lo

R ChChe

Importance analysis

losicheelt tofin cnt o

mic grmarkeserveseen deies folnstruct

designation. For system in design, FTA can provide an estimate of thefailure probability and contributors using generic data and also can beusedas a supporting tool of a performance-baseddesign. In an existingsystem, FTA can identify weaknesses, evaluate possible upgrades,monitor and predict behavior. For those merits, FTA technique hasbeen extensively used in many elds, such as nuclear power, electric

In order to handlesied real applica-in situations intoto be effective ondaries and preciseuresh, Babar, & Raj,eng (1994) carried

out systemreliability analysis byusing fuzzy set theory. Dong andYu(2005) applied fuzzy theory to estimate the failure probabilities ofBEs. Tanaka, Fan, Lai, and Toguchi (1983), Pan et al. (2007), Sureshet al. (1996), and Miri Lavasani, Wang, Yang, and Finlay (2011)implemented fuzzy theory into the FTA technique for certain sys-tem safety assessment. In this paper, the imprecise failure data ofBEs of the COTFE fault tree are replaced with fuzzy numbers and anapproach of fuzzy based fault tree analysis (FFTA) is introduced toestimate the probability of occurrence of the COTFE. Further, the

* Corresponding author. Tel.: 86 13658001455.

Contents lists availab

n

w.

Journal of Loss Prevention in the Process Industries 26 (2013) 1390e1398E-mail address: wdqmnn@126.com (D. Wang).According to statistics, the crude oil tank re and explosion (COTFE)is the most frequent type of accident in petroleum reneries, oilterminals or storage (Fan, 2005). Besides China, yearly losses due tothe COTFE are substantial all over the world (Chang & Lin, 2006).

Fault tree analysis (FTA) is a systematic approach to estimate safetyand reliability of a complex system, qualitatively as well as quantita-tively. FTA can be applied both to an existing system and a system in

system questionable by conventional methods.inevitable imprecise failure information in divertions, many researches have taken the uncertaconsideration. Fuzzy set theory has been provensolving problems where there are no sharp bounvalues, while it is also efcient (Onisawa, 1990; S1996; Zadeh,1965). Chen (1994) andMon and Chdesign and safe management of storage tanks and their accessories,there is always the possibility of re or explosion for various causes.

components or BEs (Dong & Yu, 2005; Liang & Wang, 1993; Pan &Yun, 1997). And this makes quantitative analysis of a fault tree of a1. Introduction

Recent years see sustainable econoturbulence in international crude oilneed for much larger strategic oil rescale crude oil storage tanks have bpresently. Although most companguidelines and standards for the co0950-4230/$ e see front matter 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.jlp.2013.08.022tance measure of basic events and the cut sets importance measure, is performed to help identifying theweak links of the crude oil tank system that will provide the most cost-effective mitigation. Also, a casestudy and analysis is provided to testify the proposed method.

2013 Elsevier Ltd. All rights reserved.

owth of China,while thet has stimulated Chinas. More and more large-signed and constructedlow strict engineeringion, material selection,

power, chemical process, oil and gas transmission, etc (Dong & Yu,2005; Prugh, 1992; Sadiq, Saint-Martin, & Kleiner, 2008).

In traditional FTA, the failure probabilities of the basic events(BEs) are expressed by exact values (Dong & Yu, 2005; Ferdous,Khan, Sadiq, Amyotte, & Veitch, 2009; Sadiq et al., 2008). Howev-er, in reality, the vagueness nature of a system, the working envi-ronment of a system, and the lack of sufcient statistical inference,all raise difculties in the estimation of occurrence probabilities ofFuzzy fault tree analysisOccurrence probability probability. Further, importance analysis for the COTFE fault tree, including the FusselleVesely impor-Crude oil tankFire and explosion such uncertain problems. Hence, this article investigates a hybrid approach of fuzzy set theory and fault

tree analysis to quantify the COTFE fault tree in fuzzy environment and evaluate the COTFE occurrenceFuzzy fault tree analysis for re and exp

Daqing Wang a, *, Peng Zhang b, Liqiong Chen a

a School of Petroleum Engineering, Southwest Petroleum University, 610500 Chengdu, Pb School of Civil Engineering and Architecture, Southwest Petroleum University, 610500

a r t i c l e i n f o

Article history:Received 9 January 2013Received in revised form16 March 2013Accepted 28 August 2013

Keywords:

a b s t r a c t

Crude oil tank re and expoil terminals or storage whIn this paper, with fault tridentied and a COTFE fauthe occurrence probabilityoften very difcult to obtadata, changing environme

Journal of Loss Preventio

journal homepage: wwAll rights reserved.sion of crude oil tanks

inangdu, PR China

ion (COTFE) is the most frequent type of accident in petroleum reneries,often results in human fatality, environment pollution and economic loss.qualitative analysis technique, various potential causes of the COTFE areree is constructed. Conventional fault tree quantitative analysis calculatesthe COTFE using exact probability data of the basic events. However, it isorresponding precise data and information in advance due to insufcientr new components. Fuzzy set theory has been proven to be effective on

