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The Risk of Safety: An integration of psychological and mathematical approaches.

S.I. SUDDLE1 & P.H. WAARTS

2

1Delft University of Technology & Corsmit Consulting Engineers Rijswijk, The Netherlands

S.I. Suddle

Delft University of technology & Corsmit Consulting Engineers

Faculty of Civil Engineering and Geosciences

Division Structural and Building Engineering

Stevinweg 1

P.O. Box 5048

2600 GA Delft

The Netherlands

Phone +31 15 278 7755

Fax +31 15 2781560

Mobile +31 6 4240 3274

E-mail: S.I.Suddle@citg.tudelft.nl

2TNO, Delft, The Netherlands

P.H. Waarts

TNO Building & Construction Research

Civil Infrastructure department

P.O. Box 49

2600 AA Delft

The Netherlands

Phone +31 15 276 3231

Fax: +31 15 276 3018

Mobile: +31 6 53 304720

Email: P.Waarts@bouw.tno.nl

http://www.bouw.tno.nl

A paper for special issue of the journal Risk Decision and Policy (26/08/03)

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Abstract

Safety is nowadays one of the main items on the agenda during the planning, realisation and

management of most large-scale projects. In this paper relations between safety and risk are suggested.

In order to quantify the safety in objective terms, risk (analysis) is used as an important tool. However,

definitions of risk vary from global and informal to objective variants and consists both psychological

and mathematical elements (Vlek, (1990; 2001; 2002); Hypothese, (2001)). In this paper, both

psychological and mathematical risk definitions and their interrelation is described. An essential

element in risk assessment is risk evaluation. When a risk analysis is performed, it is important to

realise that decision making about risks is very complex and that not only technical aspects but also

economical, environmental, comfort related, political, psychological and societal acceptance play an

important role. Finally, a recommendation has been made for narrowing the gap between deterministic

and probabilistic approach by use of Bayesian Networks.

1 Introduction

Safety is a wide notion. Safety is defined as the state of being adequately protected against hurt or

injury, freedom from serious danger or hazard (Vrouwenvelder et al., (2001)). In the philosophy of

safety, safety is usually classified into social safety and physical safety (Durmisevic, (2002); Suddle,

(2002A); Voordt & Wegen, (1990)). Social safety implicates the behaviour among persons. Crime

incentive factors, spatial factors, institutional factors and social factors of an area are characteristics of

social safety (Durmisevic, (2002)). In contrast, physical safety contains both the probability of a

person being killed or injured by natural hazards, like bad weather, an earthquake, floods and the

probability by man-made hazards like traffic, calamities by transport of dangerous materials,

calamities by nuclear reactors etc. In some cases, like fire, it is difficult to classify the kind of safety.

A subdivision within physical safety is made by internal safety and external safety (see e.g. Vrijling et

al., (1998)). The following subdivision, here ranked according to increasing benefit to the persons at

risk is frequently found (Suddle, (2002G)):

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Safety

Social Safety Physical Safety

Natural & Man-made hazards

Crime incentive factors Spatial factors

Institutional factors Social factors

Internal

Users Passengers Personnel

External

Third parties

Figure 1: Subdivision of safety (Suddle, (2002G)).

2 Safety and Risk

2.1 Introduction

Generally, safety consists both of subjectivity and objectivity elements. A person who experiences that

he is safe from a psychological point of view, does not automatically implies he is safe from a

mathematical point of view and visa versa. The relation between subjectivity and objectivity

components of safety can be presented with aspects of behaviour (Bouma, (1982)):

Subjective Safe

Subjective Unsafe

Obj

ecti

ve

Saf

e Healthy unconcern

Unhealthy anxiety

Obj

ecti

ve

Uns

afe

Unhealthy unconcern

Healthy anxiety

Figure 2: Aspects of behaviour.

Subjective safety is related to psychological aspects (see also (Stoessel, (2001)), while objective safety

is based on mathematical grounds. Note that sometimes the objective safety is also based on subjective

estimates. To define and to quantify the objective elements of safety, it is vital to link safety with risk.

