Kristiansen Svein. Maritime Transportation: Safety Management and Risk Analysis
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course involve its monetary price but may also involve, for example, poor quality, he alth
hazards, effect on the environment, etc. It is important to bear this in mind when
performing all kinds of cost-benefit analyses (CBAs), as it may be difficult to examine all
costs and benefits on a common scale.
This chapter will, as mentioned above, focus primarily on CBA in the context of safety
and risk assessment. The first section of this chapter presents some basic theory that it
is necessary to be aware of before performing CBAs in a risk assessment context. This
involves a brief introduction to the ALARP (¼ as low as reasonably practicable) principle,
the concept of risk aversion, as well as some very basic economic and cost-optimization
theory that enables us to calculate monetary costs and benefits. The second section of
this chapter looks closer at CBA in a risk assessment context. The main princi ples and
a general approach to such a CBA are presented together with some useful cost-benefit
analysis methodologies. The third part of this chapter looks at some alternative problem-
solving approaches to CBA, predominantly methods involv ing ranking of different
concepts. Finally, a CBA example analysing design spill prevention measures for tankers
is presented.
9. 2 BASIC THEORY
9.2.1 The A LARP Pri nc ip le
When applying cost-benefit analys is (CBA) concepts in a risk assessment context, a major
challenge is to find an appropriate balance between costs and risk. The UK Health
and Safety Executive (HSE, 1992), which is the United Kingdom’s governmental safety
department, developed the so-called ALARP principle (or concept) to provide some
guidance on finding such an appropriate balance. ALARP is an abbreviation for ‘as low
as reasonably practicable’, and the main principle is that the risks related to a system
regarding possible damage to life, property and the environment should be reduced to a
level that is as low as reasonably practicable (i.e. ALARP). For example, if the risk
reduction achieve d by implementing particular safety measures is insignificant compared
with the costs of these proposed measures, meaning that there is a gross imbalance
between the risk reduction and the related costs, it would not be reasonably practicable to
implement them. On the other hand, if a significant risk reduction can be achieved for an
acceptable cost, meaning that ‘low-priced’ safety may be gained, it would be reasonably
practicable to implement the risk-reducing measures. Hence, the ALARP principle
states that a safety (or risk-reducing) measure should be implemented unless it can be
demonstrated that the costs of implementing the safety measure are grossly dispropor-
tionate to the expected safety improvements (i.e. benefits).
The ALARP principle can be illustrated by Figure 9.1. The application of the principle
is based on the evaluation of risk. Through the use of a risk acceptance criterion the risks
of specific hazards, or the total risk of the system under consideration, can be regarded as
intolerable, tolerable or negligible. Intolerable risks are by definition unacceptable and
must be made tolerable through the implementation of safety measures. The ALARP
principle states that risks in the tolerable risk region can only be accepted if they are made
as low as reasonably practicable using risk reduction measures. For risks in the negligible
246 CHAPTER 9 COST -BENE FIT ANALYS IS
risk region, there is no need to demonstrate ALARP. Risk reduction using the ALARP
principle is illustrated in Figure 9.2.
The ALARP risk region (see Figure 9.1) is dependent on what is exposed to the
hazards (and their corresponding risks) under consideration. If people are exposed, the
level where costs are grossly disproportionate to the achieved safety improvements is
extremely low , as serious injuries and fatalities are regarded as unacceptable. Depending
Figure 9.1 . The ALARP principle.
Figur e 9.2. Risk reduction using the ALARP principle.
9. 2 B A S I C T HE ORY 247
on the system under consideration, the ALARP regions for damage to the environment
and property may be defined differently. For physical assets and equipment (i.e. property)
net present value calculations may, for example, be used to establish the ALARP region.
It can be argued that the ALARP principle is too vague as it could possibly be
interpreted in many different ways. What should be considered as reasonably practicable
will always be a matter of discussion. A major benefit of the principle is that it can be
easily adapted to individual situations and different contexts for application in a wide
range of ind ustries.
9.2.2 Risk Aversion
The concept of risk aversion is important to understand in terms of applying cost-benefit
analysis (CBA ) in the context of risk. Briefly explain ed, risk aversion is the tendency for
people (e.g. managers, consumers, decision-makers, etc.) to avoid undertaking risks and
to choose less risky alternatives. Risk aversion can be illustrated by an example related to
gambling.
Consider a bet/gamble that has only two possible outcomes with equal probability.
Given a bet of USD 100, there is a 50% probability of winning USD 200 and a 50%
probability of losing the bet and all the money. This bet may be illustrated by Figure 9.3.