le at ScienceDirect

in the Process Industries

elsevier .com/locate/ j lp

OR

Tank fire and explosion

Ignition sources

AND

Vapor-air mixtures within explosive range

A

Electrical apparatus sparks

Mobile

telephone

Other n

on- e

xplosion

proof electrical equipm

ents

X19

X16

X17

Non-e

xplosion proof m

onitor

or detector

X18

Audio-visual or photographic equipm

ent

OR

Impact sparks

Collision

of metal

tools and

tankw

all during

maintenance

operation

Using

non- e

xplosion proof tools

Wearing iron

nail

-shoes

X1

X2

X3

OR

Open fires

Smoking

Lighter

X5X4

X7

X6

X8

OR

Vehicles w

ithout flam

e arresters

Fire work

Match

Static sparks

B

Electrified railw

ay

OR

Stray current

X20 X21

X22

Cathodic protection

Electric leak agenearby

Lightning sparks

AND

Ground rod

damaged

Air terminal

damaged

X12

Deflector

damaged

X13

X14

X15

X9

X11

X10

Lightning induction

OR

Lightningstroke

OR

OR

Imperfect earth

Arrester faults

Without installing

lightning protection

facilities

Lightninginvasio

n

along pipelines

Directlightning

flash

AND

Operator close

to a conductorOR

Broken ground wire

High oil flow

velocity

Friction between splashing oila

nd air

Oil lashing again

st m

etalmaterials

AND

OR

Friction between fiber

and hum

an

body

Without installing

anti

- static grounding device

Floating metal

debris on oil surf ace

X32

X31

X30

X28 X29

X24

X25

X23

X34

X33

Static sparks

Non-standard

apparatus

Not enough

standing time

X26

X27

OR

Measuring operational

error

OR

Electrostatic accumulation

Bad grounding

Non

-standard gro

und resistance

B

Oil tankelectrostaticdischarge

Human body electrostaticdischarge

Rough inner

wall ofpipeline

AND

X38

X37

Flexible co

nnection pipe

rupture

X42

X43

X40 X41

A

OR

Vapor-air mixtures within explosive range

Oil spill

Bre

athingvalve

openby

breakdown

Tank top

unattended

Excessive loading

Wrong valve

opened

X35

X36

OR

Oil leakage

Tankw

all broken

by external force

Po

or se

al aroundm

anhole

High

degreeco

rrosion

ofta

nkw

all

OR

Operational error

Gauge hatch

often open

X39

Fig. 1. Schematics of the COTFE fault tree.

D. Wang et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1390e1398 1391

often open, breathing valve open by breakdown or oil leakage. Next,

XX X XXX

in thi n

XiXnX37 j

X33X34Xj s r j

XsXrXjAXi

Xj

XiXjconsider these sub-events as the new intermediate events, and theneach of them will be substituted by the lower events. Continuedeveloping the fault tree until its all branches have been terminatedby basic or undeveloped events. Finally, a complete fault tree of theCOTFE is constructed as shown in Fig. 1. The proposed fault tree in-cludes 43BEs that contribute to the occurrence of theCOTEFaccident.

2.2. Evaluation of COTFE fault tree

After the COTFE fault tree is fully drawn, both qualitative andquantitative evaluation can be performed. The aim of qualitativeanalysis of a fault tree is to nd out the minimal cut sets (MCSs). TheMCSs relate the TEdirectlywith the basic event causes andaMCS is thesmallest combination of BEs which if they all fail will cause the occur-rence of the undesired event. TheMCSs are very useful for determiningthe various ways in which a top undesired event could occur. In thisstudy, the MCSs of the COTFE fault tree are obtained by using thecombination of Fussell-Vesely algorithm and the rules of Booleanalgebra (Fussell & Vesely, 1972; Wang, 1999). The proposed fault treeyields 392MCSs for just 43BEs, including90MCSsof order2, 234MCSsof order 3 and 68 MCSs of order 4. The MCSs equation is as follows:

T MCS1 MCS2 .MCSN

X

m

Xk

Xn

XmXkXnX37 Xn

X33X34XnX37

Xs

Xr

Xn

XsXrXnX37

!0@X

m

Xk

Xj

XmXkXj

1proposed approach is used to perform importance analysis of theCOTFE fault tree in order to help decisionmaker determinewhetherand where to take preventive or corrective action on the crude oiltank system in the risk management process.

2. Traditional FTA of COTFE

2.1. Construction of COTFE fault tree

FTA is a deductivemethod for identifying ways inwhich hazardscan lead to accidents. The approach starts with a top undesiredevent and work backwards towards the various scenarios that cancause the accident. In a fault tree, the top, intermediate and basicevents are connected together by logic gates. The gates show re-lationships of input events needed for the occurrence of a fault atthe output of the gate. AND gates combine input events, all of whichmust exist simultaneously for the output to occur. OR gates alsocombine input events, but any one is sufcient to cause the output.

Inpresentpaper, theCOTFEaccident is considered as the topevent(TE). Two intermediate events must occur together for the COTFE:ignition sources and vapor-air mixtures within explosive range, sothey must be connected to the TE by an AND gate. Various ignitionsourcesmay exist in the tank park: impact sparks, static sparks, openres, lighting sparks, electrical apparatus sparks and stray current.Any one of them could ignite an explosive mixture if contacted, sothese must be connected by an OR gate. Also there are many causesthat can lead to the explosive mixtures, such as oil spill, gauge hatch

D. Wang et al. / Journal of Loss Prevention1392(1)where 1 i 8 and 16 i 22, 38 j 43, 26 k 32,23 m 25, 35 n 36, 12 r 15, 9 s 11; N is the serialnumber of MCS, 1 N 392; X represents BE.

The aim of quantitative analysis of a developed fault tree is toprovide ameasure of the probability of occurrence of the TE and themajor faults contributing to the TE. The quantitative evaluation re-quires the gathering of exact failure data of BEs for input to the faulttree. However, for the COTFE fault tree, it is difcult to have a preciseestimationof theBEprobability due to insufcient data; in factmanyBEs of the COTFE fault treemay not have quantitative data at all dueto its inherent uncertainty and imprecision. Therefore, it is notpossible to assign a single value of probability to each BE. In order toovercome such limitations in traditional FTA, a fuzzy basedapproach is developed and discussed in the following sections.