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The survey of Vlek, (1990) yielded 20 definitions of risk, which vary from global informal definitions

to objective variants. The 11 formal definitions of risk or riskiness, which can be distinguished from

those 20, are presented in table 1.

Table 1: Formal definitions of risk or riskiness (adapted from Vlek, (1990)).

Formal definitions of risk or riskiness

1. Probability of undesired consequence. 2. Seriousness of (maximum) possible undesired consequence. 3. Multi-attribute weighted sum of components of possible undesired consequence. 4. Probability x seriousness of undesired consequence (”expected loss”). 5. Probability-weighted sum of all possible undesired consequences (”average expected loss”). 6. Fitted function through graph of points relating probability to ext ent of undesired consequences. 7. Semivariance of possible undesired consequences about their average. 8. Variance of all possible undesired consequences about mean consequences. 9. Weighted sum of expected value and variance of all possible consequences. 10. Weighted combination of various parameters of the probability distribution of all possible consequences (encompasses 8 en 9). 11. Weight of possible undesired consequences (”loss”) relative to comparable possible desired consequences (”gain”).

This collection of risk definitions may be considered by viewing risk as the characterization of: (a) a

single possibility of accident, loss or disease (defs 1 - 4), (b) a collection of accident possibilities (defs

5 - 7), and (c) an activity having accident (and other) possibilities (defs 8 - 11) (Vlek, (1996)). The

definitions of table 1 are hardly related to social and psychological aspects. Still, the community

demands that engineers and designers take both social and psychological aspects into account when

doing and evaluating risk analysis.

2.2 Psychological definitions of risk

One of the first conceptual analyses of risk is carried out by Vlek, (1990). This analysis is based on

decision-making and empirical-psychological work on the nature and the dimensions of risks and

hazards. Examples of psychological (informal) definitions from Vlek, (1990) and Schaalsma et al.,

(1990) are ”lack of perceived controllability”, ”set of possible negative consequences” and ”fear of

loss”. From Vlek, (1990), it can be concluded that one has to consider the way people interpret risk in

risk management, also called risk perception.

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The interpretation is different for a single person and a group of persons (Gezondheidsraad, (1995;

1996)). The perception of risk differs by factors in relation with (Vlek, (1990; 1995; 2001; 2002)):

q The origin of the hazard

q The social context

q The personal remarks

It may be assumed that these aspects are related to the risk perception and aspects of subjective safety,

as presented in figure 2. According to Vlek, (1996) dimensions of underlying perceived riskiness,

which are related to risk perception, must be taken into account in risk management, as presented in

table 2:

Table 2: Basic dimensions underlying perceived riskiness (adapted from (Vlek, (1996)).

Basic dimensions underlying perceived riskiness

1. Potential degree of harm or fatality. 2. Physical extent of damage (area effected). 3. Social extent of damage (number of people involved). 4. Time distribution of damage (immediate and/or delayed effects). 5. Probability of undesired consequence. 6. Controllability (by self or trusted expert) of undesired consequences. 7. Experience with, familiarity, imaginability of consequences. 8. Voluntariness of exposure (freedom of choice). 9. Clarity, importance of expected benefits. 10. Social distribution of risks and benefits. 11. Harmful intentionality.

Note that these dimensions of underlying perceived riskiness consists mainly variants of both

subjectivity and objectivity (as presented in figure 2). Definitions 2, 4, 6, 7, 8 and 11 of table 2 are

characterised by the elements of subjectivity. While definitions 1, 3, 5, 9 and 10 consists objective

variants. Vlek, (1996) also suggests different scale -levels of risk and risk management, which amplify

the aspects of subjectivity. These psychological definitions, however, are basic ingredients for the

assessment of risk. Besides, these add value to the perception of risk and play a vital role in risk

acceptance and decision-making. Additionally, in Vlek, (1990), it is recommended to take additional

measures for the comfort of safety, especially for persons who feel themselves as unsafe, while

objectively it is safe. Moreover, it is recommended in the survey of Vlek, (1990) not only to comply

with the risk acceptance criteria, but also to apply the safest option regarding measures in accordance

with the budget of the project. Therefore in some conditions one may deliberate the costs and the

benefits of that project.

