Aa

Sa

b

1

Icutntcm

cuttpatFo

h0

Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88

Contents lists available at ScienceDirect

Process Safety and Environmental Protection

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

n extension to Fuzzy Fault Tree Analysis (FFTA)pplication in petrochemical process industry

eyed Miri Lavasania,∗, Anousheh Zendegania, Metin Celikb

Sciences & Research Branch, Tehran Science and Research Branch University, Hesarak, Tehran, IranDepartment of Marine Engineering, Istanbul Technical University, Tuzla, 34940 Istanbul, Turkey

a b s t r a c t

Fault Tree Analysis (FTA) is an established technique in risk management associated with identified hazards specific

to focused fields. It is a comprehensive, structured and logical analysis method aimed at identifying and assessing

hazards of complex systems. To conduct a quantitative FTA, it is essential to have sufficient data. By considering the

fact that sufficient data is not always available, the FTA method can be adopted into the problems under fuzzy envi-

ronment, so called as Fuzzy Fault Tree Analysis (FFTA). This research extends FFTA methodology to petrochemical

process industry in which fire, explosion and toxic gas releases are recognized as potential hazards. Specifically, the

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 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

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

modelling

state, aggregating stage, defuzzification process, transforming

. Introduction

n conventional FTA, the Failure Probabilities (FP) of systemomponents (i.e. Basic Events (BEs)) are treated as exact val-es. However, for many systems, it is very difficult to estimatehe precise failure rate or probabilities of individual compo-ents or failure events in the quantitative analysis of faultree structures. In other word, the crisp approach has diffi-ulty in conveying imprecision or vagueness nature in systemodeling (Liang and Wang, 1993; Lavasani et al., 2012).To remedy the gap about the mentioned inadequacy of the

onventional FTA, extensive research has been performed bysing fuzzy set theory. The pioneering work on this belongso Tanaka et al. (1983), which treated probabilities of BEs asrapezoidal fuzzy numbers, and applied the fuzzy extensionrinciple to determine the probability of Top Event (TE). Linnd Wang (1997) developed a hybrid method which can simul-aneously deal with probability and possibility measures in aTA. Sawer and Rao (1994) applied �-cuts to determine the FP

f the TE in mechanical systems modeling with Fuzzy Fault

∗ Corresponding author. Tel.: +98 912 3585034.E-mail address: mohammadrezamirilavasani@rocketmail.com (S.M

Available online 14 May 2014ttp://dx.doi.org/10.1016/j.psep.2014.05.001957-5820/© 2014 The Institution of Chemical Engineers. Published by

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 fire 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, rating

. Lavasani).

Crisp Failure Possibility (CFP) of BEs into FP, calculating all

Elsevier B.V. All rights reserved.

76 Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88

prop

Fig. 1 – Structure of

Minimal Cut sets (MCs) and FP of TE, and ranking of MCs areprovided in Section 2. In Section 3, a case study on an impor-tant section of petrochemical plant is demonstrated. The lastsection emphasis the highlights of the research.

2. Research methodology

In circumstances where the lack or incompleteness of dataexists, there is a need to incorporate expert judgment intothe FTA study. A framework proposed based on the fuzzy settheory with the FTA method is capable of quantifying thejudgment from experts who express opinions qualitatively.The new proposed framework is developed in eight differentstages. In the first stage, BEs with known failure rates isseparated from those BEs with a vague failure rate. Thesecond stage is to obtain the FPs of BEs with known failurerates. In the third stage, expert judgments are assignedto the vague BEs. These ratings are fuzzy numbers. Thefourth stage is an aggregation procedure. It is performed byaggregating of experts’ opinions. A defuzzification processwill then be adopted to transform the experts’ judgments(fuzzy possibility) to corresponding crisp possibility valuesby employing an appropriate algorithm. The sixth stage is toconvert crisp possibilities values to the FPs. MCs are identifiedand quantified in the seventh stage. In the last stage, rankingof all MCs can consequently be produced. Fig. 1 presents thestructure of proposed methodology.

2.1. Identifying BEs

As mentioned, the first step of the methodology is to iden-tify hazards with known failure rates from vague hazards.

Occurrence failure rate of some hazards are available from PDS(2010).

osed methodology.

2.2. Obtaining Failure Probability (FP) of BEs withknown failure rate

The foundation of a good analysis is the pedigree of failurerate or event probability data that is assigned to BEs. There arepredominantly three methods that can be used to determinethe occurrence probability of an event namely (Preyssl, 1995):

1. Statistical method.2. Extrapolation method.3. Expert judgment method.

The statistical method involves the treatment of direct testof experience data and the calculation of the probabilities. Theextrapolation method involves the use of model predictionand similar condition or using standard reliability handbook.The expert judgment method involves direct estimation ofprobabilities by specialists.

A component is tested periodically with test interval. A fail-ure may occur at any time in the test interval, but the failureis only detected in a test. After a test/repair, the componentis assumed to be “as good as new”. This is a typical situationfor many safety-critical components, like sensors and safetyvalves. If an event failure of a kind which can be inspected,the component failure probability can be obtained from Eq. (1)(Spouge, 2000; Rausand and Hoyland, 2004).

P(t) = 12

�� (1)

where � is the component failure rate and � is the inspectioninterval.

Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88 77

Tu

P

wiP

P

2

Irsusaecpa

n

•

•

••

tiieosihh

ff

tB

2

StisCpe

Table 1 – Weighting score of different expert.