3. Fuzzy based FTA of COTFE

3.1. Fuzzy numbers to dene probabilities of the BEs

The concept of fuzzy set theory was introduced by L.A Zadeh(1965) to deal with uncertain or vague information. A fuzzy setdened on a universe of discourse (U) is characterized by a mem-bership function, m(x), which takes values from the interval [0, 1]. Amembership function provides a measure of the degree of simi-larity of an element in U to the fuzzy subset. Fuzzy sets are denedfor specic linguistic variables. Each linguistic term can be repre-sented by a triangular, trapezoidal or Gaussian shape membershipfunction. The selection of a membership function essentially de-pends on the variable characteristics, available information andexperts opinion. Here, triangular fuzzy numbers (TFNs) and trap-ezoidal fuzzy numbers (ZFNs) are employed for their simplicity andefciency to quantify the probabilities of the BEs. The triangularrepresentation shows the fuzzy possibility of a BE can be denotedby a triplet (a1, a2, a3) and the corresponding membership functionis written as (Wang, 1997):

m~Ax

8>>>:

0 ; x a1x a1=a2 a1 ; a1 x a2a3 x=a3 a2 ; a2 x a3

0 ; x a3(2)

A ZFN denoted by a quadruple (a1, a2, a3, a4) is dened asfollows:

m~Ax

8>>>>>>>:

0 ; x a1x a1=a2 a1 ; a1 x a2

1 ; a2 x a3a4 x=a4 a3 ; a3 x a4

0 ; x a4

(3)

3.2. Aggregation of fuzzy numbers of the BEs

Since each expert may have a different opinion about the sameBE according to his/her experience and expertise in the relevanteld, in order to achieve agreement among experts conictedviews, the fuzzy numbers assigned by different experts should beaggregated to a single one. A consistency aggregation method (Wei,Qiu, &Wang, 2001) is proposed in this paper. This methodology is arevised version of the Hsu and Chens algorithm (Hsu & Chen,1996),which overcomes the assumed restriction that the opinions of allexperts represented by fuzzy numbers should have a commonintersection. The proposed method is described as follows:

(1) Calculate the similarity degree s~A ; ~A of the opinions ~A and ~A

e Process Industries 26 (2013) 1390e1398i j i jof a pair of experts Ei and Ej.

i1 i1 i1 i1

in thCOTFE.Giving the fuzzy possibilities for all BEs, ~p1; ~p2;.; ~pn, the fuzzy

possibilities of the MCSs (~P ) are estimated using followingas follows:

~pj Xni1

wi5~pij j 1;2;.;m (10)

where ~pj is the aggregated fuzzy number of BEj; ~pij is the fuzzynumber of BEj assigned by expert Ei;m is the number of experts; n isthe number of BEs; wi is a weighting factor of the expert Ei.

3.3. The fuzzy COTFE possibility estimation

To minimize the error due to uncertainty in BE probabilitydata, the present algorithm uses fuzzied possibility data of BE forquantication of a fault tree. Fuzzy arithmetic operations rules(Liang & Wang, 1993; Tanaka et al., 1983) are employed to esti-mate the fuzzy possibility of the MCSs and the same for thewi a$EIDi 1 a$RADi i 1;2;.;n (9)

where a (0a 1) is a relaxation factor which shows the impor-tance EIDi over RADi; EIDi (0 EIDi 1 and

PEIDi 1) can be

determined by using Delphi method (Dong & Yu, 2005) or analytichierarchy process (Bryson & Mobolurin, 1994).

(5) The aggregation result of the experts opinions can be obtained(4) The aggregation weight (wi) of each expert Ei is the combina-tion of the RADi and the importance degree (EIDi) of experts Ei.isjj 1

(3) Calculate the relative agreement degree (RAD) of each expert.

RADi AEi=Xni1

AEi (8)s~Ai; ~Aj

EVi=EVj; EVi EVjEVj=EVi; EVj EVi (4)

where s~Ai; ~Aj [0,1] is the similarity function; ~Ai and ~Aj are twostandard fuzzy numbers, respectively; EVi and EVj separatelyrepresent the expectancy evaluation for ~Ai or ~Aj. The EV of a trap-ezoidal fuzzy number ~A a1; a2; a3; a4 is dened as:

EV~A 1

2

hE~A E

~Ai

(5)

where E(A) (a1 a2)/2, E(A) (a3 a4)/2.

(2) Construct the consensus matrix M and calculate the averageagreement degree A(Ei) of the experts.

M

0BB@

1s21sn1

s121sn2

//1/

s1ns121

1CCA (6)

where sij s~Ai; ~Aj, if i j, then sij 1. A(Ei) is dened as:

AEi 1n

Xnsij~Ai; ~Aj

(7)

D. Wang et al. / Journal of Loss Preventionc

expressions. For trapezoidal fuzzy number (ai1, ai2, ai3, ai4):3a1 a2 a3 (16)~Pc ORF~p1; ~p2; :::; ~pn 1QYni1

1Q~pi

1

Yni1

1 ai1;1Yni1

1 ai2;1Yni1

1 ai3!

(14)

Hence, the fuzzy possibility of the COTFE (~PTE) can be calculatedusing the following equation:

~PTE 1Yni1

1 ~Pci

1h1 ~Pc1

51 ~Pc2

5.5

1 ~Pcn

i(15)

where ~pc1; ~pc2;.; ~pcn denote the fuzzy possibilities of all MCSs; ~PTEis the fuzzy COTFE possibility.

3.4. Defuzzication of the fuzzy COTFE possibility

To provide a useful outcome for decision making, the fuzzy pos-sibility of the COTFE must be rst mapped to crisp possibility score(CPS) through defuzzication. A number of defuzzication methods(Ross, 2004; Wang, 1997) are available, including mean max mem-bership, centroid method, weighted average method, center oflargest area, center of sums and so on. In this paper, the center of areadefuzzication technique (Miri Lavasani et al., 2011; Wang, 1997) isadopted for its simplicity and usefulness. Defuzzication of TFN ~A a1; a2; a3 can be obtained by the following expression:

P*TE

Zxm~AxdxZm~Axdx

Za2a1

x a1a2 a1

xdxZa3a2

a3 xa3 a2

xdx

Za2a1

x a1a2 a1

dxZa3a2

a3 xa3 a2

dx

1

where P* is the defuzzied output; x is the output variable.~Pc ANDF~p1; ~p2;.; ~pn Yni1

~pi

Yn

i1ai1;

Yni1

ai2;Yni1

ai3;Yni1

ai4

!(11)

~Pc ORF~p1; ~p2;.; ~pn 1QYni1

1Q~pi

1

Yni1

1 ai1;1Yni1

1 ai2;

1Yni1

1 ai3;1Yni1

1 ai4!