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Thus, according to Vlek, (1990; 1996) it may be concluded that (safety) measures are desired, and

must be explored in the risk management process to increase the subjective level of safety. However,

these argumentations are psychological and do not provide and sometimes do not need to the answer

to the question ”how much safe or unsafe is an activity or what is the effect of a safety measure in

accordance with safety and financial aspects”. In order to answer such question in objective terms and

to determine safety, there is a need for a quantifiable (mathematical) approach and not an informal

psychological. Besides, a mathematical approach enables to compare risk of different activities and

use the risk analysis as a basis for rational decision-making. It is therefore useful to quantify the

aspects of subjectivity of table 2 and to integrate in decision-making.

2.3 Mathematical definitions of risk

In essence, it can be assumed that safety, either internal or external, is complementary with the level of

risk (see e.g. Suddle, (2002A)) (see figure 3).

Figure 3: Model safety vs risk (Suddle, (2002A)).

This means to reach a low-risk level, one has to make investments for safety measures, while one may

expect both human and financial risks, such as casualties and loss of human live in accordance with a

minimum level of safety (high-risk level).

Sa

fety

Ris

k

Undesirable Situation -

Norm

Desirable Situation

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If the level of acceptability and tolerability of risk would be embedded correctly, the optimum level of

safety would have laid on the minimum of the sum of investments and expecting risks.

The common definition of risk (associated with a hazard) is a combination of the probability that

hazard will occur and the (usually negative) consequences of that hazard (Vrouwenvelder et al.,

(2001); Vrijling et al., (1998); Vrouwenvelder & Vrijling, (1997)). In essence, it comes down to the

following expression, which is the same definition as definition 4 of table 1:

ff CPR ⋅= (1) where:

R = risk [fatalities or money year-1];

Pf = probability of failure [year-1];

Cf = consequence of the unwanted event [fatalities or money].

This definition mostly is used in risk analysis. Consequences (Cf) to be taken into account include:

q Injury, or loss of life, due to structural collapse

q Reconstruction costs

q Loss of economic activity

q Environmental losses

Most of the time, there is a (reverse) relation between the probability that a hazard will occur and the

consequences of that hazard. More complicating still is the gradual unfolding of a host of differing

definitions of risk (see e.g. Coombs, (1972); Libby & Fishburn, (1977); Vlek & Stallen, (1980)).

According to Kaplan & Garrick, (1981), risk consists of three components:

q Scenario

q Probability of scenario

q Consequence of scenario

Following Kaplan & Garrick, (1981) risk cannot be properly expressed in terms of a single number or

even a single curve. In their view the best formal definition of risk is a probability distribution of

possible (future) frequencies of harmful consequences, which themselves may be multidimensional in

nature.

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2.4 Comparison of Psychological and Mathematical definitions

The description of risk given by Kaplan & Garrick, (1981) hardly differs from the mathematical one of

Vrijling & Vrouwenvelder, (1997), because both probability and consequence of scenario are

included. According to Kaplan & Garrick, (1981) one has to consider all hazards in account, which

can be accomplished by summing up all possible hazards (scenarios) with their consequences for an

activity. Therefore as an obvious extension, multiple scenarios (indexed i) may be taken into account.

This can be presented in the following formula:

∑=

⋅=1i

ff iiCPR (2)

According to Vrouwenvelder et al., (2001) probability is, generally speaking, the likelihood or degree

of certainty of a particular event occurring during a specified period of time. Assuming that a system

may be found in mutually exclusive situations Hi, and the failure F of the system (e.g. of the structure

or its element) given a particular situation Hi occurs with the conditional probability P(F | Hi), then the

total probability of failure Pf is given by the law of total probability as:

∑=

=1

)|()(i

iif HFPHPP (3)

Substitution of formula (3) in (2) gives:

)|()|()(1

FHCPHFPHPR ii

ii ∩= ∑=

(4)

where:

P(C| Hi ∩ F) = the probability of a consequence given that Hi and F occur.

