Risk assessment modeling in aviation safety management

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Journal of Air Transport Management 12 (2006) 267273

Risk assessment modeling in aviation safety management

Wen-Kuei Lee

Department of Industry and Business Management, The Open University of Kaohsiung, 436 Daye North Road, Siaogang, Kaohsiung 812, Taiwan

Abstract

Safety risk management is important in aviation. This paper develops a quantitative model for assessing aviation safety risk factors as

a means of increasing the effectiveness of safety risk management system by integrating the fuzzy linguistic scale method, failure mode,

effects and criticality analysis principle, and as low as reasonably practicable approach. The model is developed by evaluating all relatedestimation factors based on their importance, how hazardous they are, their detectability, probability, criticality, and frequency. An

empirical study demonstrates the modeling process.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Risk assessment; Safety management; FMECA principle; ALARP approach

1. Introduction

Safety analysis of accidents is an important but

challenging issue in the civil aviation industry. Air

passenger transportation is growing, with annual increases

exceeding 5% forecast for the next 20 years. From a safetyperspective, this means that continuous improvement is

necessary to maintain high safety levels (Button et al.,

2004). During recent decades, the focus has been on

qualitative analysis or post-event studies of accidents.

Nevertheless, whether considering the qualitative/quanti-

tative analysis or the post-event/pre-event approach, these

methods are generally based on either reactive or proactive

analysis (Lee and Chang, 2005b). The reactive approach is

a method of taking precautions following a loss, and its

efficacy in preventing air accidents is limited by its ex post

facto nature. Consequently, a before-the-fact diagnostic

and predictive method may be more useful for safety riskmanagement (SRM). In Taiwan, the Civil Aeronautics

Administration (CAA) has promulgated some fundamental

SRM measures for use by airlines and airports. It even

announced a reward system integrated with the allocation

of aviation resources, such as air routes, operational rights,

and flight frequency quotas, to monitor SRM performance.

The airlines and airports, however, lack an adequate

method for accurately assessing the significance of SRM

systems.

From the perspective of prevention, if risks can be

efficiently diagnosed before serious failure occurs the

incident may be markedly reduced. The failure mode,

effects and criticality analysis (FMECA) principle is auseful tool for considering risk. It has been extensively

applied in the national safety defense (US Department of

Defense, 1980). Subsequently, the FMECA was universally

used in high risk industries, for example nuclear energy,

chemical engineering, and petrochemical manufacturing.

However, in it for multiple estimation factors has a fatal

weaknessthe dilution phenomenon. To avoid this, Lee

and Chang (2005b)designed a unique method of formulat-

ing the combined measurement scores. To obtain a rapid

and convenient risk analysis model, the graphic analysis

integrated the as low as reasonably practicable (ALARP)

approach. ALARP evolved from the safety case conceptdeveloped in the UK (Health and Safety Executive, 1992).

Through proper application of graphic analysis, the SRM

overseer can monitor individual risk factor without

constraints of time and place and immediately adopt the

preventive measures to avoid imminent accidents.

Finally, because of the intangible nature of judging

measurement scores of aviation risks for certain estimation

factors, such as importance and detectability, and to reflect

the inherent subjectivity and imprecision of even expert

judgments, the fuzzy linguistic scale method (Buckley,

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1984) can be used to derive fuzzy judgments. The fuzzy

membership functions can be deduced, and then the a-cut

technique is used to calculate the risk levels of the risk

factor.

2. Methodology

2.1. Nouns definition

To develop the risk assessment model, all considered

estimation factors are assessed in terms of importance,

hazardousness, detectability, probability, criticality, and

frequency. These are divided into two groups. The

endogenous group, comprising importance, hazardousness,

detectability based on the absolute judgments of experts,

and probability, the four of which must generally remain

constant during a risk assessment period. The exogenous

group, containing criticality based on inspectors absolute

judgments, and frequency, both of which must change

according to each inspection result. To reflect the inherent

imprecision of the survey and inspection process, these

expert assessment and inspector examination results are

represented by triangular fuzzy numbers, while probability

and frequency are crisp values.

The factor importance ( ~I) represents the safety signifi-

cance of a risk factor; a high degree of influence of the

significance is positively associated with high importance.

The failure hazardousness ( ~H) indicates the possible

severity of the disaster resulting from the failure of a risk

factor. Degree of hazardousness may vary among risk

factors. Some risk factors may cause only light injury or

light property damage or loss, while others may causeheavy casualties or considerable property damage or loss.

