International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 5
Number 3
September 2011
The MDTC (Minimum Distance To Collision) mod-
el for ship-ship collision probability estimation is a
geometrical model, with a detailed description given
in the following papers: (Montewka et al. 2010),
(Montewka et al. 2011). In order to provide the
probability of an accident, the model uses the com-
monly adopted approach, which combines a fre-
quency of ship-ship meeting situations given an as-
sumption of blind navigation, and a causation factor,
which quantifies the proportion of cases in which
such a meeting ends up as a collision, due to human
or technical reasons.
The causation factor is a sensitive part of a mod-
el, very much location dependent, thus it is not justi-
fied to use the same value for the different models
(Gluver and Olsen 1998). Applying a causation
probability value derived from a study in another sea
area may save some effort, but then the actual condi-
tions are not addressed at all (Hanninen and Kujala
Two approaches can be recognized in the litera-
ture in order to estimate the causation factor. The
simplified approach is based on a historical data,
where the causation factor is assumed a ratio be-
tween the registered number of accidents and the es-
timated number of collision candidates (Fujii and
Siobara 1971), (MacDuff 1974), (Inoue and Kawase
A second approach is more sophisticated, based
on the concept of either event tree (Pedersen 1995),
(Martins and Maturana 2010) or Bayesian Networks
(DNV 2003), (Hanninen and Kujala 2009). This way
of modelling is undoubtedly more time consuming
than the first approach, however it allows getting an
insight into the chain of events leading to an acci-
dent instead of providing just a number.
In order to determine the causation factor for the
MDTC model for three different ship-ship encoun-
tering types (crossing, head-on and overtaking), we
based our study on a modified first approach, which
is relatively quick and straightforward thus robust.
We perform two stage analysis, which combines the
statistical data on maritime accidents and an analysis
of near-collisions based on recorded AIS data.
The causation factor is being defined here as a ra-
tio between the modelled number of collision candi-
dates and the actual number of accidents. However
the available statistics on maritime accidents are not
very detailed, and the type of an accident is not in-
cluded there. Thus there is a need to find a proxy be-
tween a recorded number of accidents and a mod-
elled number of collision candidates (Heinrich et al.
1980), (Inoue and Kawase 2007), (Gucma and
Marcjan 2010).
A Method for Assessing a Causation Factor for
a Geometrical MDTC Model for Ship-Ship
Collision Probability Estimation
J. Montewka*, F. Goerlandt, H. Lammi & P. Kujala
*Aalto University, School of Engineering, Finland; Maritime University of Szczecin, Poland
Aalto University, School of Engineering, Finland
ABSTRACT: In this paper a comparative method for assessing a causation factor for a geometrical model for
ship-ship collision probability estimation is introduced. The results obtained from the model are compared
with the results of an analysis of near-collisions based on recorded AIS data and then with the historical data
on maritime accidents in the Gulf of Finland.
The causation factor is obtained for three different meeting types, for a chosen location and prevailing traffic
conditions there.
It seems justified to analyze the safety of naviga-
tion on the basis of the numbers of both accidents
and near-miss situations. Such a combination of
analyses may better reflect the collision hazard, as
pointed out by (Inoue et al. 2004) and (Inoue and
Kawase 2007).
In air transportation there has been a tendency to
seek out proxy for aviation safety. One commonly
used measure is that of the ”air-miss”, often called a
”near-miss”. According to (Button and Drexler
2006) ”a near-miss involves an aircraft intruding
upon a predetermined safety zone or envelope
around another aircraft”. The reporting procedures
of near-miss in aviation are well founded providing
valuable statistics. In the maritime sector similar
procedures are missing, thus the near-miss can be
detected only by analysis of recorded data and back
propagation of recorded events.
Following this idea, this paper proposes also a
methodology to evaluate the occurrence of near
ship-ship collisions in an open sea area, based on the
AIS data. The method for near-collisions analysis
presented in this work is rooted in a well-established
concept of a ship domain proposed by (Fujii and
Tanaka 1971). An overview of the near collision de-
tection method is then given and applied to the
summer traffic in the Gulf of Finland.
Finally, we compare the results obtained from the
MDTC model, expressed as the number of ”collision
candidates” with the number of near-collisions and
the number of accidents recorded in the chosen area
of the Gulf of Finland. This approach allows us to
quantify the number of modelled ”collision candi-
dates”, with blind navigation assumption behind, to
the number of cases that ended up as close encoun-
ters, where collision evasive actions were taken.
Such quantification is carried out for three major
types of meeting scenario (crossing, head-on, over-
taking). By combining this accurate enough data
with an average annual number of accidents that
happened (which are random, and almost non pre-
dictable), the causation factor for the MDTC model
is obtained.
2.1 Accident analysis
The annual number of ship-ship collisions in the an-
alyzed location of the Gulf of Finland (the water-
ways junction between Helsinki and Tallinn) is ob-
tained from HELCOM database, that covers a time
period between 1987 and 2007 (Pettersson et al.