Constitution Classification Score

Title

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

Service time

≥30 years 520–29 410–19 36–9 2≤5 1

Education time

PHD 5Master 4Bachelor 3HND 2School level 1

If a component is of a kind which cannot be inspected.he component failure probability P, which is also called thenreliability, is determined from Eq. (2).

(t) = 1 − e−�t (2)

here � the component failure rate and t is the relevant timenterval. Based on the Maclaren series, the above equation for

can be obtained from Eq. (3) if �t � 0.1

(t) = 1 −(

1 + −�t

1!+ �2t2

2!+ �3t3

3!+ · · · + �ntn

n!

)∼= �t (3)

.3. Rating state

n this stage, experts express their opinions for each BE withespect to each subjective attribute. Expert elicitation is theynthesis of experts’ opinions of a subject where there isncertainty due to insufficient data because of physical con-traints or lack of resources. Experts’ elicitation is essentially

scientific consensus methodology. Expert elicitation gen-rally quantifies uncertainty. Examples of fields that haveontributed to probability elicitation are decision analysis,sychology, risk analysis, Bayesian statistics, mathematicsnd philosophy.

Quantification of subjective probabilities is employed in aumber of circumstances (Korta et al., 1996):

Evidence is incomplete because it cannot be reasonablyobtained.

Data exists only from analogous situations (one might knowthe solubility of one mineral and might use this informationto infer the solubility of another mineral).

There are conflicting models or data sources. Scaling up from experiments to target physical processes

is not direct (scaling of mean values is often much simplerthan rescaling the uncertainties).

Expert knowledge is influenced by individual perspec-ives and goals (Ford and Sterman, 1998). Therefore, completempartiality of expert knowledge is difficult to achieve. Anmportant consideration is the selection of heterogeneousxpert (e.g. both scientists and workers) or homogenous groupf experts (e.g. only scientists). The effect of difference in per-onal experience on expert judgment is assumed to be smallern homogenous group compared to a heterogeneous group. Aeterogeneous group of experts can have an advantage over aomogenous group through considering all possible opinions.

In this study, a heterogeneous group of experts is selectedor evaluating the probability of vague events. The weightingactors of experts are determined according to Table 1.

Rating of expert judgment can be carried out by linguisticerms which are used for soliciting expert opinions for eachE.

.4. Aggregating stage

ince each expert may have a different opinion accordingo his/her experiences and expertise in the relevant field, its necessary to aggregate expert’s opinion to reach a con-ensus. Different types of aggregation can be used (Hsu andhen, 1994; Aqlan and Ali, 2014). Aqlan and Ali (2014) pro-

osed a new method for aggregation of expert judgment bymploying triangle fuzzy numbers. As mentioned, Aqlan and

Ali (2014) model can just aggregate triangle fuzzy numberswhilst Hsu and Chen (1994) model is able to aggregate triangleand trapezoidal fuzzy numbers. Linguistic terms of this paperare mixture of triangle and trapezoidal fuzzy numbers. There-fore, Hsu and Chen (1994) method of aggregation is used inthis paper.

Hsu and Chen (1994) presented an algorithm to aggregatethe linguistic opinions of a homogenous/heterogeneous groupof experts. Suppose each expert, Ek (k = 1, 2, . . ., M) expresseshis/her opinion on a particular attribute against a specific con-text by a predefined set of linguistic variables. The linguisticterms can be converted into corresponding fuzzy numbers.The detailed algorithm is described as follows:

1. Calculate the degree of agreement (degree of similarity)Suv(Ru, Rv) of the opinions between each pair of expertsEu and Ev, where Suv(Ru, Rv). According to this approach,A = (a1, a2, a3, a4) and B = (a1, a2, a3, a4) are two standardtrapezoidal fuzzy numbers. Then the degree of similarityfunction of S, which is defined as:

S(A, B) = 1 − 14

4∑i=1

|ai − bi| (4)

where (A, B) ∈ [0, 1], the larger value of S(A, B), the greatersimilarity between two fuzzy numbers of A and B.

2. Calculate the Average Agreement (AA) degree AA(Eu) of theexperts.

AA(Eu) = 1M − 1

4∑u /= v

v = 1

S(Ru, Rv) (5)

3. Calculate the Relative Agreement (RA) degree, RA(Eu) of theexperts.

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

u=1AA(Eu)(6)

4. Estimate the Consensus Coefficient (CC) degree, CC(Eu) ofexpert, Eu(u = 1, 2, . . ., M):

CC(Eu) = · W(Eu) + (1 − ˇ) · RA(Eu) (7)

78 Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88

diag

Fig. 2 – Process flow

where ˇ(0 ≤ ≤ 1) is a relaxation factor of the proposedmethod. It shows the importance W(Eu) over RA(Eu). When

= 0 no importance has been given to the weight of anexpert and hence a homogenous group of experts is used.When = 1, the consensus degree of an expert is the sameas its importance weight. The consensus degree coefficientof each expert is good measure for evaluating the relativeworthiness of each expert’s opinion. It is responsibility ofthe decision maker to assign an appropriate value to ˇ.

