International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 4

Number 1

March 2010

1 INTRODUCTION

The Gulf of Finland is a sensitive geographical area.

The Baltic Sea, including the Gulf of Finland, has

been categorized as a Particularly Sensitive Sea Area

(PSSA) by the International Maritime Organization

(IMO, 2005). Maritime traffic is continuously in-

creasing in the Gulf of Finland. Especially the in-

creasing number of oil tankers is raising concern in

the coastal countries. Russia is building new oil ter-

minals, and the annual oil transports via the Gulf of

Finland are estimated to increase even up to 250 mil-

lions of tons by 2015 (Finnish Environment Institute

2007). The increasing maritime traffic increases the

risks of accidents, which could lead to oil spills. An

oil disaster would most probably have serious effects

on the Gulf of Finland ecosystem (Ihaksi et al.

2007).

Based on maritime accident statistics, groundings

and collisions are the dominant accident types in the

Gulf of Finland (Kujala et al. 2009). A commonly

applied approach for estimating the probability of

collisions or groundings in maritime traffic was de-

fined by Fujii et al. (1971, 1974) and Macduff

(1974). In this approach, the number of ships that

would collide or run aground, if no evasive manoeu-

vres are made is calculated first. In the calculations

it is assumed that the ships are sailing “blindly” in

the waterway. This so-called number of collision

candidates depends on the properties of ship traffic

such as geometric traffic distribution on the studied

waterway and ship sizes and speeds. In order to es-

timate the potential number of collisions or ground-

ings, the number of collision candidates is then mul-

tiplied by the probability of not making evasive ma-

noeuvres, so-called causation probability, which is

conditional on the blind navigation assumption. The

causation probability thus quantifies the proportion

of cases when an accident candidate ends up ground-

ing or colliding with another vessel. This approach

for estimating the potential number of collisions or

groundings can be expressed as

PNP ×=

(1)

where N

= the number of collision or grounding

candidates; and P

= causation probability, i.e. the

probability of not making evasive manoeuvres.

Not making an evasive manoeuvre while being on

a collision or grounding course can be a result of a

technical failure such as failure of steering system or

propulsion machinery, human failure, or environ-

mental factors. Technical failure was reported as the

primary reason of the accident in 9.4 % of collision

and grounding accidents in the Gulf of Finland, and

in 25 % of the cases the primary reason had been

conditions outside the vessel (Kujala et al. 2009).

Human failure has been commonly stated as the

most typical cause group of marine traffic accidents:

different studies have shown that 43 % - 96 % of the

accidents had been caused by humans (Grabowski et

al. 2000, Hetherington 2006, Rothblum 2006, Kujala

et al. 2009).

Causation probability values for crossing encoun-

ters in the literature have varied between 6.83 ∙ 10

-5

The Effects of Causation Probability on the

Ship Collision Statistics in the Gulf of Finland

M. Hanninen & P. Kujala

Helsinki University of Technology, Helsinki, Finland

ABSTRACT: In this study the marine traffic safety in the Gulf of Finland is studied by examining the colli-

sion probability estimates in a heavily used crossing area. In a commonly applied approach for estimating the

probability of collision accidents, so-called number of collision candidates is multiplied with a so-called cau-

sation probability. In this study a Bayesian network model for the causation probability estimation is applied

with different parameter values in order to examine the effects of weather and human factors on collision

probability in the crossing of Helsinki-Tallinn traffic and vessels navigating east- or westbound. The results

show that the probability of collisions is very sensitive to the causation probability value and it should be

modelled with great care to obtain reliable results.

– 6.00 ∙ 10

-4

(Macduff 1974, Fujii 1983, Fowler &

Sørgård 2000, Otto et al. 2002, Rosqvist et al. 2002).

The values have been either general values on some

sea area, or reflecting certain ship types or condi-

tions. In good visibility within VTS zone, Fowler &

Sørgård (2000) estimated a causation probability of

6.83 ∙ 10

-5

, and in poor visibility the value was 4.64 ∙

-4

. For collisions in the Gulf of Finland within

VTS zone where at least one of the colliding vessels

was a tanker, Rosqvist et al. (2002) estimated the

value to be 5.1 – 6.0 ∙ 10

-4

, depending on the other

ship type.