Although the expected value of the bet is USD 100, as calculated in Figure 9.3 below,
experiments show that most people are willing to bet only about half of this, i.e.
approximately USD 50. The difference between what people are willing to bet and the
expected value of the bet is a measure of risk aversion. Since USD 100 is quite a lot of
money for most people, the risk of losing that amount is perceived as too large to offset
the possible benefits of winning USD 200. The grade of risk aversion does, however, vary
with social and psychological factors.
People’s risk aversion can be recognized in relation to many different activities. For
example, risk aversion is the underlying principle of insurance. Most people are willing to
pay a fixe d small and acceptable amount of money to be secured (or insured) against the
probable loss of a large and unacceptable amount of money. Insurance companies secure
their customers against large losses or costs that may be the result of accidents or other
undesirable events/situations by receiving regular payments from them. This payment
is calculated on the basis of the estimated risk, which involves both the probability of
the undesirable event and the consequence (i.e. the possibl e insurance payment), and a risk
premium that compensates for the insurance offered to the customers. It is this risk
Figure 9.3. A bet of two possible outcomes with equal probability.
24 8 CHAPTER 9 COST -BENE FIT ANALYS IS
premium that makes it possible for the insurance companies to earn money in the long
term. Risk aversion is also evident in business investment projects. Where an investment
project risks making a loss that is so large as to endanger the existence of the company in
question, the managers of that company would normally act with great risk aversion and
thus require a large premium to induce them to take the risk.
The characteristics of risk aversion described above have an analogous relation in risk
analysis. As was seen in the previous chapter, the risk (R) is normally defined as the
product of the probability (P) of an event and its expected consequence (C):
R ¼ C P ð9:1Þ
Based on this equation, the following three alternatives are of equal risk:
. 1 fatality per year (R ¼ C P ¼ 1 1 ¼ 1).
. 10% probability (per year) of an accident resulting in 10 fatalities
(R ¼ C P ¼ 10 0.10 ¼ 1).
. 1% probability (per year) of an accident resulting in 100 fatalities
(R ¼ C P ¼ 100 0.01 ¼ 1).
In reality, however, this is not the case. Based on our knowledge of people’s risk
aversion, it can be shown that the perceived consequence is larger than the calculated
risk expresses. This situation can be illustrated by Figure 9.4, in which the perceived
consequence is sketched as a function of the num ber of fatalities. The more severe the
objective (or real) consequence is, the farther the perceived consequence moves away from
the linear risk relationship, which is due to people’s risk aversion.
Based on the relationship between the perceived and objective consequence shown in
Figure 9.4, the basic risk equation (i.e. R ¼C P) has to be modified. The risk equation
should include the perceived consequence instead of the objective consequence because
Figur e 9.4. Perceived consequence as a function of the number of fatalities.
9. 2 B A S I C T HE ORY 249
this would more correctly reflect the willingness to pay for risk reduction. The perceived
consequence C
P
can, for example, be expressed as a function of the objectively calculated
consequence C
O
:
C
P
¼ fðC
O
Þð9:2Þ
where C
P
¼perceived consequence and C
O
¼objectively calculated consequence. This
modification implies that the curve for constant risk has to be modified to fit the perceived
consequence, as shown in Figure 9.4. Such a modification is shown in Figure 9.5. The
constant risk curve based on perceived consequences is, as expected, steeper than the
constant objective risk curve.
9. 2 . 3 Economic Th e or y
In relation to cost-benefit analyses it is important to study monetary costs and benefits on
a common scale. There may also be non-monetary costs and benefits involved in a CBA,
but in this part of the chapter we are not concerned with these. Both costs and benefits
may aris e at different points in time, and because the value of money changes over time
due to inflation and ‘time value of money’ factors, one must be able to calculate the value
of all monetary costs and benefits at one specific point in time. In order to calculate the
value of a present amount P at some future point in time, the following simple equation
can be used:
F ¼ P ð1 þ iÞ
n
ð9:3Þ
where:
P ¼ Present monetary amount (currency)
F ¼ The value of P after n years/periods (currency)
Figure 9.5. Constant risk curves for perceived and objective risk.
250 CHAPTER 9 COST -BEN EFIT ANALYS IS
i ¼ Rate of interest per year/period (corrected for inflation) given as a decimal
fraction (e.g. 5% ¼0.05)
n ¼ Number of years/periods
With the use of Eq. (9.3) the value of a present amount some time in the future can be
calculated. To perform the opposite calcul ation, i.e. to calculate the present value P of a
future amount F, the following equation can be directly deducted from Eq. (9.3).