The greater the level of death or injury and property

damage or loss resulting from the failure, the higher the

hazardousness. The failure detectability ( ~D) of a risk factor

indicates whether the failure can easily be detected. If the

failure can easily be detected, then it has low detectability.

The probability (P) of air accidents represents the number

of global air accidents occurring during a risk assessment

period. The failure criticality ( ~C) represents the extent of

risk factor failure. The inspector must clearly detect and

record the failure, the failure mode, and its criticality

during the routine examination. The failure frequency (f) of

a risk factor refers to the number of failures per unit during

a risk assessment period. The measurement unit can be the

number of take-offs and landings, the flight-hours, the

number of departures, and the duration of air traffic

control. The failure frequency is calculated for each risk

factor based on different failure criticalities.

Failure follows a malfunction, fault, breakdown, bad

reaction, or loss of normal function of a risk factor. Most

failures are discovered during routine maintenance, repair,

and inspection. Numerous types of failure exist, including

the fuselage fractures, the mechanical breakdowns, failure

of landing gear to rise/fall normally, attrition of tire

integrity, and so on. These types of fractures, breakdowns,

unable to rise/fall, attrition, etc., are called failure modes.

Numerous random factors also affect risk factor failure,

for example artificial operations, weather effects, mechan-

ical faults, and organizational culture.

2.2. Constructing risk assessment model

The level of risk (LoR) index, an integrated concept

(Fig. 1), is deduced from the risk gradient (RG) and risk

magnitude (RM) indexes. The RG index comprises

endogenous estimation factors, and the RM index com-

prises exogenous estimation factors. To avoid the dilution

effect, this study proposes a coordinate-combination

method for constructing the risk-space diagram (RSD),

and then employs the Euclidian distance formulae to

calculate the RG and the RM indexes. To reflect the

subjectivity and imprecision of the questionnaire survey

and routine inspection, the judgments made by experts and

inspectors regarding the scores of each fuzzy estimation

factor, excluding probability and frequency, are repre-

sented using a fuzzy linguistic scale.

The triangle fuzzy questionnaire surveys are used to

obtain the fuzzy measurement scores owing to their ease of

comprehension and operation. A five-point linguistic scale

{very high, high, middle, low, and very low} is used for

designing the fuzzy questionnaires (Buckley, 1984). The

triangle fuzzy measurement scores of importance ( ~Imkj) are

provided by Eq. (1), and the sub-total triangle fuzzy

measurement scores (Amk, Bmk, Cmk) are then determined

by Eq. (2), whereBmk is calculated using geometric means.

Given

~Imkj Amkj; Bmkj; Cmkj

; 8m; k;j, (1)

then

Amk min Amkj

; k 1; ; K; j2Nmk,

BmkYNmkj1

Bmkj

!1=Nmk,

Cmk max Cmkj

; k 1; ; K; j2 Nmk, 2

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Risk gradient (RG) index

a. FactorImportance of a riskfactor

b. Failurehazardousnessof a risk factor

c. Failuredetectability of a risk factor

d.Probability of air accidents

Level of risk (LoR) index

Risk magnitude (RM) index

a. Failurecriticalityof a risk factor

b. Failurefrequencyof a risk factor

Fig. 1. The integrated concept of level of risk (LoR) index.

W.-K. Lee / Journal of Air Transport Management 12 (2006) 267273268


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where ~Imkj represents the fuzzy importance of the jth

expert, the kth linguistic scale of risk factor m; Nmkrepresents the number of the kth linguistic scale for

assessing the importance of risk factor m.

Subsequently, the fuzzy membership functions are used

to calculate the aggregate triangle fuzzy measurement

scores ( ~Im) by

~Im XKk1

Nmk Amk; Bmk; Cmk

( )=nI

ImL; ImM; ImR ; 8m, 3

where nI PK

k1Nmk.

The aggregately triangle fuzzy measurement scores of

hazardousness ~Hm HmL; HmM; HmR and detectability ~Dm DmL; DmM; DmR can be obtained in the same way.

