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Journal of Industrial Engineering and Management Studies (JIEMS), Vol. 2, No. 1 Page 2 uncertainty is not only due to an accident use of probability theory to deal with uncertainty is not enough and fuzzy logic theory should be used. Because unlike the classical reliability theory, a system does not comprise only two conditions, the failure mode and the operation mode, rather, the system performance is on a scale ranging from complete failure to full health and thus fuzzy logic theory is more appropriate to express the state of a system. In real world the information about system parameters always cannot be determined precisely and even with the most accurate experiments cannot be said decisively that how long is the lifetime of a system.

In 1974, for the first time, Mamdani et al studied in fuzzy control and fuzzy logic controllers and employed this theory in the field of control (control of the steam engine). During the years 1986 and 1987, for the first time fuzzy logic was used to automatic control of subway in Japan and shortly after hundreds fuzzy controller was designed and applied in Japan (Faghih et al. 1383). The use of fuzzy set theory in reliability has stated since Kaufman`s research (1975),he used possibility theory Instead of using probability theory to calculate the reliability.But at that time he could not justify the effectiveness of his theory in terms of the engineering and math. In fact, the major part of the application of fuzzy methodology in reliability has been after 1980. Most of these models have focused on determining the reliability of system components and simple systems (Cai. 2000).Here some of the most relevant articles in the field of fuzzy reliability are shown in Table 1.

Table 1: Classification of studies in the field of fuzzy reliability

Subjects year

Human reliability assessment for medical devices (Lin et al. 2014) 2014

solving multi-objective reliability optimization problems by fuzzy optimization technique (Garg et al. 2014)

Using fuzzy logic for allocating reliability in design process and initial development of engineering systems (Khanmohammadi et al. 2013)

A non-linear fuzzy regression for estimating reliability in a degradation process (Gonzalez et al. 2013)

2013 _{Interval optimization based line sampling method for fuzzy and random reliability analysis}

(Luyi et al. 2013)

A novel approach for analyzing fuzzy system reliability using different types of intuitionist fuzzy failure rates of components (Kumar et al. 2012)

2012 A new fuzzy parameters reliability analysis model (Chen et al. 2012)

Fuzzy structural analysis based on fundamental reliability concepts (Hurtado et al. 2012)

Interpretations of alternative uncertainty representations in a reliability and risk analysis context (Aven et al. 2011)

2011 Simulation PATROL-F system in form of fuzzy to achieve reliability levels ₂₀₁₁₎ (Tajeddine et al.

Reliability optimization by using an ant colony approach (Ahmadizar et al. 2011)

Bayesian system reliability assessment under the vague environment (Taheri et al.2011)

Fuzzy Bayesian reliability and availability analysis of production systems (Görkemli et al. 2010)

2010

Hybrid probabilistic fuzzy and non-probabilistic model of structural reliability (Ni et al. 2010) Reliability analysis on competitive failure processes under fuzzy degradation data (Wang et al. 2011)

Fuzzy logic-based direct load control(DLC) of air conditioning loads(ACL) considering nodal reliability characteristics (Goel et al. 2010)

Reliability estimation based on fuzzy lifetime data (Viertl. 2009)

2009

A production inventory model with fuzzy random demand and with flexibility and reliability

considerations (Bag et al. 2009)

Calculation fuzzy shortest path with the highest reliability (Keshavarz et al. 2009)

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Calculation of the fuzzy reliability in Neishabour train disaster; a case study

Journal of Industrial Engineering and Management Studies (JIEMS), Vol. 2, No. 1 Page 3 Fuzzy universal generating functions for multi-state system(MSS) reliability assessment (Ding et al. 2008)

2008

Moment Method Based on Fuzzy Reliability Sensitivity Analysis for a Degradable Structural System (Jun et al. 2008)

Assessment of human reliability factors by fuzzy approach (Bertolini. 2007) 2007

Bayesian reliability analysis for fuzzy lifetime data (Huang et al. 2006)

2006

Fuzzy Bayesian system reliability assessment based on exponential distribution 9Wu et al. 2006) Fuzzy multi-objective mathematical programming on reliability optimization model (Mahapatra et al. 2006)

Fuzzy reliability-based optimum design of laminated composites (Junhong et al. 2006)

Impact of interconnection photovoltaic/wind system with utility on their reliability using a fuzzy scheme (El-Tamaly et al. 2006)

Time-dependent reliability under consideration of fuzzy randomness (Moller et al. 2006) Reliability assessment method for pressure piping based on fuzzy probability (Zhou. 2005) 2005 Composite system reliability assessment using fuzzy linear programming(FLP) (Verma et al.