(12)

whereQ

denotes fuzzy multiplication; Q denotes fuzzysubtraction.

For triangular fuzzy number (ai1, ai2, ai3):

~Pc ANDF~p1;~p2; :::;~pn Yn

~pi Yn

ai1;Yn

ai2;Yn

ai3

!(13)

e Process Industries 26 (2013) 1390e1398 1393TEDefuzzication of ZFN ~A a1; a2; a3; a4 is:

BEs, those pathways can be further evaluated to estimate the COTFE

knowledge provided by different experts. Here the proposed con-

in thidentifying the most likely path that leads to the TE. In order tomeasure the CS importance, the output fuzzy possibility of eachP*TE

Za2a1

x a1a2 a1

xdxZa3a2

xdxZa4a3

a4 xa4 a3

xdx

Za2a1

x a1a2 a1

dxZa3a2

dxZa4a3

a4 xa4 a3

dx

13$a4 a32 a4a3 a1 a22 a1a2

a4 a3 a2 a1(17)

3.5. Convert crisp possibility score (CPS) into probability value (PV)

In traditional FTA the nal result is an exact probability value. Infuzzy based FTA, however, the output is crisp possibility score (CPS)because the occurrence probability of each BE is represented byfuzzy numbers. There is inconsistency between the real probabilitydata and the possibility score. This issue can be solved by trans-forming the CPS into the form of probability of occurrence. Thefollowing conversion function (Onisawa, 1988, 1990) is proposed:

PV (

110m; CPSs0

0; CPS 0(18)

where

m 1 CPSCPS

13

2:301 (19)

and P*TE CPS, PTE PV; PTE is the probability of occurrence of theCCOTFE.

3.6. Importance analysis of the COTFE fault tree

At the time of decision making process, it is useful to have theevents sorted according to some criteria. This ranking is enabled byimportance analysis. In this study, the importance analysis of theCOTFE fault tree is carried out based on the investigation of theimportance measures of the BEs and the MCSs in the proposed tree.

3.6.1. FusselleVesely importance of BEsThe FusselleVesely importance (FV-I) is employed to evaluate

the contribution of each BE to the occurrence probability of theCOTFE. This importance measure is sometimes called the topcontribution importance. It provides a numerical signicance of allthe BEs in the COTFE fault tree and allows them to be prioritized.The FV-I of a BE is calculated by the following equation (Vinod,Kushwaha, Verma, & Srividya, 2003):

IFVxi PTE Pxi0TE

PTE(20)

where IFVxi is the FV-I index of ith BE; Pxi0TE is the occurrence prob-

ability of the COTFE by setting the probability of ith BE to 0. Deci-sion makers use this importance index to improve the safetyfeatures of the analyzed crude oil tanks.

3.6.2. Cut sets importanceCut sets importance (CS-I) is used to evaluate the contribution of

each MCS to the TE occurrence probability. This importance mea-sure provides a method for ranking the impact of each MCS and

D. Wang et al. / Journal of Loss Prevention1394MCS of the COTFE fault tree needs to be converted into a probabilityvalue using the methods described in Section 3.4e3.5. Then thesistency aggregation method is adopted to achieve it. In addition,for the ease of analysis, the TFNs dening the BE probabilitiesshould rst be converted into the corresponding ZFNs; for example,a TFN (a1, a2, a3) can be expressed as a ZFN (a1, a2, a2, a3). Then,according to Eqs. (4)e(10), the aggregated fuzzy possibility valuesfor each BEs involved in COTFE tree are obtained (see Table 1),which will be taken as the input data for fuzzy COTFE probabilitycalculation. As an example, the detailed aggregation calculationsfor BE36 are given in Table 2, which include the calculations such assimilarity degree s~A ; ~A , average agreement degree A(E ), relativeoccurrence probability and nd out the most vulnerable pathwaysand BEs.

4.1. Fuzzy-based approach

4.1.1. Fuzzy numbers dening probabilities of BEsDue to lack of the precise probability data of BEs of the COTFE

tree, the approach synthesizing the fuzzy set theory and expertslinguistic judgments is proposed to quantify the occurrence pos-sibilities of the BEs. In this study, three experts, including a reli-ability analyst and two senior eld engineers, are invited toperform the assessments. In order to capture experts linguisticnotions of probabilities for the BEs, a seven level linguistic ratingscale, i.e. {Very Low (VL), Low (L), Mildly Low (ML), Medium (M),Mildly High (MH), High (H) and Very High (VH)}, has been pro-posed. Then, the linguistic expressions are transformed into fuzzynumbers using a numerical approximation system as shown inFig. 2 (Chen, Hwang, & Hwang, 1992). The result of the expertjudgments for all the BEs is shown in Table 1.

4.1.2. Aggregating fuzzy numbers assigned by different expertsAggregation provides an agreement among the conictedMCS importance is estimated by calculating the ratio of the MCSprobability to the COTFE probability. The calculation is performedas follows:

ICSj PjMCSPTE

(21)

where ICSj is the CS-I index of the jth MCS; PjMCS is the occurrence

probability of the jth MCS.