5. Finally, the aggregated result of the experts’ judgment RAG,can be obtained as follows:

RAG = CC(E1) × R1 + CC(E2) × R2 + · · · + CC(EM) × RM (8)

2.5. Defuzzification process

Defuzzification is the process of producing a quantifiableresult in fuzzy logic. Defuzzification problems emerge fromthe application of fuzzy control to the industrial processes(Zhao and Govind, 1991). The center of area defuzzificationtechnique is selected here. This technique was developed bySugeno in 1985 (Sugeno, 1999). This method can be expressedas:

∫

X∗ = �i(x)xdx∫

�i(x)dx(9)

ram of Deethanizer.

where X* is the defuzzified output, �i(x) is the aggregatedmembership function and x is the output variable. The aboveformula can be shown as follows for triangular and trape-zoidal fuzzy numbers. Defuzzification of fuzzy number A =(a1, a2, a3) is

X∗ =∫ a2

a1

x−a1a2−a1

xdx +∫ a3

a2

a3−xa3−a2

xdx∫ a2

a1

x−a1a2−a1

dx +∫ a3

a2

a3−xa3−a2

dx= 1

3(a1 + a2 + a3) (10)

Defuzzification of trapezoidal fuzzy number A =(a1, a2, a3, a4) can be obtained by Eq. (11).

X∗ =∫ a2

a1

x−a1a2−a1

xdx +∫ a3

a2xdx +

∫ a4

a3

a4−xa4−a3

xdx∫ a2

a1

x−a1a2−a1

dx +∫ a3

a2dx +

∫ a4

a3

a4−xa4−a3

dx

= 13

(a4 + a3)2 − a4a3 − (a1 + a2)2 + a1a2

(a4 + a3 − a1 − a2)(11)

2.6. Transforming CFP of BEs into FP

As aforementioned, there are data available for failure ratesof some events whilst the data associated with the othersare vague. There is inconsistency between FPs of certain BEs

and CFPs of vague events. This issue can be performed byusing Eq. (12). Onisawa (1988) has proposed a function which

Process

Safety

an

d En

viro

nm

enta

l Pro

tection

9

3

( 2

0 1

5 )

75–88

79

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 dryersdeficiency1.2.2.2 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

80

Process

Safety

an

d En

viro

nm

enta

l Pro

tection

9

3

( 2

0 1

5 )

75–88

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 fire proofing in case offire in adjacent area

Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88 81

tatio

cbhta1

F

2

Bitc

P

s

2

OiiiSi

Fig. 3 – Fault tree represen

an be used for converting CFP to FP. This function is derivedy addressing some properties such as the proportionality ofuman sensation to the logarithmic value of a physical quan-

ity. The probability rate can be obtained from possibility rates follows (Onisawa, 1988, 1990, 1996; Onisawa and Nishiwaki,988; Lin and Wang, 1998):

P ={

1/10K, CFP /= 0

0, CFP = 0, K =

[(1 − CFP

CFP

)]1/3

× 2.301 (12)

.7. Calculating all MCs and FP of TE

y definition, a MC is a combination (intersection) of BEs lead-ng to the TE. The combination is a “minimal” combination inhat all failures are needed for the TE to occur. TE probabilityan be obtained from Eq. (13).

(t) = P(MC1 ∪ MC2 ∪ . . . ∪ MCN) = P(MC1) + P(MC2) + · · ·+ P(MCN) − P(MC1 ∩ MC2) + P(MC1 ∩ MC3) + · · ·+ P(MCi ∩ MCj)) + (−1)N−1P(MC1 ∩ MC2 ∩ . . . MCN) (13)

Where P(MCi) is the occurrence probability of minimal cutet i.

.8. Ranking of MCs

ne of the most important outputs of an FTA is the set ofmportance measures that are calculated for the TE. Suchmportance measures establish the significance for all the MCsn the FT in terms of their contributions to the TE probability.

ensitivity Analysis (SA) is the study of how the uncertainty

n the output of a mathematical model or system (numerical

n of Deethanizer failure.

or otherwise) can be apportioned to different sources ofuncertainty in its inputs. In other words, SA can be used asmethod for testing robustness of a model results in presenceof uncertainty. SA of FTs is estimated by Importance measurestechniques. The following probabilistic importance measuresare currently in use for FTA:

• Criticality importance• Risk Reduction Worth (RRW) or Top Decrease Sensitivity

(TDS)

SA can be useful for a range of purposes, including:

• Testing the robustness of the results of a model or systemin the presence of uncertainty.

• Increased understanding of the relationships between inputand output variables in a system or model.

• Uncertainty reduction: identifying model inputs that causesignificant uncertainty in the output.

• Searching for errors in the model (by encountering unex-pected relationships between inputs and outputs).

• Model simplification – fixing model inputs that have noeffect on the output, or identifying and removing redundantparts of the model structure.

Fussell-Vesely Importance (F-VI) is the contribution of theMC to the TE probability. F-VIs are determinable for every MCmodeled in the FT. This provides a numerical significance ofall FT elements and allows them to be prioritized. The F-VI iscalculated by summing all the causes (MCs) of the TE involving

the particular event. This measure has been applied to MCs todetermine the importance of individual MC. Where Qi(t) is the

