3.5. Ag

In this stagtive BE. As aof 1.1.1 are 0.5 in aggre

These caculation, sudegree of agation calcTable 9.

Table 13 Importance level of each MC.

No of MCs FP of MCs F-V IM Ranking ofMCs

MCs1 0.0027 0.0089 19MCs2 0.01 0.0331 12MCs3 0.015 0.0496 6MCs4 0.0006 0.0020 23MCs5 0.0012 0.0040 22MCs6 0.0149 0.0493 7MCs7 0.005 0.0165 18MCs8 0.0012 0.0040 22MCs9 0.0083 0.0274 15MCs10 3.73e8 0.0000 26MCs11 0.0085 0.0281 14MCs12 0.0006 0.0020 23MCs13 0.0002 0.0007 24MCs14 0.002 0.0066 20MCs15 0.0013 0.0043 21MCs16 0.014 0.0463 8MCs17 0.018 0.0595 4MCs18 0.0002 0.0007 24MCs19 0.02 0.0661 2MCs20 0.012 0.0397 10MCs21 0.008 0.0265 16

2 0.014 0.0463 83 0.009 0.0298 134 0.013 0.0430 95 0.014 0.0463 86 0.009 0.0298 137 0.011 0.0364 118 0.0085 0.0281 149 0.017 0.0562 50 0.005 0.0165 181 0.023 0.0760 12 0.017 0.0562 53 0.00001 0.0000 254 0.02 0.0661 25 0.019 0.0628 36 0.006 0.0198 177 0.015 0.0496 68 0.0002 0.0007 249 0.012 0.0397 100 0.0012 0.0040 22

Table 12

MCs

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 ts of experts are not equal. Experts weights cand based on their proles and competencies. Inthree experts are employed for performing the

Table 6 shows the experts proles and decision

dgment on the BEs with unknown failure rates areby Table 7.

gregation of BEs

e, all the ratings are aggregated under each subjec-n example, detailed aggregation calculations for BEgiven in Table 8. (Relaxation factor) is consideredgation calculation of subjective BEs.lculations contain attribute based aggregation cal-ch as average degree of agreement (AA), relativegreement of each expert (RA), etc. After the aggre-ulations, the results of all the BEs are presented in

MCs2MCs2MCs2MCs2MCs2MCs2MCs2MCs2MCs3MCs3MCs3MCs3MCs3MCs3MCs3MCs3MCs3MCs3MCs4 this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Tree Analysis (FFTA) application in petrochemical processrocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016/j.psep.2014.05.001

FP of all MCs.

FP MCs FP

1.1.1 0.0027 21 3.2.2 0.0081.1.2.1 0.01 22 4.1.1 0.0141.1.2.2 0.015 23 4.1.2 0.0091.1.2.3 0.0006 24 5.1 0.0131.2.1.1 0.0012 25 6.1.1.1 0.0141.2.1.2.1 0.0149 26 6.1.1.2 0.0091.2.1.2.2 0.005 27 6.2.1 0.0111.2.1.3.1 0.0012 28 6.2.2 0.00851.2.1.3.2 0.0083 29 6.2.3.1 0.0171.2.2.1 1.2.2.2 1.2.2.3 3.73e8 30 6.2.3.2 0.0051.3.1 0.0085 31 6.3 0.0231.3.2 0.0006 32 7.1.1 0.0171.3.3 0.0002 33 7.1.2.1 7.1.2.2 0.000012.1.1 0.002 34 7.1.3 0.022.1.2 0.0013 35 7.1.4.1 0.0192.2.1 0.014 36 7.1.4.2 0.0062.2.2 0.018 37 7.2.1 0.0152.3 0.0002 38 7.2.2 0.00023.1 0.02 39 7.2.3 0.0123.2.1 0.012 40 7.2.4 0.0012



Table 14 Result of SA.