4. A case study

The COTFE accident erupted in Hunan oil depot (Fan, 2005),which result in four people died and two injured, is selected hereas a case study. The proposed fuzzy based FTA is performed toevaluate the occurrence probability of the COTFE accident. Andthe implementation of the proposed approach also provides anopportunity to reinvestigate the causes of accident, which ishelpful to prevent or reduce the occurrence of such accidents inthe future. One of the other aims of the study is to compare theresults obtained by the fuzzy FTA with the results reached bytraditional FTA.

Considering the COTFE as an undesired top event, the COTFEtree has been constructed as shown in Fig. 1. Once the fault tree hasbeen developed, it can be evaluated to identify the possible basiccauses (or BEs) and pathways (minimum combination of BEs) thatwould lead to the undesired event. As previously concluded,quantitative analysis shows there are 43 BEs and 392 MCSs in theCOTFE tree. Subsequently, using the failure probability data of the

e Process Industries 26 (2013) 1390e1398i j i

agreement degree (RAD), aggregation weight (wi), etc.

4.1.3. Estimating fuzzy possibility of the COTFEQuantitative analysis of the COTFE tree attempts to calculate

occurrence probability of the top event. In this study, the proba-bilities for all BEs are represented in a form of ZFNs, so calculationsof the fuzzy possibility of the COTFE and the MCSs must follow thefuzzy arithmetic operation rules (Liang &Wang, 1993; Tanaka et al.,1983). According to Eqs. (11)e(15) and the fuzzy possibilities of theBEs in Table 1, the fuzzy possibility of occurrence of the COTFE is

estimated, which is also a continuous ZFN (0.523, 0.897, 0.995,1.000). Obviously, the fuzziness of the COTFE event is determinedby that of the BEs. And the information about the real state of thecrude oil tank system is revealed sufciently when such fuzzydescription is reserved.

4.1.4. Defuzzifying fuzzy possibility of the COTFEThe result obtained above is a fuzzy variable, which needs to be

further converted into a crisp possibility score (CPS) by defuzzica-tion. The CPS is a single crisp numeric value, which represents themost likely score that an event may occur (Dong & Yu, 2005). Here,the centre of area defuzzication method Eq. (17) is adopted toachieve it. The crisp defuzzed result (as shown in Fig. 3) allowsdisplaying the percentage contributionof the COTFE fuzzy possibilitynumber in fuzzy set representing fuzzy possibility range. The CPSvalueof the COTFE is 0.833 andbelongs to two sets:High (H)with themembership degree of 67% and Very High (VH) in 33%. The resultmakes the decision-making in risk assessment more convenient.

4.1.5. Converting CPS of the COTFE into a probability valueIn order to ensure compatibility between the CPS and the exact

probability data obtained from sufcient statistical inference, the

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.2

0.4

0.6

0.8

1.0Very Low Low Mildly Low Medium Mildly High High Very High

Possibility, p

Mem

bers

hip

funct

ion

,

Fig. 2. Fuzzy numbers represent linguistic value.

Table 1Fuzzy possibility values and FV-I measures for BEs in fuzzy COTFE FTA.

BE Description Linguistic judgments of experts Aggregation of fuzzy numbers FV-I measure

Expert 1 Expert 2 Expert 3 Index Ranking

X1 Using non-explosion proof tools L VL L (0.065, 0.130, 0.165, 0.265) 0.0634 9X2 Collision of metal tools and tank wall during

maintenance operationL VL L (0.073, 0.147, 0.173, 0.273) 0.0711 8

X3 Wearing iron nail-shoes VL VL VL (0.000, 0.000, 0.100, 0.200) 0.0017 35X4 Smoking ML L ML (0.167, 0.267, 0.333, 0.433) 0.1536 5X5 Fire work M L M (0.319, 0.419, 0.419, 0.519) 0.2873 2X6 Vehicles without ame arresters L VL VL (0.030, 0.059, 0.130, 0.230) 0.0298 15X7 Match L L VL (0.064, 0.128, 0.164, 0.264) 0.0623 10X8 Lighter ML L L (0.136, 0.236, 0.273, 0.373) 0.1279 6X9 Direct lightning ash VL VL L (0.034, 0.068, 0.134, 0.234) 0.0204 20X10 Lightning invasion along pipelines L VL VL (0.040, 0.080, 0.140, 0.240) 0.0238 18X11 Lightning induction VL L VL (0.037, 0.074, 0.137, 0.237) 0.0288 16X12 Without installing lightning protection facilities L VL VL (0.030, 0.059, 0.130, 0.230) 0.0045 34X13 Air terminal damaged ML L L (0.138, 0.238, 0.277, 0.377) 0.0182 21X14 Deector damaged M L L (0.213, 0.313, 0.313, 0.413) 0.0261 17

ML (0.132, 0.232, 0.265, 0.365) 0.0117 26

D. Wang et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1390e1398 1395X15 Ground rod damaged L LX16 Mobile telephone VL LX17 Audio-visual or photographic equipment VL VLX18 Non-explosion proof monitor or detector VL VLX19 Other non-explosion proof electrical equipments L VLX20 Cathodic protection VL VLX21 Electried railway VL VLX22 Electric leakage nearby L VLX23 Without installing anti-static grounding device L VLX24 Non-standard ground resistance VL VLX25 Broken ground wire ML L