82 Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88

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 Icing due to dryers deficiency (Suction P-401) 1.2.2.1 Linguistic term11 Hydrate formation (Suction P-401) 1.2.2.2 Linguistic term12 Chocking of strainer (Suction P-401) 1.2.2.3 Linguistic term13 Lack of knowledge (Training) 1.3.1 Linguistic term14 Lack of skill (experience) 1.3.2 Linguistic term15 Lack of perception/carelessness 1.3.3 Linguistic term16 Loss of IA from source (Mobin) 2.1.1 Failure rate17 Human error to close the IA valves in plant/offsite battery limit 2.1.2 Linguistic term18 Equipment Failure (FIC of FV-40071A) 2.2.1 Failure rate19 Loose connections in IA network (FIC of FV-40071A) 2.2.2 Failure rate20 Human error in DCS to close the FV 2.3 Linguistic term21 Failure of C-501 due to poor PM 3.1 Failure rate22 Internal (inside erosion) (E-420) 3.2.1 Failure rate23 External (humidity) (E-420) 3.2.2 Failure rate24 Equipment failure (TIC of TV-40075) 4.1.1 Failure rate25 Loose connections in IA network (TIC of TV-40075) 4.1.2 Failure rate26 Failure/error of PIC (PV-40102) 5.1 Failure rate27 Equipment failure (TIC of TV-40104) 6.1.1.1 Failure rate28 Loose connections in IA network (TIC of TV-40104) 6.1.1.2 Failure rate29 Failure of FV-40091 6.2.1 Failure rate30 Failure of C-501 6.2.2 Failure rate31 Internal corrosion (E-422) 6.2.3.1 Failure rate32 External corrosion (E-422) 6.2.3.2 Failure rate33 Chocking due to polymerization (E-422) 6.3 Failure rate34 Bad manufacturing (design) (external body of T-402) 7.1.1 Failure rate35 Poor welding Procedure (external body of T-402) 7.1.2.1 Linguistic term36 Poor welding Supervision (external body of T-402) 7.1.2.2 Linguistic term37 Vibration (external body of T-402) 7.1.3 Failure rate38 Internal corrosion (external body of T-402) 7.1.4.1 Failure rate39 External corrosion (external body T-402) 7.1.4.2 Failure rate40 Bad manufacturing (supports) 7.2.1 Failure rate41 Poor welding (supports) 7.2.2 Linguistic term42 Vibration (supports) 7.2.3 Failure rate

(supp

43 Lack of fire proofing in case of fire in adjacent area

contribution of MC i to failure of the system, the importancemeasure can be quantified as follows (Modarres, 2006):

IFVi (t) = Qi(t)

QS(t)(14)

Qi(t) = probability of failure of MCi, QS(t) = probability of failureof TE due to all MCs.Risk Reduction Worth (RRW) measures thedecrease in the probability of the TE if a given MC is assurednot to occur. This importance measure can also be called the

Top Decrease Sensitivity (TDS) (Shu et al., 2006). RRW for a MCshows the decrease in the probability of the TE that would be

Table 4 – FP of the BEs with known failure rate.

BEs FP of BEs BEs FP of BEs

1.1.2.1 0.01 3.2.1 0.012

1.1.2.2 0.015 3.2.2 0.008

2.1.1 0.002 4.1.1 0.014

2.2.1 0.014 4.1.2 0.009

2.2.2 0.018 5.1 0.013

3.1 0.02 6.1.1.1 0.014

orts) 7.2.4 Linguistic term

obtained if the MC did not occur. Therefore, the RRW can becalculated by re-quantifying the FT with considering of theprobability of the given MC to 0. It thus measures the maxi-mum reduction in the TE probability. RRW can be used to testmodel robustness.

3. Case study

A petrochemical plant is built to manufacture Medium DensityPolyethylene (MDP) and High Density Polyethylene (HDP) for

the plastics processing industry. The facility has a capacityof 300,000 t/a based on 7920 h/y. The products are marketed

BEs FP of BEs BEs FP of BEs

6.1.1.2 0.009 7.1.1 0.0176.2.1 0.011 7.1.3 0.026.2.2 0.0085 7.1.4.1 0.0196.2.3.1 0.017 7.1.4.2 0.0066.2.3.2 0.005 7.2.1 0.0156.3 0.023 7.2.3 0.012

Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88 83

Fig. 4 – Chen and Hwang conversion scale.

Table 5 – Fuzzy number of conversion scale 6.

Linguistic terms Fuzzy sets

Very low (VL) (0,0,0.1,0.2)Low (L) (0.1,0.25,0.25,0.4)Medium (M) (0.3,0.5,0.5,0.7)High (H) (0.6,0.75,0.75,0.9)Very high (VH) (0.8,0.9,1,1)

up

SaD

3

ApiDttcpiswtao

Table 7 – Expert judgment on vague BEs.

BEs Expert judgment on vague BEs

E1 E2 E3

1.1.1 L M M1.1.2.3 VL L M1.2.1.1 L L M1.2.1.2.1 M H H1.2.1.2.2 M M M1.2.1.3.1 L L M1.2.1.3.2 M M H1.2.2.1 M M M1.2.2.2 L L L1.2.2.3 M H H1.3.1 M H M1.3.2 VL L M1.3.3 L VL L2.1.2 M L L2.3 L VL L7.1.2.1 L L M7.1.2.2 M H M7.2.2 L L VL7.2.4 L M L

nder the brand name LUPOLEN. For easy comprehension, thelant is divided into four main sections:

Plant Section 01: Purification (Area 700) and dosing of feed-stock (Area 100)Plant Section 02: Polymerization (Area 200) and powder hand-ling (Area 300 & 400)Plant Section 03: Extrusion and product handling (Area 500)Plant section 04: Granulate handling and logistic

Additionally, plant facilities are provided in Area 600.ection 02 is one of the most important plant sections. Deeth-nizer is one of the main equipment of this section. Therefore,eethanizer is selected as case study in this paper.