P ¼
F
ð1 þ iÞ
n
¼ F ð1 þ iÞ
n
ð9:4Þ
where:
P ¼ Present value (currency)
F ¼ Future amount that is incurred n years/periods into the future (currency)
i ¼ Rate of interest per year/period (corrected for inflation) given as a decimal
fraction (e.g. 5% ¼0.05)
n ¼ Number of years/periods before the future amount F is incurred
If a chain of n equal future amounts F are incurred at regular intervals (e.g. inspection
costs, maintenance costs, loan payments, etc.), and the rate of interest i for those intervals
can be assumed as constant, it can be shown that the present value P of this chain of future
amounts F is as follows:
P ¼ F
ð1 þ iÞ
n
1
i ð1 þ iÞ
n
¼
X
n
i¼1
F ð1 þ iÞ
n
ð9:5Þ
These equations are simp le but very important tools in relation to CBA.
9. 2 .4 Co st Optimiz ation
Safety measures are implemented into a system in order to improve its safety by reducing
the inherent risks. Through such measures future undesirable events are made less likely,
less severe, or a combination of the two. The costs involved in implement ing safety
measures may as such be understood as preventive costs, i.e. costs related to preventing
danger to people, property and the environment. Safety can be improved through the use
of a wide range of measures such as physical safety equipment/systems, organizational
safety programmes, improved operating procedures, etc., and preventive costs would
therefore typically include:
. Costs related to the design and development of safety measures/programmes
. Cost of equipment and installation
. Costs related to the inspection and maintenance of safety equipment in all its life
. Staff operating costs
. Training costs
9. 2 B A S I C T HE ORY 251
. Enforcement costs
. Inspection and auditing costs
. Administration costs, etc.
On the other hand, the implementation of safety measures also results in benefits
of reduced cost of losses related to the economic consequences that are more likely to be
avoided because of reduced risks. In a maritime context, typical cost of losses includes:
. Total loss of ship, additional costs of getting a new vessel into operation
. Degraded operability/operation resulting in unscheduled delays
. Loss of future income (due to total loss or ineffective operation)
. Repair costs
. Fines and penalties
. Compensation to third parties
. Negative publicity (may be difficult to quantify), etc.
Based on the above discussion, a pure economic exercise can be performed to establish
the optimal level of preventive safety measures that should be implemented. This can be
done by studying the total safety cost, being the sum of preventive costs and cost of losses,
and finding where this total cost is at its lowest. Such a cost optimization is illustrated in
Figure 9.6. For this to be valid it must be possible to directly value the costs and benefits of
safety measures in economic terms. In practice the economic consequences of accidents
have a dominant position, but as mentioned earlier other factors may be taken into
consideration as well.
The cost curves for preventive costs (C
P
) and cost of losses (C
L
) in Figure 9.6 are
symmetrical. This does not, however, have to be the case, and the curves will generally
vary greatly depending on the type of system under consideration.
In this section we have focused on establishing the cost-optimal safety level, but the
type of cost optimization illustrated by Figure 9.6 has many applications, e.g. in terms of
Figure 9.6. Optimal implementation of safety measures.
252 CHAPTER 9 COST -BENE FIT ANALYS IS
establishing an eco nomically optimal level of preventive maintenance. Cost optimization
can be a very useful tool in relation to cost-benefit analysis. Below some results from a risk
assessment study of bridges with respect to ship collisions are presented (Sexsmith, 1983).
This case shows how basic mathematical theory can be used to perform simple cost-benefit
analyses.
Exam p le
Problem
A bridge designer is to establish the optimal energy capacity of a bridge design that is
exposed to ship traffic (Sexsmith, 1983). The energy capacity in 10
6
joule (MJ) denotes the
energy that the bridge can absorb without collapsing. That is, if the impact energy from a
ship colliding with the bridge is larger than the bridge’s energy capacity, the bridge will
experience catastrophic collapse. Increas ing the energy capacity of the bridge requires the
implementation of protective measures that come at a considerable cost. Table 9.1 gives
information about the different bridge design alternatives.
There is also an assumed loss of USD 2 10
8
in the event of catastrophic collapse,
including both the economic losses associated with the bridge structure and losses that
occur as a result of loss of use of the bridge. The real rate of interest (i) is assumed to be
3% ¼0.03 (per year).
Develop a mathematical model that enables the calculation of the most cost-optimal
bridge concept of the three presented in Table 9.1.