2005)

Evaluation of a power plant fuzzy reliability (Mohanta et al. 2004) 2004 Fuzzy reliability analysis of concrete structures (Biondini et al. 2004)

Fuzzy-based approaches to substation reliability evaluation (Bai et al. 2004) A numerical algorithm of fuzzy reliability (Jiang et al. 2003)

2003 A fuzzy logic based approach to reliability improvement estimation during product development (Yadav et al. 2003)

Analysis of structure reliability through fuzzy numerical software approach (Moller et al., Savoia. 2002)

2002

Incorporating fuzzy operators in the decision network to improve classification reliability (Chiang et al. 2002)

A practical engineering method for fuzzy reliability analysis of mechanical structures 9Bing et al. 2000)

2000 A fuzzy-based approach for generation system reliability evaluation (Narasimhan et al. 2000) Reliability analysis of slopes using fuzzy sets theory (Dodagoudar et al. 2000)

Before 2000, articles are emphasized on basic concepts and researches such as Fuzzy theory in reliability analysis, modeling concepts of fuzzy reliability analysis, analysis of reliability and fault tree On fuzzy sets, evaluation of fuzzy human errors in the Chernobyl accident and etc are done.

Before 2000

In this paper, Neishabour train disaster has been studied in terms of man- machine reliability and with describing the accident based on the relevant documents and evidences, accident system modeling provided.

2. Background of the Neishabour event

The incident began in near the city of Neishabour on 18 February 2004, where 51 railway wagons carrying sulfur, fertilizer, petrol and cotton broke loose from their siding at Abu Muslim Station and after taking a few kilometers some of them are upside down and catch on fire. In this accident over 300 people were killed and several villages were destroyed (IRNA news agency. 29 Bahman 1382, Mehr news agency. 29 Bahman 1382, Fars news. 3 Aban 1384, Mehr news agency. 30 Bahman 1382). This incident Damage is listed in Table 2.

Table 2: Neishabour accident damage [Mehr news agency. 29 Bahman 1382, Mehr news agency. 30 Bahman 1382, IRNA news agency. 7 Esfand 1382, Mehr news agency. 16 Esfand 1382 ]

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Journal of Industrial Engineering and Management Studies (JIEMS), Vol. 2, No. 1 Page 4 state workers 150, ordinary people 139 Deaths

460 people Injured

250-300 billion rials Financial losses

10 km Destruction radius

90 100% damaged buildings

Depth of 25 to 30 meters, width between 80 and 150 m and 150 m Crater caused by the explosion

51 The number of wagons

20 No. of villages affected

In order to further investigate two categories of propositions are collected in Table 3:Certain propositions and uncertain propositions of accident, using these propositions unreliability circuit of event (Figures 1 and 2) can be drawn.

Table 3: Classification of certain propositions and uncertain propositions of Neishabour accident

1. Scene of disaster (Abu Muslim Station, near Neishabour)

2. Time of the accident (18 February 2004)

3. wagons Freight: sulfur, fertilizer, petrol and cotton

4. Sloping road

5. Overturning of 48 wagons

Certain propositions

1. Breaking brake shoe due to Load pressure

2. Technical defect in the braking system of wagons

3. Probability of Staff carelessness in dragging the Parking

brake

4. Probability of Staff carelessness in placing the brake shoes

5. Earthquake

6. Due to human error

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2. Probability of ammonium nitrate explosion due to clash or

fire caused by clash. 2.Fire

1. Unlike the regulations, transportation of fuel, fertilizer,

sulfur and cotton together.

2. Wrong analysis by firefighters for selecting extinguishing

method.