In the earliest collision probability estimations the

causation probability was estimated based on differ-

ence between the registered number of accidents and

the estimated number of collision candidates (Fujii

1971, 1974; Macduff 1974). Applying a causation

probability value derived from a study in another sea

area or estimating it based on the difference in acci-

dent statistics and geometrical probability may save

some effort, but then the actual elements in accident

causation are not addressed at all, as opposed to con-

structing a model for the estimation. Getting a nu-

merical value for the probability of not making an

evasive manoeuvre is only one outcome of a model,

the acquired model structure itself and the depend-

encies of the parameters may be at least equally im-

portant.

Risk analysis tools such as fault tree analysis

have been used in modelling the causation probabil-

ity (e.g., Pedersen 1995). In 2006, utilization of

Bayesian networks in Step 3 of the Formal Safety

Assessment was suggested in a document submitted

by the Japanese agency for maritime safety to the

IMO Maritime Safety Committee (2006). Bayesian

networks are directed acyclic graphs that consist of

nodes representing variables and arcs representing

the dependencies between variables (e.g. Jensen

2007). Each variable has a finite set of mutually ex-

clusive states. For each variable A with parent nodes

,…, B

there exist a conditional probability table

P(A | B

, …, B

). If variable A has no parents it is

linked to unconditional probability P(A). For identi-

fying the relevant nodes and the dependencies be-

tween nodes, and constructing the node probability

tables, both hard data and expert opinions can be

used and mixed. Bayesian networks can also be used

as an aid in decision-making under uncertainty.

Bayesian networks have been applied in causation

probability estimation such as in the maritime traffic

risk assessment software GRACAT (Friis-Hansen &

Simonsen, 2002) and in Øresund sound risk assess-

ment (Rambøll, 2006).

The study described in this paper is a part of a

cross-disciplinary approach for minimising the risks

of maritime transport in the Gulf of Finland, where,

based on growth predictions, the maritime traffic in

the Gulf of Finland in the year 2015 is modelled and

the accident risk, the direct environmental effects

and the risk of environmental accidents are evaluat-

ed, and the effects of national and international leg-

islation and other management actions are modelled

(Klemola et al. 2008). In the previous work ship col-

lision probabilities for two locations in the Gulf of

Finland were estimated by applying causation prob-

ability values derived from literature (Kujala et al.

2009). This paper describes the application of a

Bayesian network model for the causation probabil-

ity modelling as a part of collision probability esti-

mation for the traffic in a crossing area in the Gulf of

Finland. The network is utilized for studying the ef-

fects of weather, human factors, and extra vigilance

on the collision probability.

Figure 1. The studied crossing area between Helsinki and Tallinn marked in grey on the map.

2 STUDIED AREA: CROSSING BETWEEN

HELSINKI AND TALLINN

The studied location (Fig. 1) is one of the highly

trafficked crossings of waterways in the Gulf of Fin-

land. In this area the vessel traffic between Helsinki

and Tallinn is crossing the main route of the Gulf of

Finland, i.e. vessels heading to and from Russia and

eastern ports of Finland. Based on AIS records, in

July 2006 there had been 2122 ships navigating

north- or southbound, majority being fast ferries or

passenger ships, and 2303 ships heading to and from

eastern part of Gulf of Finland in July 2006 (Kujala

et al. 2009). According to accident statistics, one

collision of ships had been reported to occur in the

area during six year period (Kujala et al. 2009).

3 MODEL USED FOR GEOMETRIC

PROBABILITY

The number of collision candidates in the studied ar-

ea during one summer month was estimated with a

model presented by Pedersen (1995), which fol-

lowed the concept introduced by Fujii (1971). The

number of collision candidates in a time period was

calculated as

tdADV

zfzf

ijij

i j

∆⋅

⋅

∑∑

∫∫

Ω

)()(

)2(

),(

)1(

)2()1(

(2)

where N

= the number of collisions if no evasive

manoeuvres were made; i and j = ship classes of

the colliding vessels; Q

= the number of class i

vessels at waterway 1 in time unit; Q

= the number

of class j vessels at waterway 2 in time unit; V

(1)

the average velocity of class i vessels at waterway

1; V

(2)

= the average velocity of class j vessels at

waterway 2; f

(1)

= the lateral distribution of traffic

in waterway 1; f

(2)

= the lateral distribution of traffic

in waterway 2; V

= the relative velocity of ships de-

pending on velocities and meeting angle; D

= so-

called geometrical collision diameter depending on

vessel lengths, beams and velocities; and Δt = time

period under review.