.1. Identifying BEs of Deethanizer

vent system on propylene side of the E-420 and E-422 isrovided to evacuate non-condensable components contained

n propylene that could accumulate. Bottom temperature ofeethanizer T-402 must be controlled carefully because at a

oo high temperature the heavier olefins in the bottom tendo form gums and polymers, thus fouling the bottom of theolumn and the reboiler. For this reason, a spare reboiler isrovided and when reboiling becomes inefficient due to foul-

ng, operator has to switch from the operating reboiler to thepare one. The reboiling control valve is on the steam inlet linehere it controls the condensing pressure and hence tempera-

ure. Steam is injected in order to get a maximum temperature

t Deethanizer bottom of about 82 ◦C. A piping pot is providedn the steam condensate line to make hydraulic guard.

Table 6 – Experts’ profiles and decision weights.

No of expert Title Servicetime (Year)

Edu

1 Senior 10–19 M2 Senior <5 P3 Junior 6–9 M

The overhead specification for the Deethanizer is thepropylene content in the hydrogenated C2 cut. Normal value is0.3 wt% (0.4 wt% max.). The liquid reflux flow rate is adjustedby FV-40071 to reach this specification. A polymerizationinhibitor is injected by the Polymerization Inhibitor InjectionPackage W-402 in the feed and at bottom of Deethanizer inorder to limit the fouling tendency. Based on Process FlowDiagram (PFD) which is shown in Fig. 2.

Considering the working principles and process flow dia-gram of Deethanizer unit, BEs associated with this section areidentified and listed in Table 2.

Fault tree representation of the Deethanizer failure is illus-trated in Fig. 3.

Considering the Deethanizer process flow diagram andrelated failure states, it is the next issue to determine whetherthe BEs are known or unknown.

cationallevel

Weighting factor Weighting score

aster 5 + 3 + 4 = 12 12/33 = 0.363hD 5 + 1 + 5 = 11 11/33 = 0.333aster 4 + 2 + 4 = 10 10/33 = 0.304

84 Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88

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 identified for Deethanizer failure.24 of them are BEs with known occurrence probabilities whilstthere are not historical data available for the other 19 BEs.Table 3 presents all of the BEs associated with the proposedFT.

3.3. Calculating FPs of BEs with known occurrenceprobabilities

As aforementioned, the foundation of a good analysis isthe pedigree of failure rate or event probability data that isassigned to BEs. Therefore, occurrence probabilities of haz-ard with known failure rate can be estimated by using Eqs.(1)–(3). For example, the rate of mechanical failure of homoge-nizer is 2.4 × 10−3 with 4 inspections in a year. Therefore, FP ofmechanical failure of homogenizer can be obtained by usingEq. (1) as follows:

1 −3 4 −3

FPmechanical failure of homogenizer =2

× 2.4 × 10 ×12

= 4 × 10

Table 9 – Aggregation calculation for each subjective BE.

BEs Aggregation of eachsubjective BE

1.1.1 (0.23,0.42,0.42,0.6)1.1.2.3 (0.13,0.24,0.27,0.42)1.2.1.1 (0.16,0.33,0.33,0.49)1.2.1.2.1 (0.5,0.67,0.67,0.83)1.2.1.2.2 (0.3,0.5,0.5,0.7)1.2.1.3.1 (0.16,0.33,0.33,0.49)1.2.1.3.2 (0.39,0.58,0.58,0.76)1.2.2.1 (0.3,0.5,0.5,0.7)1.2.2.2 (0.1,0.25,0.25,0.4)1.2.2.3 (0.5,0.67,0.67,0.83)1.3.1 (0.39,0.58,0.58,0.76)1.3.2 (0.13,0.24,0.27,0.42)1.3.3 (0.07,0.17,0.2,0.34)2.1.2 (0.17,0.33,0.33,0.5)2.3 (0.07,0.17,0.2,0.34)7.1.2.1 (0.16,0.33,0.33,0.49)7.1.2.2 (0.39,0.58,0.58,0.76)7.2.2 (0.07,0.17,0.2,0.34)7.2.4 (0.16,0.33,0.33,0.49)

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 totheir corresponding fuzzy numbers. There are generic verbalterms in the system where scale 1 contains two verbal terms(linguistic terms) and scale 8 contains 13 verbal terms (linguis-tic terms). The typical estimate of a human memory capacity,is seven plus-minus two chunks, which means that the suit-able number for linguistic term selection for human beingsto make an appropriate judgment is between 5 and 9 (Miller,1956; Nicokis and Tsuda, 1985). Therefore, conversion scaleof 6 which contains 5 verbal terms is selected for performingthe subjective assessment of hazards with unknown failurerate. Fig. 4 presents the fuzzy linguistic scale that is used inthis paper to involve the judgments of experts with respect tohazards with unknown failure rate.

The given linguistic terms are in the form of both triangu-lar and trapezoidal fuzzy numbers. Table 5 represents all thefuzzy numbers in the form of trapezoidal numbers.

As mentioned, a heterogeneous group of experts is

employed to perform the judgment for the vague events.

Table 10 – Deffuzification process for all subjective BEs.

