International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 1
Number1
March 2007
19
Innovative Probabilistic Prediction of Accident
Occurrence
K. Inoue
Kobe University, Graduate School of Maritime Sciences, Japan
M. Kawase
Japan Marine Science Inc., Japan
ABSTRACT: In the present paper, a safety evaluation index that determines the probability of accident
occurrence of collision and stranding when the experiment is executed using a ship handling simulator is
proposed, by noting Unsafe Ship Handling Situations. The number of Unsafe Ship Handling Situation was
counted from the results of simulator trials, and the accident ratio was surveyed from the past records of sea
casualties in the corresponding water area. The correlation between the appearance ratio of Unsafe Ship
Handling Situation and the accident ratio showed reasonable coincidence with the order of 10
-3
. When port
administrator tries to assess the effectiveness of safety improvement planning of port and harbour facilities, it
can be said that this kind of probabilistic prediction model of accident occurrence is indispensable from the
aspect of introducing cost effectiveness analysis.
1 INTRODUCTION
A ship-handling simulator has been used as a
powerful tool to assess the effectiveness of safety
improvement planning of port and harbour facilities.
Ship handling simulator oriented experiments are
already practiced broadly and globally for verifying
the adequacy of the countermeasure taken by port
administrator from the safety aspect.
In the present paper, a model to evaluate accident
occurrence probability is proposed by introducing
“Unsafe Ship Handling Situation”. An Unsafe Ship
Handling Situation can be determined, in each time
section, in terms of whether or not the Time To
Collision (TTC) exceeds the Short Stopping Time
(SST) under the corresponding speed. Time To
Collision (TTC) is calculated as the time until the
ship makes contact with the obstacle or other ship on
the predicted ship’s path.
According to the Heinrich’s Law, an Unsafe
Situation corresponds to the detection of some
several thousand hidden unsafe situations behind one
obvious case of an accident. If the appearance ratio
of the proposed Unsafe Ship Handling Situation and
the accident ratio in the corresponding sea area
coincide with the order of 10
-3
, this means that, by
deriving the number of Unsafe Ship Handling
Situations from a series of ship-handling processes,
the underlying accident risk in the process of ship
handling may be estimated from the relation with
this ratio of 10
-3
.
To verify this relationship, calibration was
attempted using ship-handling simulator. In trails,
several scenarios of the existing ports in Japan in
which the ship encountered other ships in a curved,
narrow waterway were prepared. The number of
Unsafe Ship Handling Situation was counted from
the results of trials, and the accident ratio was
surveyed from the past records of sea casualties in
the corresponding port.
The correlation between the appearance ratio of
Unsafe Ship Handling Situation and the accident
ratio showed reasonable coincidence with the order
of 10
-3
. The proposed safety evaluation index is
20
considered to be an objective index that is unbiased
towards subjectivity, and to contribute to
maintaining the universality of the results on a
probabilistic basis.
This prediction model of accident occurrence
probability by noting Unsafe Ship Handling
Situation as an index is a practical model for
evaluating the ship handling risk in topographically
restricted and congested waterways, and in ports and
harbours.
2 DEFINITION OF UNSAFE SHIP HANDLING
SITUATIONS
Heinrich’s law, as can be seen in Fig. 1, explains that
there are 29 accidents with slight damage and 300
near misses, furthermore, there are several thousand
latent unsafe situations behind one obvious accident.
When evaluating the level of safety in a ship-
handling simulator oriented experiment, one method
is to estimate the potential risk of accident at a ratio
of 1: 300 by counting the number of near misses
from experiments.
However, it is difficult for us to perform many
cases of experiments using a ship-handling
simulator, and it is more difficult to objectively
determine near misses. In this study, latent unsafe
situations behind near misses are noted. That is, by
detecting physically unsafe events, the objective
level of accident risk may be estimated. Such
physically unsafe situations are termed Unsafe Ship
Handling Situations in this paper. (Inoue, 2000)
Fig.1. Heinrich’s accident triangle
During the process of executing ship handling
operation, ship handling is considered not to be
dangerous when there is no obvious risk when
maintaining the present maneuvering condition;
however, such ship handling includes the possibility
of an accident when there is an obvious risk in the
near future by maintaining the present maneuvering
condition. As stated above, an Unsafe Ship Handling
Situation is defined as a condition in which the risk
becomes obvious in the near future by maintaining
the present condition in spite of an accident not
having occurred.
3 METHOD OF DETECTING UNSAFE SHIP
HANDLING SITUATION
The concept of Potential Area of Water (PAW) is
introduced as a means of determining whether or not
there is a latent Unsafe Ship Handling Situation
during execution of ship handling. (Inoue, 1990)
PAW can be estimated by predicting ship’s vector
and ship’s track in the future. Predicted tracks are
obtained by the following procedures:
1 With time constant, quantitative conditions of all
operational means acting on the ship such as
rudder angle, main engine revolutions, tugs,
thrusters, mooring lines, and holding power of
anchors and anchor chain, and quantitative
conditions of ship movement such as ship’s
heading, velocity, yaw rate and acceleration
component are extracted. These quantitative
conditions, along with quantitative conditions of
external force become input conditions for
calculations of predicted tracks.
2 With time constant, ship movement is estimated
by substituting value (1) above into the equation
of motion under the condition that quantitative
conditions of operation, ship movement and
external forces are fixed, and predicted tracks are
obtained.
As illustrated in Fig.2, Unsafe Ship Handling
Situations are detected by inspecting whether or not
the PAW obtained at each time segment overrides
obstacles such as a wharf and quay wall, buoy and
breakwater or another ship under way. (Inoue, 1998)
Fig. 2. Illustration of unsafe situation
21
Fig. 3. Flowchart of detection procedure
Concretely, as shown in flowchart of Fig.3, an
Unsafe Ship Handling Situation is detected by the
following procedure:
1 A series of ship handling maneuvers is divided
into time segments.