The parameters of the collision candidate model

were based on analysis of AIS records from the stud-

ied area in July 2006. The lateral distributions were

approximated with normal distributions whose pa-

rameters were based on AIS records. For the calcula-

tions the vessels were grouped into five ship classes:

passenger ships, cargo vessels, tankers, high speed

crafts (HSCs), and other ships. Each class was di-

vided into four size groups: length less than 100 me-

tres, length at least 100 but less than 200 metres,

length at least 200 m, and length unknown for which

the average values of length and width of the ship

class in question were used. The angle between

crossing ships had been varying at the crossing

point, so the average angle of arrival of each ship

class from each approach direction was used in the

calculations.

Figure 2. The applied Bayesian network structure for causation probability adapted from (Det Norske Veritas 2003, 2006).

Table 1. Causation probability network node states whose

probability were set to 1.0 in good and poor environmental and

human performance conditions

_________________________________________________

Node Environmental Human

conditions performance

good poor good poor

_________________________________________________

Daylight day night - -

Visibility > 1 nm < 1 nm - -

Weather good storm - -

Attention - - high low

Communication - - beyond sub-

level standard standard

Communication - - yes no

with other vessel

Competence - - high low

Distraction level - - low moderate

Duties - - normal extreme

Stress level - - low high

Tired - - no yes

_________________________________________________

4 MODEL USED FOR CAUSATION

PROBABILITY

The applied Bayesian network model for estimating

the causation probability, i.e. the probability of not

making evasive manoeuvres, was based on frag-

ments of a collision model network in the Formal

Safety Assessment of large passenger ships (Det

Norske Veritas 2003) and a grounding model in the

FSA of ECDIS chart system (Det Norske Veritas

2006). The network estimated the probability of a

collision given that two ships were on a collision

course, one ship had lost control and the other ship

did not give way. The network included parameters

related to navigational aids, conditions, safety cul-

ture, personnel factors, management factors, other

vigilance, and technical reliability. The network re-

flected the following events for making an evasive

manoeuvre while on collision course. At first the Of-

ficer On Watch (OOW) had to detect the dangerous

situation either visually or with navigational aids.

Detection was influenced by parameters related to

external and internal conditions as well as attention.

After the detection, OOW had to make a correct as-

sessment of the situation, which was influenced by

OOW’s performance level. Situation might have al-

so been assessed correctly even without OOW’s de-

tection if other vigilance such as a pilot or VTS op-

erator was present to detect the danger. If situation

was assessed correctly, OOW had to make an avoid-

ing act. If control was lost because of either wrong

or no action or steering failure, the collision might

have still been avoided if the other ship gave way.

The network was modified so that it was suitable to

be applied to an analysis including multiple ship

types. The network structure can be seen in Figure

Most of the probability values related to the

Bayesian network parameters were derived from the

original models and had been mostly based on ex-

pert judgment. Ship type distributions in the water-

ways of the studied area were obtained from AIS-

data. The probability distributions of “Weather”

states were based on Finnish Meteorological Insti-

tute’s statistics on the average number fog days at

Isosaari in July during 1961-2000, the average num-

ber of storm days at Finnish sea areas in July during

1990-2008 thinned by the average portion of storm

observations from the Gulf of Finland in 2006-2007,

and the average number of strong wind days at Iso-

saari in July during 1961-2000 (Finnish Meteorolog-

ical Institute, 2008). The daylight distribution de-

scribing the probability of a ship navigating in the

dark, conditional on ship class, was based on AIS in-

formation and sunrise and sunset times at the studied

location at 15.7.2006. The probability of “VTS”

state “yes” was set to 1.0 because the studied area is

monitored by VTS stations.

The effects of conditions outside the vessel and

factors related to human performance on collision

probability were studied by constructing scenarios

describing different environmental conditions and/or

factors related to human performance. The states of

the nodes, the probability of which was set to 1.0 in

the different environmental and human performance

conditions are shown in table 1. For example, the

environmental conditions were defined as “poor”, if

all of the following probabilities in the network were

equal to 1.0:

− P(Weather = ”storm”)

− P(Visibility = “< 1 nm”)

− P(Daylight = “night”)

Causation probability was estimated for scenarios

where 1) there was no evidence on any of the net-

work parameters; 2) it was known that environmen-

tal conditions were “good” and the factors related to

human performance were “good”; 2) it was known

that environmental conditions were “good” and the

factors related to human performance were “poor”;

3) it was known that environmental conditions were

“good” but there was no information on other pa-

rameters; 4) it was known that environmental condi-

tions were “poor” and the factors related to human

performance were “good”; 5) it was known that en-

vironmental conditions were “poor” and the factors

related to human performance were “poor”; 6) it was

known that that environmental conditions were

“poor” but there was no information on other pa-

rameters; 7) it was known that the factors related to

human performance were “good” but there was no

information on other parameters; 8) it was known

that the factors related to human performance were

“poor” but there was no information on other pa-

rameters. In addition, causation probability was es-

timated for situations where 10) there was no extra

vigilance present for detecting the danger; and 11)

danger was detected by VTS or other internal vigi-

lance. In situations 10 and 11 there was no evidence

on any other parameters than the node “Vigilance”.