Solution
Assuming that a loss C
f
will occur at a definite time in the future, the present value of
this loss can be expressed as follows:
C
0
¼ C
f
e
it
ð9:6Þ
where:
C
0
¼ The present value of the future loss
C
f
¼ The future loss in present monetary units (not inflated)
Ta b l e 9. 1 . Crucial bridge design parameters and cost of protective measures (C
C
)
Bridge energy
capacity (MJ)
Return period
for exceedence
T (years)
Annual rate
of exceedence
¼1/T (–)
C
C
(USD)
Concept 1 800 500 0.002 3.0 10
6
Concept 2 1000 1000 0.001 6.0 10
6
Concept 3 5000 5000 0.0002 12.0 10
6
Source: Sexsmith (1983).
9. 2 B A S I C T HE ORY 253
i ¼ The real interest rate (excluding inflation)
t ¼ The time to the future loss
When the time to occurrence of the loss is a random variable (i.e. loss is stochastically
distributed), the present expected value of the future loss (i.e. C
0
) can be expressed as
follows:
C
0
¼ EðC
f
e
it
Þ
C
0
¼ C
f
Z
T
0
e
it
fðtÞdt
ð9:7Þ
where:
E() ¼ The expected value function
f(t) ¼ The probability density function for the time t (i.e. the time to occurrence of
catastrophic collapse)
Ship collisions with bridges are rare and independent random events in time. The events
can therefore be considered as Poisson events, and the time to first occurrence is therefore
exponentially distributed:
fðtÞ¼ e
t
ð9:8Þ
where:
¼ Annual rate of exceedence of bridge energy capacity
t ¼ The time to the future loss
It then follows that the present value of the loss can be expressed as follows:
C
0
¼ C
f
Z
T
0
e
it
e
t
dt
C
0
¼
C
f
i þ
ð9:9Þ
Equation (9.9) can be implemented into a CBA to establish the optimum total cost
consisting of the cost of loss (C
0
) and the cost of protective measures (C
C
), both costs that
will depend upon the concept selected:
Total cost C
T
¼C
0
þC
C
By increasing the implementa tion of safety measures, the exceeding of the bridge’s
energy capacity will statistically happen more seldom, resulting in decreasing cost of
254 CHAPTER 9 COST -BEN EFIT ANALYS IS
losses, while the cost of the preventive measures increases. The total co st (C
T
) for the three
design concepts is calculated in Table 9.2. Here C
0
, i.e. the present value of future loss of
the bridge, is calculated using Eq. (9.9) with C
f
¼USD 2 10
8
and i ¼3% ¼0.03.
Based on the developed model, the secon d concep t is the most cost-optimal of the three
concepts, resulting in an energy capacity of 1000 MJ for the bridge. However, it must be
recognized that such a model is quite crude and very sensitive to the assumed parameters.
9. 3 CBA IN A RISK ASSES SMENT CONTEXT
9. 3.1 Principle
As briefly mentioned in the introduction to this chapter, the implementation of safety
measures directed at reducing the risks of severe accidents related to a system unavoidably
incurs costs. However, there are also benefits related to improved safety, predominantly
the reduced cost of losses. In this context there are two dominant views on cost-benefit
analysis (CBA), which are both described below.
The first view on CBA recognizes that for all systems there will be an economic limit to
how much can be spent on safety measures before the system (e.g. an oil tanker) becomes
uneconomic or uncompetitive, and there will therefore always be a trade-off between
the costs of implementing safety measures and the residual risk level. In this context the
challenge will be to achieve the best possibl e safety level within given economic limits.
The second view on CBA is based on weighing the costs of implementing a safety
measure against the benefits gained through this implementation with the objective of
implementing cost-effective measures. Cost optimization can be a useful tool in this regard
as it also enables us to estimate the optimal amount to spend on preventive (i.e. safety)
measures and the economic break-even point for such measures.
Both views on CBA are important. However, given the very competitive business
environment in shipping and the fact that maritime acti vities happen within a relatively
strict safety regime of prescriptive regulations/requirements, only cost-effective safety
measures will normally be implemented. In a risk assessment context this favours the
second view on CBA, in which the main principle is to find safety measures that cost-
effectively reduce risk. With regard to risk reduction one often has several different
possible safety measures to choose from, and CBA enables us to identify for implemen-
tation those that are cost-effective.
Ta b l e 9. 2 . Calculation of total cost
Bridge energy
capacity (MJ)
Return period
for exceedence
T (years)
Annual rate
of exceedence
¼1/T (–)
C
C
(USD)
C
0
(USD)
C
T
¼C
C
þC
0
(USD)
Concept 1 800 500 0.002 3.0 10
6
12.5 10
6
15.5 10
6
Concept 2 1000 1000 0.001 6.0 10
6
6.5 10
6
12.5 10
6
Concept 3 5000 5000 0.0002 12.0 10
6
1.3 10
6
13.3 10
6
9.3 CBA IN A RISK ASSESSMENT CONTEXT 255