2 In each time segment, the PAW is estimated.
3 The Time To Collision (TTC) is calculated. TTC
is the time until own ship collides with another
ship and or strands on the predicted tracks.
4 An Unsafe Ship Handling Situation is detected if
the TTC value exceeds the judgment criteria of
the Unsafe Ship Handling Situation.
4 JUDGMENT CRITERIA FOR UNSAFE SHIP
HANDLING SITUATION
An Unsafe Ship Handling Situation is determined in
each time segment if Short Stopping Time (Time to
stop with crash astern engine, SST) corresponding to
the ship’s velocity at the time exceeds the TTC
value. The purpose is to determine potential risks
physically, that is, for a certain TTC, if TTC ≤ SST,
it is determined that the ship is in an Unsafe Ship
Handling Situation (hereinafter called SST criterion).
On the other hand, when berthing or un-berthing,
ship speed is decreasing sufficiently, and the main
component of ship motion is no longer ahead (u), but
drift (v), turn (r), and occasionally astern (-u) are
taking place. Under such conditions of ship motion
in the vicinity of a berth, it is not reasonable to
follow an SST criterion that controls only ahead
motion. In general, the motion of drift (v), turn (r),
and occasionally astern (-u) or their coupled motion,
are eliminated by main engine, thrusters and tugs,
but the same methods cannot be applied to them all.
When simulating the time required to eliminate
typical ship motions in the vicinity of a berth using a
tug or a thruster, it was found, for any type of ship,
that the above time to eliminate ship motions
coincides with the time required to eliminate a
headway of 2 knots with full astern engine.
Therefore, in the speed range of 2 knots or less, it is
concluded that Unsafe Ship Handling Situations are
to be determined by SST criteria based on the time
required to eliminate a headway of 2 knots with full
astern engine. Fig.4 illustrates the judgment criteria
of Unsafe Ship Handling Situations.
Fig. 4. Schematic diagram of judgment criteria
5 EXAMPLE OF UNSAFE SHIP HANDLING
SITUATION DETECTED
Fig.5 shows the calculation results of TTC over time
with the speed-reduction sequence while proceeding
to a wharf. The following elements are shown on the
figure: time series on the abscissa, TTC on the left
ordinate and ship velocity on the right ordinate.
0 500 1000 1500 2000 2500
Simulation Time (sec)
0
50
100
150
200
250
300
Time (sec)
0
2
4
6
8
10
12
V (m/s)
TTC
Ship Speed (V)
Judgment Criteria
Fig. 5. Calculation results of TTC
To determine Unsafe Ship Handling Situations, an
SST criterion is also shown in this figure. If the TTC
value plotted falls under the line showing judgment
22
criteria, the ship is determined to be in an Unsafe
Ship Handling Situation. The passing of the ship
through a breakwater entrance corresponds to 1,000
seconds on the abscissa, where an Unsafe Ship
Handling Situation is perceived. After entering port,
the Unsafe Ship Handling Situation is decreased due
to sufficient speed-reduction.
In Fig.6, the occurrence ratio of Unsafe Ship
Handling Situation detected during experiments on a
ship-handling simulator in major ports in Japan are
compared with the accident ratio of collision and
stranding occurred in the corresponding ports. A
characteristic read from the figures above is that the
occurrence ratio of the proposed Unsafe Ship
Handling Situation and the accident ratio in the
corresponding ports approximately coincide with an
order of 10
-3
in any case. That is, according to the
Heinrich’s law, the Unsafe Ship Handling Situation
corresponds to the detection of some several
thousand latent unsafe situations (order of 10
-3
)
behind one obvious case of an accident. This means,
by deriving the number of Unsafe Ship Handling
Situations from a series of ship handling maneuvers,
it may be possible that the underlying accident risk
in the process of ship handling is estimated from the
relation with the ratio of 10
-3
.
6 CONCLUSION
If there is a little time until collision or stranding to
recover, an error by the mariner or misjudgement
will lead to an actual collision and stranding, so we
proposed an evaluation model that extracts an
Unsafe Ship Handling Situation under a certain
judgment criterion from the events inherent in a
series of ship handling maneuvers.
This safety evaluation index is considered to be
an unbiased yardstick that objectively determines the
quantitative risks of collision and stranding, and to
be practical for maintaining the universality of the
results on a reasonable probabilistic basis.
Fig. 6. Comparison of occurrence ratio of unsafe situation and marine accident
When port administrator tries to assess the
effectiveness of safety improvement planning of port
and harbour facilities, it can be said that this kind of
prediction model is indispensable. Furthermore, to
deepen mutual understanding and to create
consensus-building among the parties concerned in
different situations such as the port administrator
and ship handler, scientifically based explanations
are indispensable for problems of maritime safety.
From this point of view, it is expected that the new
yardstick developed in this study will contribute to
the utilization of ship-handling simulators for safety
evaluations.
REFERENCE
Inoue Kinzo, 1990, Concept of Potential Area of Water as an
Index of Risk Assessment of Ship Handling, The Journal of
Navigation, The Royal Institute of Navigation, Vol.43,
No.1, pp.1-7
Inoue Kinzo, Sera Wataru and Masuda Kenji, 1998, Evaluation
of Ship Handling Safety based on the Concept of PAW, The
Journal of Japan Institute of Navigation, No.99, pp.163-171
Inoue Kinzo, Sera Wataru, Masuda Kenji and Usui Hideo,
2000, Guidelines to Assess the Safety of Marine Traffic-IV,
–Estimation of Potential Danger of Near Miss-, The Journal
of Japan Institute of Navigation, No.102, pp.203-209