No of MCs FP of MCs F-V IM MCs Rank Revised TE value RRW (TEinitialTErevised) RRW rank

MCs1 0.0027 0.0089 19 0.3006 0.0019 19MCs2 0.01 0.0331 12 0.2954 0.0070 12MCs3 0.015 0.0496 6 0.2918 0.0106 6MCs4 0.0006 0.0020 23 0.3020 0.0004 23MCs5 0.0012 0.0040 22 0.3016 0.0008 22MCs6 0.0149 0.0493 7 0.2919 0.0106 7MCs7 0.005 0.0165 18 0.2989 0.0035 18MCs8 0.0012 0.0040 22 0.3016 0.0008 22MCs9 0.0083 0.0274 15 0.2966 0.0058 15MCs10 3.73e8 0.0000 26 0.3024 0.0000 26MCs11 0.0085 0.0281 14 0.2965 0.0060 14MCs12 0.0006 0.0020 23 0.3020 0.0004 23MCs13 MCs14 MCs15 MCs16 MCs17 MCs18 MCs19 MCs20 MCs21 MCs22 1 MCs23 MCs24 8 MCs25 1 MCs26 MCs27 MCs28 MCs29 MCs30 MCs31 MCs32 MCs33 MCs34 MCs35 MCs36 MCs37 MCs38 MCs39 MCs40

3.6. De

The centercalculate thshows the

3.7. Con

CFP of the sponding Fthe subject0.0002 0.0007 24 0.3023 0.002 0.0066 20 0.3010 0.0013 0.0043 21 0.3015 0.014 0.0463 8 0.2925 0.018 0.0595 4 0.2897 0.0002 0.0007 24 0.3023 0.02 0.0661 2 0.2882 0.012 0.0397 10 0.2940 0.008 0.0265 16 0.296820.014 0.0463 8 0.292540.009 0.0298 13 0.296110.013 0.0430 9 0.293250.014 0.0463 8 0.29254 this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Trrocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016

0.009 0.0298 13 0.29611 0.011 0.0364 11 0.294687 0.0085 0.0281 14 0.296465 0.017 0.0562 5 0.290382 0.005 0.0165 18 0.29894 0.023 0.0760 1 0.286024 0.017 0.0562 5 0.290382 0.00001 0.0000 25 0.302438 0.02 0.0661 2 0.288209 0.019 0.0628 3 0.288935 0.006 0.0198 17 0.298235 0.015 0.0496 6 0.291823 0.0002 0.0007 24 0.302306 0.012 0.0397 10 0.293973 0.0012 0.0040 22 0.301607

fuzzication process of subjective BEs

of area deffuzication technique is employed toe deffuzication of all the subjective BEs. Table 10

result of subjective BEs deffuzication.

verting CFP of BEs into FP

subjective BEs can be transformed into the corre-P by using Equation 12. Table 11 presents FP of allive BEs.

3.8. Ca

To quantifybility for eBE probabithe Boolearules are emconsideredgated upwaMCS. Furthof FP of the

Fig. 5 Result of sensitivity analysis fo0.0001 240.0014 200.0009 210.0099 80.0128 40.0001 240.0142 20.0085 100.0056 160.0099 80.0063 130.0092 90.0099 8ee Analysis (FFTA) application in petrochemical process/j.psep.2014.05.001

0.0063 130.0078 110.0060 140.0121 50.0035 180.0164 10.0121 50.0000 250.0142 20.0135 30.0042 170.0106 60.0001 240.0085 100.0008 22

lculating FP of TE

the probability of TE of the fault tree a proba-ach BE in the fault tree must be provided. Theselities are then propagated upward to the TE usingn relationships. In other words, conventional FTAployed for TE quantication. Therefore, all BEs are

independent. The BE probabilities can be propa-rd using MCs. Table 12 presents the FP of all theermore, TE is obtained by using Eq. (13). The value

TE is 0.3024 per year.

r revised TE.



s.

3.9. Ra

Table 13 preimportance

In a SAFP is changity is detereither diffedifferent pagiven sensia time. Thimethod is proposed mcan be calcgiven eventhave the hiresult in reMCs. Theresame as theMCs31 has ability. Thethe highesremains thmodel satis

The fouafter eliminbar shows tumn 5th ofTable 14, MIf the valuethe new TEthe expecta

FVI and Results of Fcolumns of

As menerror in theproposed mFig. 6, contthe TE ratemined MCsthe Deetha

4. Co

As one of thare requireplanning atoxic gas rtion. This re

strapera

the f

zzy natiionasingiguittion,ble fead orrenvagufcief theence

imporovin

indee sy

furthcritic. Moquesost b

owle

thorand

hnicaudy o.