Formulas (1), (2) and (4) are presented as mathematical variants. However, these are also mentioned in

the psychological dimensions of risk (see table 1). The three components of formula (4) correspond

with the definitions of risk as mentioned in table 1. Therefore, from an objective safety assessment

point of view one may consider that even psychological definitions from Vlek, (1990) are integrated

into mathematical definitions of Kaplan & Garrick, (1981) combined with Vrijling & Vrouwenvelder,

(1997). The psychological part of the mathematical definition emphasises particular the consequence

of a scenario. From a mathematical point of view, all possible consequences are taken into account in

risk analysis (see formula (2) and (4)).

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Besides, the subjective aspects with accordance with psychology, which are mostly related to the

acceptability of risk, are also integrated in acceptability and tolerability of risk in terms of

vulnerability and the direct benefit of a person. From a mathematical point of view, the acceptability

and tolerability of societal risk provides a tool in which it is common to accept less the probability of

an event consisting big numbers of fatalities. This concept of risk aversion is also included in these

risk acceptance criteria (also discussed by Vrijling & Gelder, (1997)).

In some cases, especially scenarios with great consequences, weighing factors for all risk dimensions

are used in order to make them comparable to each other and to relate them to the measures that must

be taken for possible risk reduction (Coombs, (1972); Libby & Fishburn, (1977); Vlek & Stallen,

(1980); Vlek, (1990); Vrouwenvelder et al., (2001). It is, therefore, recommendable to compare and to

integrate these definitions in one-dimensional weighted risk (Rw) e.g. in terms of money as following:

∑∑==

⋅=11 i

ffj

jw ijijCPR α (5)

∑∑==

=11 i

ijj

jw RR α (6)

where:

Rw = weighted risk [year-1];

αj = value per considered loss [-].

It has to be noted that weighted risk (Rw) may consist of cost unities, which can be financial, but it is

not necessary (see Seiler, (2000)). Formulas (5) and (6) can be specified into particular risk

components:

...1

,41

,31

,21

,1 ++++= ∑∑∑∑==== l

lqualityk

ktenvironmenj

jenonomici

ihumanw RRRRR αααα (7)

where:

α1 = value per casualty or injury [-];

α2 = value per environmental risk [-];

α3 = value per economical risk [-] (mostly α3 = 1);

α4 = value per quality risk [-], and so on…

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According to Lind, (1996) safety criterions are not absolute. Cost-utility is only a part of the

economic, social, cultural and political assessments that are required for responsible decision-making.

Note that some αj may also be negative (e.g. time). Besides, the αj is in particular correlated with the

consequences (Cf), in which the correlation is not necessary to be linear. (The first component (human

risk) of formulas (7) can be subdivided into:

∑∑∑===

=1

,1

11

,1n

nkhumank

ki

ihuman RR αα (8)

where:

α1k = value per considered basic dimensions of underlying perceived riskiness as presented

in table 2 [-].

So, α1k ∈ {α1,α2,…,α11} of table 2. These values α1,α2,…,α11 are functions of subjective aspects of

table 2 and can be determined by multi criteria analysis. If one could add one dimension to all aspects

e.g. monetary value, one can integrate all kind of subjective aspects into risk analysis, such as value

for area effected (α2), value for number of people involved (α3), value for time (α4), value for

voluntariness (α3, α8, α11), etc. If these subjective aspects are quantified in the proposed weighted risk

(analysis), and thus in one (monetary) dimension, safety measures can be balanced and optimised in

respect of decision-making as following:

Minimise: ∑= +

+=1

0 )1()(

jj

wj

totr

RyCC (9)

where:

Ctot = total costs [money];

C0(y) = the investment in a safety measure [money];

y = decision parameter;

j = the number of the year;

r = real rate of interest.

Hence, one may assume that for rational decision-making it is desired to objectify the safety in terms

of probability and the consequences of all events. Therefore, both mathematical and psychological

approaches of risk can and should be quantified by the mathematical variant.

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It may also be recommended that, for safety studies and risk analysis, risk can commonly be estimated

by the mathematical expectation of the consequences of an undesired event that often leads to the sum

of the product probability x consequences combined with the monetary value per considered loss, is an

interesting approach (formula (8) and (9)).