X26 Non-standard apparatus L VLX27 Not enough standing time L VLX28 Friction between splashing oil and air L VLX29 Floating metal debris on oil surface VL VLX30 Oil lashing against metal materials L VLX31 Rough inner wall of pipeline VL LX32 High oil ow velocity L VLX33 Operator close to a conductor VL LX34 Friction between ber and human body L VLX35 Excessive loading VL LX36 Wrong valve opened VL LX37 Tank top unattended L VLX38 Breathing valve kept open since broke down M LX39 Gauge hatch often open ML LX40 Tank wall broken by external force VL VLX41 Poor seal around manhole ML LX42 High degree corrosion of tank wall L VLX43 Flexible connection pipe rupture ML LVL (0.035, 0.070, 0.135, 0.235) 0.0346 14VL (0.000, 0.000, 0.100, 0.200) 0.0017 35VL (0.000, 0.000, 0.100, 0.200) 0.0017 35L (0.065, 0.130, 0.165, 0.265) 0.0634 9VL (0.000, 0.000, 0.100, 0.200) 0.0017 35VL (0.000, 0.000, 0.100, 0.200) 0.0017 35VL (0.040, 0.080, 0.140, 0.240) 0.0396 13VL (0.038, 0.076, 0.138, 0.238) 0.0131 23L (0.034, 0.068, 0.134, 0.234) 0.0119 25L (0.132, 0.232, 0.265, 0.365) 0.0414 12L (0.026, 0.051, 0.126, 0.226) 0.0067 32VL (0.038, 0.076, 0.138, 0.238) 0.0095 27VL (0.030, 0.059, 0.130, 0.230) 0.0077 31L (0.026, 0.051, 0.126, 0.226) 0.0067 32VL (0.038, 0.076, 0.138, 0.238) 0.0095 28VL (0.037, 0.074, 0.137, 0.237) 0.0094 29L (0.065, 0.130, 0.165, 0.265) 0.0158 22VL (0.037, 0.074, 0.137, 0.237) 0.0015 36VL (0.030, 0.059, 0.130, 0.230) 0.0015 36L (0.062, 0.124, 0.162, 0.262) 0.0089 30ML (0.089, 0.147, 0.221, 0.321) 0.0121 24L (0.065, 0.130, 0.165, 0.265) 0.0212 19ML (0.250, 0.350, 0.386, 0.486) 0.3811 1ML (0.171, 0.271, 0.341, 0.441) 0.2768 3VL (0.000, 0.000, 0.100, 0.200) 0.0046 33L (0.136, 0.236, 0.273, 0.373) 0.2262 4VL (0.030, 0.059, 0.130, 0.230) 0.0539 11

L (0.060, 0.120, 0.160, 0.260) 0.1044 7

valve kept open since broke down occur simultaneously) hasmaximum probability of occurrence for this COTFE accident, whichcorresponds to the ofcial investigation results. In addition, it can beseen that these weakest MCSs are mainly composed of the top veBEs by their FV-I values. The ranking results together open up thecritical importance of the BEs including X38 (Breathing valve keptopen since broke down), X5 (Fire work), X39 (Gauge hatch oftenopen), X41 (Poor seal around manhole), X4 (Smoking) and X43(Flexible connection pipe rupture). Such results can help decision-maker take the targeted preventive measures, such as morestrictlymanagement regulation, security check andmaintenance, toeliminate or mitigate the identied safety deciencies, and hence

Table 2The aggregation calculations for the BE36.

~A1 VL (0, 0, 0.1, 0.2) EV(1) 0.0750~A2 L (0.1, 0.2, 0.2, 0.3) EV(2) 0.2000~A3 ML (0.2, 0.3, 0.4, 0.5) EV(3) 0.3500

S12 2.6667 A(E1) 3.6667S13 4.6667 A(E2) 1.6190S21 2.6667 A(E3) 2.6190S23 0.5714 RAD1 0.4639S31 4.6667 RAD2 0.2048S32 0.5714 RAD3 0.3313

X21X39

X22X39 1.264E-05 24 X22X42 1.346E-07 49X7X41 1.238E-05 25 X16X42 1.092E-07 50

D. Wang et al. / Journal of Loss Prevention in th1396CPSmust be converted into the form of probability data. This can beachieved by using Eqs. (18) and (19). The corresponding probabilityof occurrence for the COTFE is 4.514 102.

4.1.6. Importance measure for the COTFE fault treeAn important aim of many reliability and risk analyses is to

identify the most important BEs and MCSs from a reliability or riskviewpoint so that they can be given priority for improvements. Themost crucial BEs in the COTFE fault tree for causing the occurrenceof the COTFE can be justied through FV importance (FVeI) mea-sures. Using Eq. (20), The FV-I indexes of all BEs in the COTFE treeare calculated and ranked as shown in Table 1. The result helps toconclude that particular attention must be given to the events X38,X5, X39, X41, X4, X6, X43, X2, {X1; X19} and X7 as these BEs havethe greatest potential to cause the COTFE accident.

TheMCS represents the smallest collection of BEs whose failuresare necessary and sufcient to result in the COTFE accident. Themost crucial MCSs for the undesired COTFE event can be measuredby ranking of their CS-I index. Here, the MCS X4X38 is taken as anexample to illustrate the calculation procedure of the CS-I index.First, the fuzzy possibility of the MCS X4X38 is calculated based onfuzzy arithmetic operations Eq. (11), which is also a fuzzy numberof (0.042, 0.093, 0.128, 0.210). Next, the CPS of X4X38 is estimatedas 0.120 by the deffuzication technique of Eq. (17). Then, this FPS issubstituted into Eq. (18) and (19) to calculate PV and the PV ofX4X38 is 3.395 105. Finally, using Eq. (21), the CS-I index ofX4X38 is 7.521 104. The CS-I indexes of other MCSs are calcu-lated using the same procedures and the results of ranking top 50

EID1 0.38 w1 0.42EID2 0.32 w2 0.26EID3 0.30 w3 0.32

~p36 0:089;0:147; 0:221;0:321MCSs are provided in Table 3.As shown in Table 3, the MCSs ranked the top ten crucial con-

tributions to the COTFE probability are X5X38, X5X39, X4X38,X5X41, X4X39, X8X38, X8X39, X4X41, X8X41 and X5X43 respec-tively. This reveals that theseMCSs are theweakest links of the crudeoil tank system. The path MCS X5X39 (Fire work and Breathing