3. Spread of petrol fire and sulfur due to the use of water

4. Using the wrong extinguisher

5. The absence of an expert before starting to fighting fire

6. Explosion of the remaining wagons containing ammonium

nitrate

7. Explosion of Petrol wagons due to heat transfer

8. Explosion of sulfur exposed to air or oxidizing materials

3.Explosion

3. The unreliability of Neishabour accident

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on hits the ot he r Fire spr ead Frictio n Sta tic elect ri cit y

Cotton self- heatin

g Fire subs ystem F ire wit h Gaussi an ammon ium nitrate F ire wit h tria n gle ammon ium nitrate Tab le 7: Un re li ab ilit y of fire sub syst em L U L U L U L U L U L U L U L U L U L U α 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0.03 0. 9 0. 008 0.91 0. 008 0.91 0. 008 0. 908 0. 008 0.91 0.06 1 -1 .5 16 2.78 -1 .3 68 1 0. 063 0. 963 0.11 81 1 0. 1 0.06 0.9 0.01 5 0.82 0.01 5 0.82 0.01 5 0.81 5 0.01 5 0.82 0.12 0.99 9 -1 .1 64 2.42 -0 .9 15 1.00 1 0.12 6 0.92 6 0. 2266 0. 9999 0.2 0.09 0. 8 0. 02 3 0.72 0. 02 3 0.72 0. 02 3 0. 72 3 0. 02 3 0.72 0.17 0. 99 7 -0.922 2.18 -0.597 1. 00 4 0. 18 9 0. 88 9 0. 3262 0. 9997 0. 3 0. 12 0.7 0. 03 0. 63 0. 03 0. 63 0. 03 0. 63 0. 03 0. 63 0. 22 0.99 1 -0 .7 24 1. 98 -0 .3 43 1.00 8 0.25 2 0.85 2 0. 4173 0. 9987 0.4 0.15 0. 7 0. 038 0.54 0. 038 0.54 0. 038 0. 538 0. 038 0.54 0.27 0. 983 -0 .5 47 1.81 -0 .1 29 1. 014 0. 315 0. 815 0. 5003 0. 9968 0. 5 0.18 0.6 0.04 5 0.45 0.04 5 0.45 0.04 5 0.44 5 0.04 5 0.45 0.32 0.97 1 -0 .3 81 1.64 0.05 8 1.01 8 0.37 8 0.77 8 0. 5758 0. 9936 0.6 0. 21 0.5 0.05 3 0. 35 0.05 3 0. 35 0.05 3 0.35 3 0.05 3 0. 35 0. 36 0. 96 -0 .2 15 1. 47 0.22 7 1.01 9 0.44 1 0.74 1 0. 6441 0. 9897 0.7 0.24 0. 4 0.06 0.26 0.06 0.26 0.06 0.26 0.06 0.26 0.41 0. 95 5 -0 .0 38 1. 3 0. 38 4 1. 01 4 0. 50 4 0. 70 4 0. 7057 0. 9866 0. 8 0.27 0. 4 0. 06 8 0.17 0. 06 8 0.17 0. 06 8 0. 16 8 0. 06 8 0.17 0.45 0. 96 4 0. 17 1 1.09 0. 54 2 1. 00 3 0. 56 7 0. 66 7 0. 76 1 0. 9879 0. 9 0.3 0.3 0.07 5 0. 08 0.07 5 0. 08 0.07 5 0.07 5 0.07 5 0. 08 0. 49 1 0. 63 0. 63 0. 81 1 0. 63 0. 63 0. 81 04 1 1

Similarly, α-cut of explosion subsystem (which includes several parallel subsystems), can be

(11)

S u lf ur ex p los ion b ec aus e of reacti

on with ox

idizin g mat eri als S u lf ur ex p los ion b ec aus e of mi xi ng p

articles with _air

Improper use of ex

ting uishers Am moniu m Nitrat e + petrol = Ex p losi on No t opening the door of fu el so urces N ot se para ting the fue l so urce s Thermal Conducti vity Movement Tr ansf erring the radi at io n of exp losi on N ot coo

ling fuel so

(12)

Journal o Conside of event

α 0 0.1 0.2

0 0.3

0 0.4

0 0.5

0 0.6

0 0.7 0.8

0 0.9

0 1

Accordi (respect nitrate s

Fi

And to c

x∗

Thus, th case of subsyste reliabili high, th high.

of Industrial En ering the rel

t is defined

Gaussia nitrate

U 1.00004427

0.9894240 0.97749068 0.96417983 0.94874374 0.92967367 0.90495542 0.87300902 0.83512016 0.80251119

ing to the tively from subsystem, G

igure 7: The

convert the he unreliabi f triangle am

em is cons ity based on herefore the

ngineering an lationships as Table 9.