Finally, the a-cut technique (defuzzified method) is

employed to calculate the left-hand values (IamL, Ha

mL,

and DamL) and right-hand values (Ia

mR, Ha

mR, and Da

mR)

of the triangle fuzzy measurement scores of estimationfactors by

IamL ImL aImMImL;

IamR ImR a ImRImM ; 8m, 4

HamL HmL aHmMHmL;

HamR HmR a HmRHmM ; 8m, 5

DamL DmL aDmM DmL;

DamR DmR a DmR DmM ; 8m, 6

where 0.0oao1.0, and is considered a risk control

variable.The coordinate-combination method is used for avoid-

ing dilution. Fig. 2 shows the concept upon which it is

based. Each coordinate axis represents a different estima-

tion factor, and all axes construct a RSD of an RGindex

for each risk factor. In RSD, the suffix L on each axis

denotes the left-hand value of each estimation factor, while

the suffix R denotes the right-hand value of each estimation

factor; the superscript L in quadrant space denotes the left-

bound RGLm index, while the superscript R represents the

right-boundRGRm index. Each risk factor has its RSD. The

RGLm index comprises I

a

mL, Ha

mL, Da

mL, and P. Meanwhile,the RGRm index comprises I

a

mR, Ha

mR, Da

mR, and P.

Consequently, RGLm(Ia

mL, Ha

mL, Da

mL, P ) and RGRm(I

a

mR,

HamR, Da

mR, P) represent respectively the coordinate-

combination functions of the left-bound and right-bound

RG indexes of risk factor m under a-cut. Here, the

probability (P) is included in these functions and its

left-hand and right-hand values are equivalent for all

risk factors.

The probability can be based on the global air accidents.

Janic (2000) designed the probability distribution function

based on global air accidents during 19651998, and

adopted regressive analysis to deduce the global prob-

ability of an accident occurring by

PTpt 1 exp0:020t; tX0, (7)

where t is a time variable (expressed in days). Conse-

quently, the probability is 0.0198 per day t 1, 0.0392

per 2 days t 2, and so on.

Finally, the Euclidean distance formulae is used to

calculate the distances betweenxamLand xa

min,xa

mRand xa

min,

xamax and xa

min by

RGLm ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXX

x1

xamLxa

min

2

vuut , ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXXx1

xamax xa

min

2

vuut ; 8m,

RGRm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXXx1

xamR xa

min

2vuut ,

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXXx1

xamaxxa

min

2vuut ; 8m.

8

where x denotes endogenous estimation factors; xamax are

the maximum values of x under a-cut, which generally

equal 1.0 (standardized); xamin are the minimum values,

which generally equal 0.0. The denominators are the

standardized formulae.The RSD ofRMindex resemblesFig. 2, but it is really a

two-dimensional diagram. The RM index comprises ~Cmand fm. The criticalities ( ~Cm) are the aggregate triangular

fuzzy measurement scores given by

~Cm CmL; CmM; CmR; 8m. (9)

Subsequently, the left-hand values (CamL) and right-hand

values (CamR) under a-cut are calculated by

CamL CmL aCmM CmL;

Ca

mR CmR a CmR CmM ; 8m. 10

ARTICLE IN PRESS

LmRG

(0.0,1.0,1.0)

H

mR

D

mR

H

mL

D

mL

I

mR

I

mL

Dm

Hm

O:0(0.0,0.0,0.0)

(1.0,0.0,1.0)

(1.0,0.0,0.0)Im

(0.0,1.0,0.0)

G:1.0(1.0,1.0,1.0)

(1.0,1.0,0.0)

(0.0,0.0,1.0)

RGmR

Fig. 2. The RSD possessing three estimate factors.

W.-K. Lee / Journal of Air Transport Management 12 (2006) 267273 269


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Furthermore, the Euclidean distance formulae are

provided by

RMLm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPYy1

yamL ya

min

2s ,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPYy1

yamax ya

min

2s ; 8m;

RMRm ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

Y

y1

yamR ya

min

2

s ,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPY

y1

yamax ya

min

2

s ; 8m;

(11)

where y denotes the exogenous estimation factors; RMLmrepresents the left-bound RMindex of risk factor m under

a-cut, and RMRm represents the right-bound RM index of

risk factor m under a-cut. The denominators are also the

standardized formulae.

Following the calculation of RG and RM indexes, the

LoRindexes are constructed by

LoRLm ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

RMLm

2 RGLm

2

2q

; 8m;

LoRUm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRMRm 2

RGRm

2 2q

; 8m;(12)

whereLoRLm represents the lower-bound LoR index of risk

factor m under a -cut, and LoRUm represents the upper-

boundLoRindex of risk factor m under a-cut.