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.5

1.0

Mem

bers

hip

fun

ctio

n,

0.67

0.33

Possibility, p

Very Low Low Mildly Low Medium Mildly High High Very High

0.833

Fig. 3. Fuzzy possibility of the COTFE event on fuzzy scale.X2X38 7.563E-05 11 X2X43 1.507E-06 36X1X38;

X19X385.928E-05 12 X4X40 1.487E-06 37

X7X38 5.703E-05 13 X1X43; X19X43 1.152E-06 38X2X39 3.862E-05 14 X7X43 1.103E-06 39X1X39;

X19X393.033E-05 15 X3X41; X8X40;

X17X41; X18X41;X20X41; X21X41

5.941E-07 40

X7X39 2.918E-05 16 X22X43 4.401E-07 41X22X38 2.433E-05 17 X2X42 4.233E-07 42X5X42 2.410E-05 18 X11X15X38 4.004E-07 43X4X43 2.338E-05 19 X16X43 3.497E-07 44X16X38 1.956E-05 20 X1X42; X19X42 3.282E-07 45X2X41 1.663E-05 21 X7X42 3.153E-07 46X6X38 1.561E-05 22 X6X43 2.762E-07 47X1X41;

X19X411.290E-05 23 X11X15X39 1.852E-07 48Table 3The CS-I ranking of top 50 MCSs in fuzzy COTFE FTA.

MCSs CS-I MCSs CS-I

Index Ranking Index Ranking

X5X38 2.300E-03 1 X8X43 1.083E-05 26X5X39 1.229E-03 2 X16X39 1.023E-05 27X4X38 7.521E-04 3 X6X39 8.217E-06 28X5X41 6.165E-04 4 X4X42 7.421E-06 29X4X39 4.088E-04 5 X22X41 5.118E-06 30X8X38 4.007E-04 6 X5X40 4.217E-06 31X8X39 2.126E-04 7 X16X41 4.089E-06 32X4X41 1.955E-04 8 X6X41; X8X42 3.243E-06 33X8X41 9.897E-05 9 X3X38; X17X38;

X18X38; X20X38;X21X38

2.912E-06 34

X5X43 7.895E-05 10 X3X39; X17X39;X18X39; X20X39;

1.664E-06 35

e Process Industries 26 (2013) 1390e1398prevent or reduce the occurrence of such COTFE accidents.

4.2. Traditional-based approach

During the process of the traditional FTA of the COTFE, due toabsence of accurate probability data for BEs, the generic data areused to roughly estimate of the COTFE occurrence probability. Ingeneral, BE generic probability data can be derived from reliabilitydata handbook (SINTEF Industrial Management, 2002), expertjudgments and statistical data in oil depots. These probability dataare used in single-point form and are inherently uncertainty andimprecise. In this case study, the probability data for some of theBEs could hardly be obtained from reliability data handbook orstatistical data, such as the BEs X4, X7, X16, X32, X37, etc. Hence, inorder to ensure the consistency among all the BE probabilities andreasonable comparison with the fuzzy-based approach, the genericdata for the BEs in the COTFE fault tree are also obtained fromexpert judgments, but each BE probability data is represented by asingle possibility score as shown in Table 4.

Since there is no repeated BEs among all MCSs, the possibility ofoccurrence of the COTFE is achieved as follows (Wang, 1999):

PTE WNG

r1

YxiGr

qi (22)

where PTE denotes the possibility of top event; NG represents thenumber of all MCSs; r denotes the ordinal numbers of MCSs;xi Gr represents the ith BE belongs to rth MCS; qi denotes thepossibility score of the ith BE. Using Eq. (22), the occurrencepossibility of the COTFE event is 0.850. Then, according to theprobability conversion formulas of Eqs. (18) and (19), the occur-rence probability of the COTFE is obtained and the result is5.141 102.

The importance of each BE is also measured based on their FV-Iindex using Eq. (20) and results are also shown in Table 4. It showsthat the top ten critical BEs are X39, X38, X41, X5, X43, X4, X8, X42,X7 and X25 respectively. The FV-I index of all the MCSs are alsocalculated by Eq. (21) and the CS-I ranking of top 50 MCSs is listed

Table 4The generic data and FV-I measures for BEs in traditional COTFE FTA.

BE Expert judgment by a singlepossibility score

Aggregatedpossibilityscore

FV-I measures

Expert 1 Expert 2 Expert 3 Index Ranking

X1 0.14 0.08 0.12 0.115 0.1232 12X2 0.15 0.06 0.12 0.112 0.1177 13X3 0.02 0.05 0.02 0.030 0.0323 42X4 0.26 0.15 0.24 0.219 0.2299 6X5 0.35 0.24 0.30 0.300 0.3284 4X6 0.12 0.06 0.06 0.083 0.1138 14X7 0.14 0.16 0.06 0.122 0.1549 9X8 0.25 0.16 0.15 0.191 0.2248 7X9 0.05 0.05 0.12 0.071 0.0836 19X10 0.10 0.08 0.06 0.082 0.0922 16X11 0.05 0.15 0.06 0.085 0.0750 20X12 0.14 0.05 0.05 0.084 0.0460 34X13 0.26 0.16 0.14 0.192 0.0718 23X14 0.40 0.16 0.14 0.245 0.0845 18X15 0.20 0.20 0.35 0.245 0.0662 26X16 0.06 0.12 0.08 0.085 0.0906 17X17 0.04 0.02 0.04 0.034 0.0373 38X18 0.02 0.04 0.03 0.029 0.0337 39X19 0.16 0.06 0.12 0.116 0.1280 11X20 0.05 0.03 0.02 0.035 0.0385 37X21 0.04 0.05 0.02 0.037 0.0419 35X22 0.15 0.05 0.08 0.097 0.1039 15X23 0.16 0.05 0.06 0.095 0.0749 21X24 0.06 0.04 0.15 0.081 0.0746 22X25 0.30 0.15 0.20 0.222 0.1433 10X26 0.06 0.05 0.15 0.084 0.0327 41X27 0.15 0.05 0.06 0.091 0.0385 36X28 0.16 0.05 0.03 0.086 0.0579 28X29 0.04 0.05 0.15 0.076 0.0543 32X30 0.12 0.05 0.05 0.077 0.0544 31X31 0.05 0.15 0.04 0.079 0.0554 29X32 0.12 0.05 0.16 0.110 0.0667 25X33 0.05 0.15 0.04 0.079 0.0327 40X34 0.14 0.05 0.05 0.084 0.0327 40X35 0.05 0.15 0.12 0.103 0.0498 33X36 0.05 0.12 0.28 0.141 0.0588 27X37 0.12 0.08 0.15 0.116 0.0669 24X38 0.38 0.14 0.25 0.264 0.4608 2X39 0.26 0.15 0.25 0.116 0.4712 1X40 0.02 0.02 0.03 0.023 0.0548 30X41 0.28 0.12 0.15 0.190 0.3952 3X42 0.15 0.05 0.04 0.085 0.2113 8X43 0.05 0.15 0.14 0.109 0.2469 5