2.5 Value per casualty

Most decision makers prefer to treat the economic and human safety criteria completely separated. In

that case, the value of α = 0 (formula 15); this is the creation fully compatible to the approach of a

purely economic decision problem. Still, there are some decision makers who compare the advantage

of safety measures in comparison with economic investments. Having this in mind, it might be better

to assess some amount of money to the event for death or injury. For this purpose the amount for

material damage is increased with the monetary value per casualty multiplied by the expected number

of death (as presented in formula 15).

The monetary value per casualty depends on factors such as Willingness To Pay (WTP), Willingness

To Accept compensation (WTA), voluntariness, and responsibility as discussed by Jones-Lee &

Loomes, (1995). One may also perform a field research, in which a great number of people are

proposed to answer a questionnaire. By this, one may determine e.g. value of perceived controllability

or the value of a statistical life. According to the Environmental Protection Agency the value of a

citizen in the US is approximately € 5,600,000.=. It may be concluded from (@(1)), that these values

result in a wide range. According to Vrouwenvelder et al., (2001) a reasonable value seems €

1,000,000.=. Bleaij, (2003) analysed the value of a statistical life in road safety using stated preference

methodologies and empirical estimates for the Netherlands. Bleaij, (2003) concluded that the value of

a statistical life in such circumstances varies between € 1,900,000.= to € 11,400,000.=. An analysis of

the valuation of a human life is also discussed by Vrijling & Gelder, (2000). Another method to

determine this value is using the so called Life Quality Index (LQI) (see Lind, (1994)). The values per

casualty can be summarised in table 3.

Table 3: Investments in Risk Reduction, per nominal live saved (Source: University of East Anglia in 1998).

Theoretical Evaluations Value for αα [€ per person]

Human capital calculations 300,000 Willingness to pay (hypothetical) 1,600,000 Road Safety (UK, 1987) 500,000 Cost of medical procedures for comparison (real) 2,000 - 300,000

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According to Seiler, (2000), the monetary value per casualty or costs per live saved of a person

depends on the voluntariness of an activity (see table 4).

Table 4: Costs per live saved of a person depends on the voluntariness of an activity.

Voluntariness of an activity Individual Risk

[year-1] Costs per life

saved 1. Voluntary risk 10-3 € 1.500.000 2. High degree of self-determination, direct individual benefit (car driving)

10-4 € 6.000.000

3. Low degree of self-determination, individual benefit (working conditions)

5⋅10-5 € 15.000.000

4. Involuntary, imposed risk exposition, no direct benefit (local resistance of dangerous installation)

10-5 € 20.000.000

So, one may conclude that there are different approaches for determining and therefore different

monetary values per life.

3 Risk assessment

3.1 Risk management process

The risk assessment of a system consists of the use of all available information to estimate the risk to

individuals or populations, property or the environment, from identified hazards, the comparison with

targets and the search for optimal solutions (Vrouwenvelder et al., (2001)). From a technical point of

view the extent of the risks and the effects of risk reducing measures can be quantified in a

quantitative risk assessment (QRA). It is therefore that the QRA can provide a basis for the rational

decision-making about risks (Bedford & Cooke, (2001)). A Risk analysis in generally contains the

following steps (Vrouwenvelder et al., (2001); Vrijling & Vrouwenvelder, (1997)):

q Scope definition

q Hazard identification

q Modelling of hazard scenarios

q Estimation of consequences

q Estimation of probabilities

q Estimation of risks

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The place of the risk analysis in the risk management process is illustrated in figure 4 (see e.g. Høj &

Kröger, (2002)). The first three steps of the risk analysis are the qualitative part, the last three steps

risk analysis are the quantitative part. In many cases only the qualitative part is carried out and

measures are taken on an intuitive basis. Although not complete, such an analysis is certainly not

without value. Better however is to include the last three steps and perform a full quantitative risk

analysis. In this complex decision making process a clear identification of the risks and the effects of

risk reducing measures is very useful (Vrouwenvelder et al., (2001)).

Figure 4: Risk management process (Høj & Kröger, (2002)).