BEs Aggregation ofsubjective basic events

Defuzzification ofsubjective BEs (CFP)

1.1.1 (0.23,0.42,0.42,0.6) 0.4171.1.2.3 (0.13,0.24,0.27,0.42) 0.2691.2.1.1 (0.16,0.33,0.33,0.49) 0.3261.2.1.2.1 (0.5,0.67,0.67,0.83) 0.6671.2.1.2.2 (0.3,0.5,0.5,0.7) 0.51.2.1.3.1 (0.16,0.33,0.33,0.49) 0.3261.2.1.3.2 (0.39,0.58,0.58,0.76) 0.5761.2.2.1 (0.3,0.5,0.5,0.7) 0.51.2.2.2 (0.1,0.25,0.25,0.4) 0.2501.2.2.3 (0.5,0.67,0.67,0.83) 0.6671.3.1 (0.39,0.58,0.58,0.76) 0.5791.3.2 (0.13,0.24,0.27,0.42) 0.2691.3.3 (0.07,0.17,0.2,0.34) 0.1962.1.2 (0.17,0.33,0.33,0.5) 0.3332.3 (0.07,0.17,0.2,0.34) 0.1967.1.2.1 (0.16,0.33,0.33,0.49) 0.3267.1.2.2 (0.39,0.58,0.58,0.76) 0.5797.2.2 (0.07,0.17,0.2,0.34) 0.1987.2.4 (0.16,0.33,0.33,0.49) 0.329

Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88 85

Table 11 – Converting CFP into FP.

BEs Defuzzification 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

Tbtjw

i

3

Ito0

cdgT

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 3.73e−8 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 16MCs22 0.014 0.0463 8MCs23 0.009 0.0298 13MCs24 0.013 0.0430 9MCs25 0.014 0.0463 8MCs26 0.009 0.0298 13MCs27 0.011 0.0364 11MCs28 0.0085 0.0281 14MCs29 0.017 0.0562 5MCs30 0.005 0.0165 18MCs31 0.023 0.0760 1MCs32 0.017 0.0562 5MCs33 0.00001 0.0000 25MCs34 0.02 0.0661 2MCs35 0.019 0.0628 3MCs36 0.006 0.0198 17MCs37 0.015 0.0496 6MCs38 0.0002 0.0007 24MCs39 0.012 0.0397 10MCs40 0.0012 0.0040 22

he weights of experts are not equal. Experts’ weights cane obtained based on their profiles and competencies. Inhis case, three experts are employed for performing theudgments. Table 6 shows the experts’ profiles and decisioneights.

Expert judgment on the BEs with unknown failure rates arellustrated by Table 7.

.5. Aggregation of BEs

n this stage, all the ratings are aggregated under each subjec-ive BE. As an example, detailed aggregation calculations for BEf 1.1.1 are given in Table 8. (Relaxation factor) is considered.5 in aggregation calculation of subjective BEs.

These calculations contain attribute based aggregation cal-ulation, such as average degree of agreement (AA), relativeegree of agreement of each expert (RA), etc. After the aggre-ation calculations, the results of all the BEs are presented in

able 9.

Table 12 – FP of all MCs.

MCs FP MCs FP

1 1.1.1 0.0027 21 3.2.2 0.0082 1.1.2.1 0.01 22 4.1.1 0.0143 1.1.2.2 0.015 23 4.1.2 0.0094 1.1.2.3 0.0006 24 5.1 0.0135 1.2.1.1 0.0012 25 6.1.1.1 0.0146 1.2.1.2.1 0.0149 26 6.1.1.2 0.0097 1.2.1.2.2 0.005 27 6.2.1 0.0118 1.2.1.3.1 0.0012 28 6.2.2 0.00859 1.2.1.3.2 0.0083 29 6.2.3.1 0.017

10 1.2.2.1 × 1.2.2.2 × 1.2.2.3 3.73e−8 30 6.2.3.2 0.00511 1.3.1 0.0085 31 6.3 0.02312 1.3.2 0.0006 32 7.1.1 0.01713 1.3.3 0.0002 33 7.1.2.1 × 7.1.2.2 0.0000114 2.1.1 0.002 34 7.1.3 0.0215 2.1.2 0.0013 35 7.1.4.1 0.01916 2.2.1 0.014 36 7.1.4.2 0.00617 2.2.2 0.018 37 7.2.1 0.01518 2.3 0.0002 38 7.2.2 0.000219 3.1 0.02 39 7.2.3 0.01220 3.2.1 0.012 40 7.2.4 0.0012

86 Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88

Table 14 – Result of SA.

No of MCs FP of MCs F-V IM MCs Rank Revised TE value RRW (TEinitial–TErevised) 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 3.73e−8 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 0.0002 0.0007 24 0.3023 0.0001 24MCs14 0.002 0.0066 20 0.3010 0.0014 20MCs15 0.0013 0.0043 21 0.3015 0.0009 21MCs16 0.014 0.0463 8 0.2925 0.0099 8MCs17 0.018 0.0595 4 0.2897 0.0128 4MCs18 0.0002 0.0007 24 0.3023 0.0001 24MCs19 0.02 0.0661 2 0.2882 0.0142 2MCs20 0.012 0.0397 10 0.2940 0.0085 10MCs21 0.008 0.0265 16 0.29682 0.0056 16MCs22 0.014 0.0463 8 0.292541 0.0099 8MCs23 0.009 0.0298 13 0.29611 0.0063 13MCs24 0.013 0.0430 9 0.293258 0.0092 9MCs25 0.014 0.0463 8 0.292541 0.0099 8MCs26 0.009 0.0298 13 0.29611 0.0063 13MCs27 0.011 0.0364 11 0.294687 0.0078 11MCs28 0.0085 0.0281 14 0.296465 0.0060 14MCs29 0.017 0.0562 5 0.290382 0.0121 5MCs30 0.005 0.0165 18 0.29894 0.0035 18MCs31 0.023 0.0760 1 0.286024 0.0164 1MCs32 0.017 0.0562 5 0.290382 0.0121 5MCs33 0.00001 0.0000 25 0.302438 0.0000 25MCs34 0.02 0.0661 2 0.288209 0.0142 2MCs35 0.019 0.0628 3 0.288935 0.0135 3MCs36 0.006 0.0198 17 0.298235 0.0042 17MCs37 0.015 0.0496 6 0.291823 0.0106 6MCs38 0.0002 0.0007 24 0.302306 0.0001 24MCs39 0.012 0.0397 10 0.293973 0.0085 10

0

MCs40 0.0012 0.0040 22

3.6. Defuzzification process of subjective BEs

The center of area deffuzification technique is employed tocalculate the deffuzification of all the subjective BEs. Table 10shows the result of subjective BEs deffuzification.