Table 5The CS-I ranking of top 50 MCSs in traditional COTFE FTA.

MCSs CS-I MCSs CS-I

Index Ranking Index

X5X38 1.192E-04 1 X5X42 3.441E-X5X39 5.472E-05 2 X1X39 3.424E-X4X38 2.851E-05 3 X2X39 2.976E-X5X41 2.644E-05 4 X4X43 2.286E-X8X38 1.483E-05 5 X7X41 1.940E-X4X39 1.215E-05 6 X16X38 1.589E-X8X39 6.099E-06 7 X19X41 1.380E-X4X41 5.466E-06 8 X6X38 1.324E-X8X41 2.655E-06 9 X1X41 1.291E-X5X43 1.483E-06 10 X22X39 1.190E-X7X38 1.397E-06 11 X2X41 1.114E-X19X38 1.028E-06 12 X8X43 9.685E-X1X38 9.683E-07 13 X16X39 5.070E-X2X38 8.478E-07 14 X4X42 4.553E-X7X39 5.045E-07 15 X22X41 4.252E-X19X39 3.649E-07 16 X6X39 4.181E-X22X38 3.562E-07 17 X8X42 1.796E-

D. Wang et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1390e1398 1397in Table 5. As shown in Table 5, the MCSs ranked the top ten leadingcontributions to the COTFE probability are X5X38, X5X39, X4X38,X5X41, X8X38, X4X39, X8X39, X4X41, X8X41 and X5X43 respec-tively. According to the FV-I and FV-I ranking result by thetraditional-based approach, the most critical BEs which have to begiven utmost attention are X39, X38, X41, X5, X4 and X8.

4.3. Results and discussion

The calculations have been carried out by fuzzy-basedapproach and traditional approach. Table 6 presents the nalimportant results for comparison between the two approaches.The results show that: 1) the occurrence probability value of theCOTFE by the fuzzy approach is about 12% lower than the value bythe traditional approach; 2) The fuzzy FTA provides the detailedinformation about the contribution of linguistic rating scale (Hand VH) to the COTFE probability, whereas such information isunknown from traditional FTA; 3) there is slight difference in themost critical BEs and big difference in the ranking of these BEs.The main reason for the differences mentioned above is that thefuzzy FTA approach distributes all BE data uncertainty in thewhole triangular or trapezoidal region and thus attempts torepresent a more realistic scenario as compared to the traditionalapproach. In reality, it is unreasonable to evaluate the occurrenceof each BE by using a single-point estimate without considering

MCSs CS-I

Ranking Index Ranking

07 18 X16X41 1.734E-08 3507 19 X6X41 1.416E-08 3607 20 X7X43 4.272E-09 3707 21 X19X43 2.844E-09 3807 22 X1X43 2.626E-09 3907 23 X2X43 2.201E-09 4007 24 X22X43 6.955E-10 4107 25 X7X42 6.102E-10 4207 26 X19X42 3.924E-10 4307 27 X21X38 3.821E-10 4407 28 X1X42 3.600E-10 4508 29 X2X42 2.973E-10 4608 30 X16X43 2.377E-10 4708 31 X20X38 2.079E-10 4808 32 X6X43 1.865E-10 4908 33 X17X38 1.618E-10 50

08 34

the inherent uncertainty and imprecision a state has. Overall the

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Authors gratefully acknowledge the nancial support providedby the National Natural Science Foundation of China (Grant No.50974105) and the Research Fund for the Doctoral Program ofHigher Education of China (Grant No. 20105121110003).5. Conclusions

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Fuzzy fault tree analysis for fire and explosion of crude oil tanks1 Introduction2 Traditional FTA of COTFE2.1 Construction of COTFE fault tree2.2 Evaluation of COTFE fault tree

3 Fuzzy based FTA of COTFE3.1 Fuzzy numbers to define probabilities of the BEs3.2 Aggregation of fuzzy numbers of the BEs3.3 The fuzzy COTFE possibility estimation3.4 Defuzzification of the fuzzy COTFE possibility3.5 Convert crisp possibility score (CPS) into probability value (PV)3.6 Importance analysis of the COTFE fault tree3.6.1 FussellVesely importance of BEs3.6.2 Cut sets importance

4 A case study4.1 Fuzzy-based approach4.1.1 Fuzzy numbers defining probabilities of BEs4.1.2 Aggregating fuzzy numbers assigned by different experts4.1.3 Estimating fuzzy possibility of the COTFE4.1.4 Defuzzifying fuzzy possibility of the COTFE4.1.5 Converting CPS of the COTFE into a probability value4.1.6 Importance measure for the COTFE fault tree

4.2 Traditional-based approach4.3 Results and discussion

5 ConclusionsAcknowledgmentsReferences