enceFig. 6 RRW result

nking of MCs

sents the ranking of MCs based on their calculated levels (Eq. (14))., an input data parameter, such as a componented, and the resulting change in the TE probabil-mined. This is repeated for a set of changes usingrent values for the same parameter or changingrameters, e.g. changing different FPs. Usually for ativity evaluation, only one parameter is changed ats is called a one-at-a-time sensitivity study. Thisemployed here to validate the sensitivity of theodel. RRW is employed to perform SA. The RRW

ulated by re-quantifying the MCs probability of the set to 0. It is expected that eliminating of MCs thatghest contribution to the occurrence of TE shouldducing the occurrence rate of TE more than otherfore, ranking of RRW values is expected to be the

initial ranking result of MCs. As shown in Table 14,the highest contribution to the TE occurrence prob-refore, the RRW value of MCs31 is 0.0164 which ist as expected. It shows the ranking result whiche same as the previous calculation. The proposedes the aforementioned expectations.rth column of Table 14 shows the value of the TEating of MCs. Fig. 4 includes 40 bars; the red colorhe TE value which is 0.3024. All new TE values (Col-

Table 14) are presented in blue bars. As shown inC number 26 is the most critical MC of the system.

of MC 26 is reduce to zero, it would be expected value reduce more than others. Fig. 5 can conrmtion.RRW are employed for ranking of MCs in this paper.VI measure and RRW are shown in the 3rd and 6th

Table 14.tioned, one of the advantages of SA is to identify

model. Result of Table 14 and Fig. 5 show that the

demonplant olights

A fualtervent

By uambaddiexi

Instoccuthe insuity oinu

Theimpsurein th

As other ductedtechnimake c

Ackn

The auCharkhfor teccase stations

Refer this article in press as: Lavasani, S.M., et al., An extension to Fuzzy Fault Trrocess Safety and Environmental Protection (2014), http://dx.doi.org/10.1016

odel can produce robust outcomes. As obvious inrolling the rst 11 most critical MCs would reduce

from 0.3 to 0.15. It means that control of the deter- will ensure considerable safety improvement innizer section of the Arya Sasol Plant.

nclusion and discussions

e heavy industry discipline, petrochemical plantsd to implement effective and consistent safetygainst potential hazards (i.e. re, explosion andeleases) in order to ensure sustainable produc-search focused on developing a FFTA methodology

Aqlan, F., Albow-tie fPrevent.

Cai, K.Y., Wetheory oSyst. 42,

Celik, M., Laapproach48, 1827

Chen, S.J., HMaking,

Dong, H.Y., Yand gas Loss Prevting with Deethanizer failure within petrochemicaltional concept. Consequently, the research high-ollowing points:

methodology for FT evaluation seems to be anve solution to overcome the weak points of the con-l approach.

linguistic variables, it is possible to handle theies in the expression of the occurrence of a BE. In

the state of each BE can be described in a moreorm, by using the concept of fuzzy sets.f using CFP, FP is used to characterize the failurece of the system events. It can efciently expresseness of the nature of system phenomena andnt information. Further, regardless of the complex-

system, it is also possible to identify which BE can system FP the most.rtance measure can provide useful information forg the safety performance of a system. F-VI mea-x assists the analyst in identifying the critical MCsstem for reducing occurrence likelihood of a TE.

er research, application of FFTA methodology toal processes in petrochemical plant can be con-reover, multi attribute decision making (MADM)

can be adopted into the proposed methodology toenet analysis for controlling the determined MCs.

dgement

s gratefully acknowledge to HSE manager (Hossein) of Arya Sasol Petrochemical Company (A.S.P.C.)l information support in the demonstration of then Deethanizer failure in petrochemical plant oper-

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An extension to Fuzzy Fault Tree Analysis (FFTA) application in petrochemical process industry1 Introduction2 Research methodology2.1 Identifying BEs2.2 Obtaining Failure Probability (FP) of BEs with known failure rate2.3 Rating state2.4 Aggregating stage2.5 Defuzzification process2.6 Transforming CFP of BEs into FP2.7 Calculating all MCs and FP of TE2.8 Ranking of MCs

3 Case study3.1 Identifying BEs of Deethanizer3.2 Separating BEs with known failure rate from BEs with unknown failure rate3.3 Calculating FPs of BEs with known occurrence probabilities3.4 Rating state3.5 Aggregation of BEs3.6 Defuzzification process of subjective BEs3.7 Converting CFP of BEs into FP3.8 Calculating FP of TE3.9 Ranking of MCs

4 Conclusion and discussionsAcknowledgementReferences

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Documents

fuzzy extension

fp of bes

fuzzy numbers

used ffta

probabilities of bes

used fta

petrochemical process

deethanizer failure