3.7. Converting CFP of BEs into FP

CFP of the subjective BEs can be transformed into the corre-

sponding FP by using Equation 12. Table 11 presents FP of allthe subjective BEs.

Fig. 5 – Result of sensitivity

.301607 0.0008 22

3.8. Calculating FP of TE

To quantify the probability of TE of the fault tree a proba-bility for each BE in the fault tree must be provided. TheseBE probabilities are then propagated upward to the TE usingthe Boolean relationships. In other words, conventional FTArules are employed for TE quantification. Therefore, all BEs areconsidered independent. The BE probabilities can be propa-gated upward using MCs. Table 12 presents the FP of all the

MCS. Furthermore, TE is obtained by using Eq. (13). The valueof FP of the TE is 0.3024 per year.

analysis for revised TE.

Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88 87

RW

3

Ti

FiedgampcghrMsMatrm

abuTItt

Rc

epFtmt

4

Aaptt

Fig. 6 – R

.9. Ranking of MCs

able 13 presents the ranking of MCs based on their calculatedmportance levels (Eq. (14)).

In a SA, an input data parameter, such as a componentP is changed, and the resulting change in the TE probabil-ty is determined. This is repeated for a set of changes usingither different values for the same parameter or changingifferent parameters, e.g. changing different FPs. Usually for aiven sensitivity evaluation, only one parameter is changed at

time. This is called a one-at-a-time sensitivity study. Thisethod is employed here to validate the sensitivity of the

roposed model. RRW is employed to perform SA. The RRWan be calculated by re-quantifying the MCs probability of theiven event set to 0. It is expected that eliminating of MCs thatave the highest contribution to the occurrence of TE shouldesult in reducing the occurrence rate of TE more than otherCs. Therefore, ranking of RRW values is expected to be the

ame as the initial ranking result of MCs. As shown in Table 14,Cs31 has the highest contribution to the TE occurrence prob-

bility. Therefore, the RRW value of MCs31 is 0.0164 which ishe highest as expected. It shows the ranking result whichemains the same as the previous calculation. The proposed

odel satisfies the aforementioned expectations.The fourth column of Table 14 shows the value of the TE

fter eliminating of MCs. Fig. 4 includes 40 bars; the red colorar shows the TE value which is 0.3024. All new TE values (Col-mn 5th of Table 14) are presented in blue bars. As shown inable 14, MC number 26 is the most critical MC of the system.f the value of MC 26 is reduce to zero, it would be expectedhe new TE value reduce more than others. Fig. 5 can confirmhe expectation.

FVI and RRW are employed for ranking of MCs in this paper.esults of FVI measure and RRW are shown in the 3rd and 6tholumns of Table 14.

As mentioned, one of the advantages of SA is to identifyrror in the model. Result of Table 14 and Fig. 5 show that theroposed model can produce robust outcomes. As obvious inig. 6, controlling the first 11 most critical MCs would reducehe TE rate from 0.3 to 0.15. It means that control of the deter-

ined MCs will ensure considerable safety improvement inhe Deethanizer section of the Arya Sasol Plant.

. Conclusion and discussions

s one of the heavy industry discipline, petrochemical plantsre required to implement effective and consistent safetylanning against potential hazards (i.e. fire, explosion and

oxic gas releases) in order to ensure sustainable produc-ion. This research focused on developing a FFTA methodology

results.

demonstrating with Deethanizer failure within petrochemicalplant operational concept. Consequently, the research high-lights the following points:

• A fuzzy methodology for FT evaluation seems to be analternative solution to overcome the weak points of the con-ventional approach.

• By using linguistic variables, it is possible to handle theambiguities in the expression of the occurrence of a BE. Inaddition, the state of each BE can be described in a moreflexible form, by using the concept of fuzzy sets.

• Instead of using CFP, FP is used to characterize the failureoccurrence of the system events. It can efficiently expressthe vagueness of the nature of system phenomena andinsufficient information. Further, regardless of the complex-ity of the system, it is also possible to identify which BE caninfluence system FP the most.

• The importance measure can provide useful information forimproving the safety performance of a system. F-VI mea-sure index assists the analyst in identifying the critical MCsin the system for reducing occurrence likelihood of a TE.

As further research, application of FFTA methodology toother critical processes in petrochemical plant can be con-ducted. Moreover, multi attribute decision making (MADM)techniques can be adopted into the proposed methodology tomake cost benefit analysis for controlling the determined MCs.

Acknowledgement

The authors gratefully acknowledge to HSE manager (HosseinCharkhand) of Arya Sasol Petrochemical Company (A.S.P.C.)for technical information support in the demonstration of thecase study on Deethanizer failure in petrochemical plant oper-ations.