Table 9:

n ammoniu e subsystem L 0.0447 76

-0.0543 8

-0.0421 84

-0.0104 33

0.03957 47

0.1062 76

0.1871 24

0.2802 2

0.385 67

0.5481 93

Table 9, m right to lef Gaussian am

membership

fuzzy value ility in the mmonium n idered is e n the eleme unreliabilit

nd Managemen between su

: Unreliability

um m L

0.9

7103-

0.9 39544

0.9 13694

0.9 45603

0.9 71851

0.8 24393

1702 0 2393

0 599

0 1696

membership ft: regardles mmonium n

function diag

e to crisp va case of ign nitrate subsy

quivalent to ent fuzzy re

ty of the ov

nt Studies (JIE ubsystems in

y of Neishabo

triangle am nitrate su

U 1 88904642 75516423 59537397 40578028 18183003 91922972 0.8616 .827692 .792634 .764059

p function ss of ammo nitrate subsy

gram of the N

alue, follow noring the a ystem is 0. o 0.716. A eliability", t verall syste

Y.C.Z

EMS), Vol. 2, n unreliabili

our train acci

mmonium ubsystem

L 0.01 0.0617203 0.1187502 0.1816920 0.2497507 0.3211839 0.3939315 0.46595 0.53541 0.601512 0.66753

diagram o onium nitrat

ystem) is sh

Neishabour tr

wing formula ammonium n

.675 and w According to

he numeric m, which l

Zanjani, Z. Ra

No. 1 ity circuit, f

ident system

Rega n U 0.9888 364

0.975 241

0.9580 074

0.9366 792

0.9105 903

0.8798 574

0.84 1

0.81 8

0.78 2

0.76 5

f the syste te subsystem hown in Figu

rain disaster

a is used (S nitrate subs when Gaussi o "the lingu cal values 0

ed to the ac

afie Majd, A

finally the u

ardless of am nitrate subs

U 1

0. 879918

0 172048

0. 048468

0. 668086

0. 529071

0. 801499 45661 10705 8001 64059

em fuzzy u m, triangle

ure 7.

fuzzy unrelia

havandi, 13 system is 0. ian ammon uistic classi .65-0.75 ar ccident, wa

.Mirzazadeh

Page 12 unreliability

mmonium system

L 0 007999962 0.02754953

057622738 097093697 144481878 198029319 0.255895 0.316324 0.377766 0.438899

unreliability ammonium

ability

385): (13) .601, in the nium nitrate ification of re relatively as relatively h

2 y

2 8 7 8 9

y m

(13)

5. Conclusions

In accident analysis usually methods like risk analysis, crisis management and etc, are used. For more emphasis on the various components of the system, modeling and reliability analyzing can be used. In this method the relationship between the subsystems and their position in comparison with the total system will become more visible. So in this paper, the fuzzy reliability method is used to analyze the incident and the incident is considered with the systemic and humanitarian dimensions. In the first and to analyzing the incident, using certain and uncertain propositions, unreliability circuit of the event was plotted and then the whole incident was simplified to a serial trilateral system, because of the inability to provide exact values for the unreliability of each subsystem, regarding the opinion of experts, fuzzy logic was applied and depending on type of each subsystem, triangular and Gaussian membership functions were attributed to it. Then by using α-cut method, fuzzy unreliability value of system (In three cases: regardless of ammonium nitrate subsystem, triangle ammonium nitrate subsystem, Gaussian ammonium nitrate subsystem) was calculated. Finally by doing defuzzification for each of three mentioned cases separately and comparing the obtained result with the classification table of linguistic variables, unreliability of the system was identified.

Based on the results, by enhancing precision and discipline (in wagon escape subsystem), planning appropriate instruction for material arrangement inside the wagon also in putting wagons together (in fire subsystem) and finally by separating and cooling resources (in explosion subsystem), with high probability similar events do not occur.

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