2.3. Constructing risk-monitoring diagrams and analyzing

risks

The ALARP approach is an effective tools for analyzing

safety risks in personal insurance or environmental monitor-ing systems (Tam et al., 1996).Lee and Chang (2005b)have

applied this approach to develop a risk-monitoring diagram

(RMD) in aviation SRM, which integrates the RGand RM

indexes into theLoRindex for each risk factor. In RMD, the

two boundaries that divide the three zones are the LoRLmindex and the LoRUm index given by Eq. (12). The two

oblique lines represent the RM index. Notably, the baseline

of the inversed triangle increases with the RG index. Upon

checking the status of a risk factor, the inspector must

transform the inspected result into the LoR index (the new

LoRUm index is then called RS-line).

Generally, the inversed triangle can be separated into

zones:

1. Top zoneintolerable region (InTo-region ): If this

region contains the RS-line, the inspected result (the

new LoRUm index) exceeds the set LoRUm index. Conse-

quently, the SRM overseer must immediately adopt

appropriate measures to eliminate the impact of failure.

2. Middle zoneas low as reasonably practicable region

(ALARP-region): If this region contains RS-line, the

SRM overseer only needs to monitor the new risk status.

However, more rigorous measures must be adopted

when the RS-line approaches the upper section of this

region.

3. Bottom zonebroadly acceptable region (BA-region): If

this region contains theRS-line, no measures need to be

taken. Meanings vary among regions, and the related

measures that need to be adopted also differ.

Anyhow, if airlines and airports apply this model, the

checklist of FMECA for each risk factor needs to beestablished first. To monitor the RS-line, it is necessary to

implement routine inspection work to collect and com-

pletely record the failure data. Particularly, the SRM

overseer would need to continually analyze the risk status

and adopt appropriate measures to prevent worsening

failure.

3. Empirical study

3.1. Screening risk factors and deducing RG indexes

While the proactive function emphasizes all aviation

safety factors are treated as risk factors. Previous studies

were unable to determine which classifications were correct

with respect to risk factors (Lee and Chang, 2005b). The

Boeing company separated aviation safety factors into

seven groups crew, airline flight operations, airplane design

and performance, airplane maintenance, air traffic control,

airport management, and weather information. Heinrich

(1959) sorted them into five types: human, machine,

mission, management, and environment, and Edwards

(1988) categorized them into four types: livewire, hard-

ware, software, and environment. Meanwhile, the Interna-

tional Air Transport Association (IATA) classified them

into five categories human, organization, machine, envir-onment, and insufficiency (HOMEI). Among these cate-

gorizations, the categorization of the IATA is the most

widely applied and used here (Civil Aeronautics Adminis-

tration, 1999; Civil Aeronautics Administration, 2001) to

derive these screened risk factors. However, only 14 risk

factors (mechanical category) are selected.

Table 1 lists the defuzzified measurement scores of

importance, hazardousness, and detectability with respect

to expert questionnaire surveys the risk factors, with

a 0:5. The experts included 21 airline safety supervisors,10 academics, 13 research department and Aviation Safety

Council (ASC) experts, 11 directors of safety management

departments in the Taiwanese CAA and two international

airports. The survey process from March to June 2004

contained two stages of interviews and mailings; the first

aimed to screen the estimation factors (Lee and Chang,

2005a), and the second was to obtain the measurement

scores of considered risk factors. In the second stage, a

total of 55 copies were issued, and 45 were returned. The

effective response rate was around 81.82%. Since routine

inspection work is executed everyday, the probability is

0.0198 per day. In Table 1, the average scores of

importance and hazardousness all exceed 0.70, meaning

that these two estimation factors are highly represented.

The average scores of detectability are almost all below

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0.50, indicating that it is easy to examine the failures for

these 14 risk factors.

Using the data inTable 2, all left-bound and right-bound

RGindexes are calculated using Eq. (8). Risk factor F1has

the highest (RGLm, RGRm) (0.606, 0.721) indexes. Column

4 of the table reveals the critical-ranking order of these risk

factors according to the decreasing order ofRGRm indexes.

Risk factor F1is the most critical, followed by F2, and F10.

Based on the ranking, the SRM overseer can adopt

different measures relevant for different risk factors.