2010). During this time, three accidents of this type
took place. Two of them happened during summer
time, and one was related to the ice conditions,
which are out of scope of the analysis presented in
this paper.
According to the aforementioned statistics there
was, on average, one summer collision per ten years.
This assumption is simplified, as the rate of collision
occurence is random, as the first collision happened
in 1996, second in 2001 and between the years 2001
and 2007 no summer collision happened in the area
of investigation. Notwithstanding, we assume that
the annual ship-ship collision frequency in the ana-
lyzed area equals 0.1.
Unfortunately, the database provided by HEL-
COM does not contain any information regarding
type of ship-ship encounter, at which the accident
took place. Thus it is not feasible to compare a mod-
elled number of collision candidates in given en-
counter type (crossing, head-on, overtaking) with an
appropriate number of the accidents. At this point
the results of near- collisions analysis are utilized
and considered a proxy between a model and the
recorded accident data.
Figure 1: The ship domain applied in the near-collision analy-
sis, with the following axes: a = 1.6LOA, b = 4LOA (Wang et
al. 2009)
2.2 Near-collisions analysis
The near-collision analysis applied in this paper is
based on a concept of a ship domain, which accord-
ing to definition given by (Goodwin 1975), is the ar-
ea around the vessel which the navigator would like
to keep free of other vessels, for safety reasons.
Since the first introduction of the ship domain
concept by (Fujii and Tanaka 1971), various re-
searchers have attempted to quantify the size of this
domain. An overwiev of the different proposed do-
mains is given in (Wang et al. 2009). Even though
the ship domain is a well established concept, certain
problems with the application can be identified as
pointed out by (Jingsong et al. 1993). Domains can
be classified by their shape: circular, elliptical and
polygonal domains. A distinction can also be made
between fuzzy domains and crisp domains. Fuzzy
domains such as that proposed by (Pietrzykowski
2008) and (Wang 2010) seem preferable in terms of
safety analysis of marine traffic, but are at present
still under development. Crisp domains use a simple
classification of a situation between safe or unsafe,
which evidently is a simplification. Moreover, the
sizes of the domains proposed in the literature vary
quite significantly (Wang et al. 2009).
In this paper, the smallest ship domain found in
the literature, by (Fujii and Tanaka 1971), is applied.
This is justifiable, since the aim of the method pro-
posed in this paper is finding the most critical en-
counters between ships. This domain is defined as an
ellipse with the major axis along the ship’s length
(LOA)and the minor axis perpendicular to the ship’s
beam, as illustrated in Figure 1. The half-length of
the major axis is taken as 4LOA while the half-
length of the minor axis is taken as 1.6LOA. A
number of comments should be made in the use of
this domain:
the domain is symmetric, which implies that the
possible influence of the COLREGs is not taken
into account;
another consequence of this symmetry is the fact
that passing behind the stern is considered as
dangerous as passing in front of the bow;
in the meeting between ships, the largest ship has
the largest domain; this means that for the largest
vessel, the situation is classified as dangerous,
whereas for the smallest vessel, the situation may
still be evaluated as safe;
the domain is affected by ship length only, neither
ship type nor hydrometeorological conditions are
included in the analysis.
However the latter can be supported by the recent
research, which revealed that the ship domain has a
relatively low correlation with the sea state and wind
force (Kao et al. 2007).
In this section, a brief description of analysis of
AIS data in order to estimate a number of near-
collisions in the selected area of the Gulf of Finland
is given. Recorded AIS data consists of millions of
data points, containing static and dynamic infor-
mation regarding a ship. In order to analyze the mar-
itime traffic in the GOF, this data need to be grouped
into routes. Routes are defined here as a set of trajec-
tories between a departure and arrival harbor as in-
troduced by (Goerlandt and Kujala 2011). The AIS
data is first gathered per ship, based on the MMSI
number. After sorting this data chronologically, the
data per ship is further split up to form individual
ship trajectories, using a methodology described by
(Aarsther and Moan 2009). These trajectories are
then further processed and grouped per route. The
sample rate of these vessel positions in the trajecto-
ries is about 5 minutes on average. In order to enable
a comparison between vessel positions at exactly the
same time instant, the trajectory data is artificially
enhanced to contain data for each second. The ex-
trapolation for the vessel position is performed using
an algorithm suitable for data in the WGS-84 refer-
ence frame following (Vincenty 1975). The ship
speed is linearly interpolated between known values.
It should also be noted that certain vessel types are
not taken into account into the analysis, like tugs are
left out of the analyzed database. This is done be-
cause these vessels are meant to operate in a close
vicinity of merchant vessels. The near collision de-
tection algorithm is shown in Figure 2.
The basic idea is to scan the database for events
where the ship contour of one vessel (i.e. the ship
area in terms of ship length and width) enters the
ship domain of another vessel. If the domain is vio-
lated, the event is labeled as a near collision and rel-
evant details such as time of occurrence, location,
encounter type, ship types and ship flags are stored
for further analysis. The near collision detection al-
gorithm is encoded in MATLAB.
Figure 2: Near collision detection algorithm