The network was built and the probability calcula-

tions were performed with Bayesian network soft-

ware Hugin.

5 RESULTS OF THE ANALYSIS

General causation probability for the studied loca-

tion and traffic, meaning that there was no additional

knowledge on the network parameters other than the

default conditional probabilities of the network, was

estimated to be 2.70 ∙ 10

-4

. When multiplied by the

number of collision candidates, the resulting number

of collisions in one month was 1.64 ∙ 10

-2

which

equals a return period of 61 months. If it was certain

that the danger had been detected by extra vigilance,

causation probability estimate was 2.58 ∙ 10

-4

pro-

ducing return period of 64 months. On the other

hand, if there was no extra vigilance, causation

probability was 3.74 ∙ 10

-4

and the collision return

period decreased to 44 months.

Tables 2 and 3 present causation probability and

the expected number of collisions in a month esti-

mates with different environmental and human fac-

tor conditions. The lowest collision probability in

these scenarios was acquired in good environmental

conditions with good human factors, and the colli-

sion probability was highest when both the environ-

mental and human factor conditions were poor.

Table 2. Results of causation probability estimation with dif-

ferent scenarios related to environmental and human factor

conditions

____________________________________________

Environmental Human

conditions performance

Good Poor No evidence

____________________________________________

Good 2.56E-04 4.27E-04 2.68E-04

Poor 2.94E-04 1.97E-03 7.01E-04

No evidence 2.56E-04 4.44E-04 2.70E-04

____________________________________________

Table 3. Estimates of the number of collisions in a month with

different scenarios related to environmental and human factor

conditions

____________________________________________

Environmental Human

conditions performance

Good Poor No evidence

____________________________________________

Good 1.55E-02 2.59E-02 1.63E-02

Poor 1.78E-02 1.19E-01 4.25E-02

No evidence 1.55E-02 2.69E-02 1.64E-02

____________________________________________

6 CONCLUSIONS

The effects of weather and factors related to human

performance on the collision probability were stud-

ied using a Bayesian network model for estimating

the probability on not making an evasive manoeuvre

while ships were on a collision course in crossing

area between Helsinki and Tallinn in the Gulf of

Finland. The general causation probability was esti-

mated to be 2.70 ∙ 10

-4

, which is about the same or-

der than the values found in literature. With this cau-

sation probability, the return period of collisions in

the crossing area between Helsinki and Tallinn was

estimated to be 5 years. According to statistics, one

collision had occurred in the area in 6 years so it

could be stated that the model reflected well the ac-

tual situation. However, it should be noted that it is

hard to compare the results to statistics since ana-

lyzed time interval should be long but the traffic

would have to remain constant. The return periods

were estimated based on one summer month traffic

data. The traffic in the area is very different during

in winter period. Thus the effects of winter should

also be included in modelling in the future.

According to the applied model, if human per-

formance factors were poor and the ship would be

sailing in difficult conditions at dark, the probability

of a collision in the studied area would be almost

eight times as big as in good environmental and hu-

man performance conditions. If just the difference in

human performance is examined, the collision prob-

ability with poor human performance factors would

be almost twice the probability in good human per-

formance conditions. This evaluation shows that the

validity of the network parameters is important in

order to produce realistic estimates of collision

probabilities. In the future expert judgment and ship

simulator studies will be utilized in order to validate

the model to the traffic and conditions in the Gulf of

Finland. With a valid model the effects of possible

risk control options on collision probabilities can be

evaluated and the model can be used as an aid in de-

cision-making.

All theoretical analysis completed in this docu-

ment is based on data of only one month, July 2006.

The amount of traffic is largely dependent on the

season as well. Naturally this also means that the

comparison with the accident statistics and theoreti-

cal model using only data from one month raises

some concerns. This paper can, however, be consid-

ered as a good start to more profound analysis of the

causation probability in the area, which should be

conducted on monthly basis covering the whole year

and based on data from other months as well.

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