3.2. Deducing RM indexes and LoR indexes

Owing to the scarcity of safety inspection data,

hypothetical data is used to obtain the ~Cm and fmmeasurement scores for deducing the RM indexes. The

aggregately triangle fuzzy measurement score of failure

criticality is assumed to be (0.60, 0.75, 0.85), and the failure

frequency is given by 1/365 (times/days) 0.00274 for each

ARTICLE IN PRESS

Table 1

The defuzzified measurement scores of endogenous estimate factors and P(a-cut 0.5)

Risk factors of machine (Fm) Importance (Im) Hazardousness (Hm) Detectability (Dm) Prob. (P)

Left-hand Right-hand Left-hand Right-hand Left-hand Right-hand

F1 Airplane structure 0.735 0.873 0.773 0.892 0.576 0.724 0.020

F2 Engine system 0.752 0.887 0.725 0.860 0.471 0.652 0.020F3 Landing gear and tire system 0.682 0.836 0.652 0.810 0.356 0.575 0.020

F4 Flight control system 0.737 0.874 0.726 0.864 0.415 0.627 0.020

F5 Navigation system 0.656 0.804 0.631 0.781 0.394 0.587 0.020F6 Hydraulic pressure system 0.650 0.798 0.629 0.781 0.359 0.561 0.020

F7 Fuel system 0.667 0.815 0.679 0.826 0.381 0.580 0.020

F8 Automatic driving system 0.567 0.730 0.544 0.700 0.366 0.584 0.020F9 Defending ice, eradicating ice or rain system 0.691 0.833 0.717 0.857 0.392 0.566 0.020

F10Fire and smog warning system 0.771 0.903 0.775 0.889 0.390 0.585 0.020

F11Cabin pressure, lubrication, and electricity system 0.628 0.780 0.636 0.786 0.374 0.582 0.020

F12Ground proximity warning system (GPWS) 0.675 0.832 0.705 0.839 0.341 0.542 0.020F13Auxiliary approaching system 0.621 0.789 0.630 0.774 0.354 0.555 0.020

F14Early-alarm measures (TCAS, ASDE) 0.663 0.823 0.672 0.821 0.350 0.545 0.020

Table 2

TheRGm, RMm, and LoRm indexes (a-cut 0.5)

Fm Risk gradient (RGm) Risk magnitude (RMm) Level of risk (LoRm)

Left-bound Right-bound Critical ranking Left-bound Right-bound Lower-bound (C) Upper-bound (D) Critical ranking Interval

F1 0.606 0.721 1 0.477 0.566 0.369 0.436 1 0.067

F2 0.573 0.698 2 0.477 0.566 0.382 0.445 2 0.063

F3 0.504 0.649 7 0.477 0.566 0.405 0.463 7 0.058

F4 0.558 0.690 4 0.477 0.566 0.387 0.448 4 0.061

F5 0.496 0.632 10 0.477 0.566 0.408 0.469 10 0.061

F6 0.487 0.625 12 0.477 0.566 0.411 0.472 12 0.061

F7 0.513 0.649 8 0.477 0.566 0.403 0.464 8 0.061

F8 0.434 0.584 14 0.477 0.566 0.425 0.484 14 0.059

F9 0.535 0.661 5 0.477 0.566 0.395 0.459 5 0.064

F10 0.580 0.698 3 0.477 0.566 0.379 0.445 3 0.066F11 0.484 0.626 11 0.477 0.566 0.411 0.471 11 0.060

F12 0.517 0.650 6 0.477 0.566 0.401 0.463 6 0.062

F13 0.476 0.618 13 0.477 0.566 0.414 0.474 13 0.060

F14 0.503 0.642 9 0.477 0.566 0.406 0.466 9 0.060

The aggregately triangle fuzzy measurement scores of criticality and frequency are hypothetical values set as (0.60, 0.75, 0.85).

Levelofrisk(LoR)

InTo-region

ALARP-region

BA-region

RS-line

0.721

0.606

0.0000

Risk gradient (RG)

0.1000

0.2000

0.3000

0.4000

0.3687

0.4357

0.5000

LoRLm

LoRUm

Fig. 3. The RMD of risk factor F1.



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risk factor. The RMLm and RMRm indexes are calculated

using Eq. (11), with a 0:50. TheLoRLm and LoRUm indexes

are thus obtained from Eq. (12), with a 0:50.Table 2lists

the results. While all of the hypothetical RM indexes are

the same, the LoR indexes differ among the risk factors.