References

Aqlan, F., Ali, M.E., 2014. Integrating lean principles and fuzzybow-tie for risk assessment in chemical industry. J. LossPrevent. Process Ind. 29, 39–48.

Cai, K.Y., Wen, C., Zhang, M., 1991. Fuzzy states as a basis for atheory of fuzzy reliability in the possibility context. Fuzzy SetsSyst. 42, 17–32.

Celik, M., Lavasani, S.M., Wang, J., 2010. A risk-based modellingapproach to enhance shipping accident investigation. Saf. Sci.48, 18–27.

Chen, S.J., Hwang, C.L., 1992. Fuzzy Multiple Attribute DecisionMaking, 1st ed. Springer Verlag, Berlin, Heidelberg, Germany.

Dong, H.Y., Yu, D.U., 2005. Estimation of failure probability of oil

and gas transmission pipelines by fuzzy fault tree analysis. J.Loss Prevent. Process Ind. 18, 83–88.

88 Process Safety and Environmental Protection 9 3 ( 2 0 1 5 ) 75–88

Zhao, R., Govind, R., 1991. Defuzzification of fuzzy intervals.

Ford, D., Sterman, J.D., 1998. Expert knowledge elicitation toimprove mental and formal models. Syst. Dyn. Rev. 14,309–340.

Hsu, H.M., Chen, T.C., 1994. Aggregation of fuzzy opinion undergroup decision making. Fuzzy Sets Syst. 79, 279–285.

Huang, H.Z., Tong, X., Zuo, M., 2004. Posbist fault tree analysis ofcoherent systems. Reliab. Eng. Syst. Saf. 84, 141–148.

Korta, J.P., Lee, M.P., Eisenberg, N., Dewispelare, A., 1996. BranchTechnical Position on the Use of Expert Elicitation in theHigh-level Radioactive Waste Program, 1st ed. U.S. NuclearRegulatory Commission, NUREG-1563.

Lavasani, S.M., Wang, J., Yang, Z., Finlay, J., 2012. Application ofMADM in a fuzzy environment for selecting the best barrierfor offshore wells. Exp. Syst. Appl. 39, 2466–2478.

Liang, G.S., Wang, M.J., 1993. Fuzzy fault-tree analysis usingfailure possibility. Microelectron Reliab. 33, 583–597.

Lin, T.C., Wang, M.J., 1997. Hybrid fault tree analysis using fuzzysets. Reliab. Eng. Syst. Saf. 58, 205–231.

Lin, T.C., Wang, M.J., 1998. Hybrid fault tree analysis using fuzzysets. Reliab. Eng. Syst. Saf. 58, 205–231.

Liu, Y., Fan, Z.P., Yuan, Y., Li, H., 2014. A FTA-based method forrisk decision making in emergency response. Comput. Oper.Res. 42, 49–57.

Miller, G.A., 1956. The magical number seven plus or minus two:some limit on our capacity for processing information.Psychol. Rev. 63, 81–97.

Modarres, M., 2006. Risk Analysis in Engineering: ProbabilisticTechniques, Tools an Trends. CRC, USA.

Nicokis, J.S., Tsuda, I., 1985. Chaotic dynamics of informationprocessing: the magic number seven plus-minus two. Bull.Math. Biol. 47, 343–365.

Onisawa, T., 1988. An approach to human reliability in

man-machine systems using error possibility. Fuzzy Sets Syst.27, 87–103.

Onisawa, T., 1990. An application of fuzzy concepts to modelingof reliability analysis. Fuzzy Sets Syst. 37, 266–286.

Onisawa, T., 1996. Subjective analysis of system reliability and itsanalyzer. Fuzzy Sets Syst. 83, 249–269.

Onisawa, T., Nishiwaki, Y., 1988. Fuzzy human reliability on theCHERNOBYL accident. Fuzzy Sets Syst. 28, 115–127.

PDS, 2010. Reliability Data for Safety Instrument and System, 1sted. SINTEF Publisher, Trondheim, Norway.

Ping, H., Zhang, H., Zuo, M.J., 2007. Fault tree analysis based onfuzzy logic. In: Annual Reliability and MaintainabilitySymposium, vol. 10, pp. 77–82.

Preyssl, C., 1995. Safety risk assessment and management – theESA approach. Reliab. Eng. Syst. Saf. 49, 303–309.

Rausand, M., Hoyland, A., 2004. System Reliability Theory:Models, Statistical Methods and Applications, 1st ed. JohnWiley and Son, Inc., New Jersey, USA.

Sawer, J.P., Rao, S.S., 1994. Fault tree analysis of fuzzy mechanicalsystems. Microelectron. Reliab. 34, 653–667.

Shu, M.H., Cheng, C.H., Chang, J.R., 2006. Using intuitionisticfuzzy fault-tree analysis on printed circuit board assembly.Microelectron. Reliab. 46, 2139–2146.

Spouge, J., 2000. A Guide to Quantitative Risk Assessment forOffshore Installation, 2nd ed. CMPT publications, Aberdeen,UK.

Sugeno, M., 1999. Fuzzy Modelling and Control, 1st ed. CRC Press,Florida, USA.

Tanaka, H., Fan, L., Lai, S., Toguchi, K., 1983. Fault tree analysis byfuzzy probability. IEEE Trans. Reliab. 32, 453–457.

Wang, D., Zhang, P., Chen, L., 2013. Fuzzy fault tree analysis forfire and explosion of crude oil tanks. J. Loss Prevent. ProcessInd. 26, 1390–1398.

Fuzzy Sets Syst. 43, 45–50.