Part of safety management and risk control

Risk assessment

QualitativeRisk analysis

Risk analysis

QuantitativeRisk analysis

Risk estimation

Scope definition

Hazard identification

Frequency analysis

Scenario development

Consequence analysis

Risk picture

Risk evaluation

Additional risk reducing measures

Acceptable criteria

Risk red. measures

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3.2 Risk evaluation

When a risk analysis is performed, it is also important to realize that decision making about risks is

very complex and that not only technical aspects but also political, psychological and societal

processes (all) play an important role (Suddle, (2002A); Jonkman et al., (2002)). If a risk analysis is

carried out for only the qualitative part, the psychological and political aspects play a major role in risk

acceptance and decision-making. Contrarily, when risk analysis is carried out till the quantitative part,

limits for risk acceptance and economical criteria are considered for decision-making. The risk

acceptance criteria will be discussed in paragraph 3.4. Additionally, regarding safety management and

control, one has to take measures regarding safety for persons who feel themselves as unsafe, while

objective it is safe. This is exactly Vlek, (1990; 2002)) argued for the comfort of safety for all kind of

people. If one would use the proposed methodology of weighted risk, as explained in 2.4, then the

different between the qualitative and quantitative part of the risk analysis vanish.

Figure 5: Risk analysis and risk acceptance (Suddle, (2002A)).

4 Approaches for risk assessment

4.1 Deterministic and probabilistic approach

During the 1950s and 1960s two approaches emerged for analysing safety aspects of potentially

hazardous systems, including a deterministic approach and a probabilistic approach (see e.g. Weaver,

(1980) or Rosmuller, (2001)). The most significant difference between the two approaches is the way

probability is dealt with (Vrijling & Stoop, (1999)). Deterministic safety analysis is focused on the

causal processes of accident scenarios equals 1. Whereas probabilistic risk analysis takes into account

the possibility and the likelihood of uncertainty that accident scenarios might occur.

Hazard Identification (qualitative)

Risk estimation (qualitative)

Risk evaluation

Psychology Politics

Limits for risk acceptance Economic criteria

Risk acceptance

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As a result, in deterministic analysis the focus is on developing insights into accident scenarios and

consequences, whereas in probabilistic risk analysis main efforts are made on the behalf of the

quantification of probabilities (see e.g. Hale, (2000); Rosmuller, (2001)). Thus, one may assume there

is an existing gap between the probabilistic and deterministic methods in risk analysis. If a risk

analysis is performed with present models such as fault trees and event trees, this gap will not be

narrowed because of large dimensions and big complexity of such models. Nevertheless, the following

paragraphs is an introduction to the theory, which shows that the existing gap can be narrowed by use

of Bayesian Networks in risk analysis (see Suddle, (2001A)).

4.2 Use of Bayesian Networks

A Bayesian Network is a graphical tool that represents the relations between a set of variables and a

set of directed edges between variables (Hansen, (1999); Jensen, (1996; 2001)), which can be divided

into events and consequences. The major advantage of Bayesian Networks is that these networks can

replace and compact both traditional fault trees and event trees in one model (Bobbio et al., (2001)).

Thus, these networks provide an effective tool, particularly for enormous risk analysis. According to

Friis-Hansen, (2000) the potential of Bayesian Networks are an intuitive modelling tool, partly based

on artificial intelligence that adds transparency and consistency to the models. Normally, the relation

between fault trees and event trees are represented in the Bowtie model, which will expand

exponentially in case of the relations between the events will increases (Ale, (2002); Oh, (2001)). This

can now be replaced into a single compatible Bayesian Network, which grows linear, as illustrated in

figure 6 (Suddle & Waarts, (2003)).

A Bayesian network consists of a set of nodes and a set of directed arrows. Each node represents a

probability distribution, which may in principle be continuous or discrete. Arcs indicate conditional

probabilistic dependence so that the probability of a dependent variable being in a particular state is

given for each combination of the states of the receding variables. The dependence structure is thus

represented by a set of conditional probability distributions. A variable, which is dependent on other

variables, is often referred to as a child node.

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Figure 6: The size of a Bayesian Network is smaller than the traditional fault trees. Hence, a Bayesian

Network is much compacter (Suddle & Waarts, (2003)).