The critical-ranking order of these factors ranked in

increasing order of the LoRUm index shows factor F1 has

the lowest LoRUm index. Accordingly, the RS-line (new

LoRUm index) of risk factor F1exceeds this lowest threshold

by more than other risk factors. Comparatively, risk factorF8has the highestLoR

Um index, so its RS-line has difficulty

exceeding this threshold. A higher RGRm index will produce

a lowerLoRUm index. This result fits with the aviation SRM

theorem. The SRM overseer must adopt more rigorous

measures to monitor risk factors when LoRUm index is low.

Furthermore, the final column of Table 2 displays the

interval between the LoRLm and LoRUm indexes. When the

hypothetical RM indexes are the same, if the interval is

larger, the deduced ALARP-region of RMD is wider and

itsLoRUm index is lower (Figs. 3 and 4). In this situation, the

RS-line of this kind of risk factor easily falls into the InTo-

region, and should be considered a more critical risk factor.

3.3. RMDs and risk-monitoring strategies

The RMDs of risk factor F1and F8are shown inFigs. 3

and 4. Risk factor F1has the lowestLoRUm index, while risk

factor F8 has the highest one. Clearly, a rigorous risk-

monitoring strategy must be adopted for risk factor F1, but

a slack strategy can be adopted for risk factorc F8.

Matching up the RMD can enable the SRM overseer to

clearly monitor the status of each risk factor. Table 3lists

the variations of theLoRUm indexes for the 14 risk factors by

varying the a-cut value, which can be varied between 0.0

and 1.0. When a-cut is increased, the low LoRUm index isfurther reduced. On the other hand, the LoRUm index is

increased while a-cut is decreased. For example, if a-cut

varies from 0.50 to 0.65 for risk factor F1, theLoRUm index is

reduced from 0.436 to 0.430. Consequently, more rigorous

risk-monitoring measures are adopted when the larger a-cut

value is used, while otherwise looser measures are adopted.

Numerous results are obtained given different a-cut

values for each risk factor. This study emphasizes critical

risk factors with high RGRm index or low LoRUm index

require close monitoring. Fig. 5 displays the relationships

between a-cut values and ( LoRLm, LoRUm) indexes of risk

factor F1

. For risk-monitoring, the SRM overseer can

ARTICLE IN PRESS

Levelofrisk(LoR)

InTo-region

ALARP-region

BA-region

RS-line

0.584

0.434

0.0000

Risk gradient (RG)

0.1000

0.2000

0.3000

0.4252

0.4000

0.4844

0.5000

Fig. 4. The RMD of risk factor F8.

Table 3

The variations ofLoRUm indexes by varying a-cut

Fm LoRUm

a 0.8 a 0.65 a 0.5 a 0.35 a 0.2

F1 0.424 0.430 0.436 0.442 0.447

F2 0.434 0.430 0.445 0.451 0.456

F3 0.454 0.459 0.463 0.467 0.471

F4 0.437 0.443 0.448 0.454 0.459

F5 0.459 0.464 0.469 0.474 0.478

F6 0.461 0.466 0.472 0.477 0.482

F7 0.454 0.459 0.464 0.468 0.472

F8 0.474 0.479 0.484 0.489 0.494

F9 0.448 0.454 0.459 0.464 0.470

F10 0.432 0.439 0.445 0.452 0.458

F11 0.460 0.466 0.471 0.477 0.482

F12 0.453 0.458 0.463 0.468 0.473

F13 0.464 0.469 0.473 0.479 0.483

F14 0.456 0.461 0.465 0.470 0.475

RS-line

(0.8, 0.4240)(0.5, 0.4357)(0.3, 0.4435)

(0.3, 0.3496)

(0.8, 0.3971)(0.5, 0.3687)

0.300

0.350

0.400

0.450

0.500

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

LevelofRisk(LoR)

upper-bound lower-bound

Fig. 5. The relationship of a and LoR index of risk factor F1.



7/7

adjust the a-cut value to yield different LoRUm indexes to

facilitate risk monitoring for each risk factor.

Acknowledgements

The author would like to thank the National Science

Council of the Republic of China, Taiwan, for financiallysupporting this research under Contract no. NSC 95-2416-

H-408-001. Directors of the Safety Management Depart-

ment in the Taiwanese CAA and airports, airline safety

supervisors, academic professors and experts in the

research department and the Aviation Safety Council are

thanked for their assistance in problem formulation and

data collection.

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