Likewise, directly preceding variables are called parents. Nodes, which have no parents, are called

root nodes and nodes without children are leaf nodes. Bayesian networks are sometimes referred to as

directed acyclic graphs (DAGs), indicating that loops (or cycles) are not allowed. A Bayesian network

is a representation of the joint probability distribution of the entire variable domain U =

{X1,X2,…,Xn}.This is seen by applying the chain rule to factorisation of the joint distribution into a

chain of conditional probability distributions (Friis-Hansen, (2000)):

),...,,()( 21 nXXXPUP = (10)

)(),...,|(),...,|( 3221 nnn XPXXXPXXXP ⋅⋅⋅= (11)

∏=i

ii XpaXP ))(|( (12)

where P(X1,…,Xn) is the joint distribution of X1 to Xn and P(X1 | X2,…,Xn) is the conditional

distribution of X1 given X2,⋅⋅⋅,Xn. The notation pa(Xi) means the set of parent variables of the variable

Xi. From the updated joint table the marginal distributions of each individual variable may be found by

summation over all other variables. This is desired for calculating risk for all scenarios. This is known

as sum-marginalisation:

∑ ∏∑ ==}\{}\{

))(|()()(ii XU i

iiXU

iXpaXPUPXP (13)

Size

Relations

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So, if the undesired events (Hi), failure modes (F), consequences (C), safety measures (M) and risk (R)

are elements of the entire variable domain U = {X1,X2,…,Xn}, than every risk analysis with Bayesian

Networks is possible.

},...,,{,,,,, 21 ni XXXRSCMFH ∈ (14)

These safety measures may include the rescue availability or functional design, which are

characteristic for deterministic risk analysis. These measures may also consist structural measures,

which are characteristic for probabilistic risk analysis. Besides, integration of these measures is a vital

issue from the psychological point of view, as mentioned in section 2.4. This concept provides the

methodology for quantifying the effectiveness of safety measures regarding risk, which is desired from

a mathematical point of view. A standard Bayesian Network corresponding with a standard risk

analysis for basic events may be expressed as:

Figure 7: A standard Bayesian Network for risk analysis.

Considering the previous, it may be assumed that the Bayesian Networks are not only an effective tool

for narrowing the gap between the probabilistic and deterministic risk analysis, but Bayesian Networks

are useful for combining psychological and mathematical approaches towards risk (analysis). The use

of such an approach is illustrated in Suddle, (2003B).

5 Conclusions

This paper clearly presented that performing both safety and risk assessment are characterised by

many aspects, which should be to taken into account. First of all, it is recommendable to observe both

components - psychological and mathematical definitions of risk - in safety assessment studies.

Event

M

H

F

C R

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It is common to objectify the safety in terms of risk with mathematical approaches (the sum of

probability x consequences). However, one should also realise that psychological definitions should be

considered in decision-making and the risk management process. In this chapter, a model has been

presented in which the combination of both psychological and mathematical definitions of risk are

integrated. That model enables a general approach for optimising the effectiveness of safety measures

in which subjective aspects, based on psychological definitions of risk, could be quantified as well.

This approach is based on presenting a weighted risk Rw in one dimension (e.g. money) in which all

kind of benefits and losses can be taken into account, such as human, economical, environmental and

quality risks etc. For this, it is essential to quantify those risks in one dimension. Hence, one can

accomplish all risks in one (monetary) dimension including psychological aspects.

An effective tool, which provides to integrate both mathematical and psychological definitions are

Bayesian Networks. These networks provide transparency and consistency to the risk analysis and are

useful to both probabilistic and deterministic risk analysis and to combine both mathematical and

psychological definitions of risk in a risk management process.

6 References

ALE, (2002)

Ale, B.J.M., Risk assessment practices in The Netherlands, Safety Science, Volume 40, Issues

1-4, February-June 2002, pp. 105 - 126.

Bedford & Cooke, (2001)

Bedford, T., Cooke, R.M.; Probabilistic Risk Analysis: Foundations and methods; Cambridge

University Press, 2001.

BLEAIJ, (2003)

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