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Probability Estimation and Implication of Piracy
Using a Tangible Method
Dao-zheng Huang
Ph.D. Candidate
School of Naval Architecture, Ocean and Civil Engineering
Shanghai Jiao Tong University
800 Dongchuan Road, Shanghai, P.R. China.
TEL: 8621-62933091, FAX:8621-62933163
Email:[email protected]
Hao Hu
(Corresponding Author)
Ph.D., Professor
Vice Dean of Graduate School in Shanghai Jiao Tong University
Head of Department of Transportation and Shipping.
800 Dongchuan Road, Shanghai, P. R. China
TEL: 8621-62933091, FAX: 8621-62933163
E-mail: [email protected]
Yi-zhou Li
Ph.D. Candidate
Department of International Shipping, Shanghai Jiao Tong University
Room 1302(HaoRan), 1954 Huashan RD, Shanghai, China
TEL:(86)021-62933091 Fax: (86)021- 62933163
E-mail:[email protected]
Submitted to the committee of Marine Safety and Human Factor (AW040) for
possible Presentation and Publication at the Transportation Research Board 93rd
Annual Meeting
TRB 2014 Annual Meeting
Submission date: November 15th, 2013
Words count: 4038+ 3(tables) + 4(figures) = 5788
Paper revised from original submittal.
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ABSTRACT
It is an important and difficult problem to calculate the probability of encountering
pirates for a trip. This paper proposes a tangible method to estimate the probability
based on the historical data from International Maritime Bureau (IMB) and the United
Nations Conference on Trade and Development (UNCTAD). The tangible method
consists of two parts. At first, it is assumed that the probability is equal everywhere in
the sea. The average probability of piracy is estimated. Then, an adjusting coefficient is
proposed to revise the probability of piracy in each trip. The adjusting coefficient of
each trip is related to the average number of piracy in every grid which is defined in
Geographic Information System (GIS) and come across by the trip. Finally, a numerical
example of a trip from Shanghai to the Republic of Kenya is used to illustrate the
application of the proposed method. The results show the average probability of
encountering pirates in 2012 is 0.0216% when a ship travels a thousand miles. The
adjusted probability of encountering pirates is estimated to be 1.62%.
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Keywords: Piracy, Probability, Estimation, GIS
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1. INTRODUCTION
Piracy has been an international non-traditional safety issue of maritime transportation.
Piracy leads to loss of about 25 billion US dollars every year (1). Furthermore, their
geographical scope of activity is extending. Piracy and armed robbery against ships
remain a real and ever-present danger to those who use the seas for peaceful purposes
(2). Huang (2012) took piracy as one of the three main factors that threaten China’s
maritime safety (3). Li also regarded piracy as an important risk factor when assessing
risk of crude oil transportation (4, 5). The increase in the number, ferocity and
geographical scope of incidents of piracy and armed robbery against ships, too often
resulting in death, injury or the kidnapping of seafarers, has compelled the United
Nations, regional bodies, governments, military forces, shipping companies, ship
operators and ships' crews, to work together in order to rid the world of the threat
posed by piracy.
Figure 1shows that piracy cases alternate high and low spot (6). It is stressed that
piracy is a problem that will never disappear or get eradicated completely (7). In 2012,
the number of piracy decreased a lot. But nobody can guarantee that the number of
piracy will decrease continuously. From the changing tendency, the number of piracy
every year always increases after several years’ decrease. From Figure 1, it seems that
there is a general upward trend, but with cycles.
year
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FIGURE 1 The number of global piracy cases from 1994 to 2012.
Source：IMB Piracy and Armed Robbery Against Ship-2012 Annual Report
Considering that pirates have been a threat to maritime safety for a long time,
researchers have done much work on it. The literatures about piracy can be mainly
classified into three categories: the cause of piracy, the impact of piracy, and
measures to anti-piracy. Esher et al. (2010) used agent models and statistical design of
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experiments to gain insight into how meteorological and oceanographic factors can be
used to dynamically predict piracy risks for commercial shipping (8). Bowden et al.
assessed the economic costs of maritime piracy, including the direct financial costs of
piracy, such as ransoms, insurance premiums, the costs of re-routing to avoid piracy
regions, deterrent security equipment, naval forces, piracy prosecutions, and anti-piracy
organizations, and the secondary (macroeconomic) costs of piracy, such as: effects on
regional trade, fishing and oil industries, food price inflation, and reduced foreign revenue
(9). Fu et al. (2010) modeled shipping demands and competition in the Far
East-Europe container liner shipping service to investigate the economic welfare loss
effects by Somali piracy due to reduced volumes of trade and shipping, as well as
efficiency loss due to geographical re-routing of shipping networks which would be
otherwise uneconomical (10).The various counter piracy missions and the shipping
industry have worked together to produce a series of best management practices
(BMPs) (BMP4, 2011) that will deter pirates (11). Percy (2013) analyzed five
obstacles to end Somali piracy (12). Bulkeley (2003) examines the potential for the
emergence of a multilateral maritime regime in East Asia founded on regional
cooperation to reduce maritime piracy (13). Somali pirates have always been studied
as the case because piracy attacks have been most concentrated in Somali region (8,
14, 15, 16).
However, there are rare researches into the probability of piracy. There exist
some researches into the probability of accidents in maritime transportation. These
researches may be the references of study into the probability of piracy. Qu (2012)
estimated that only not more than 0.005% vessels are involved in accidents with
different severities in the Singapore Strait (17). But it only considered the accidents in
the strait. As for a trip through the strait, it may be involved in accident out of the
strait. Dobbins adapted a GIS-based highway planning traffic assignment model to
estimate the casualty rate in American coast using both accidents data and ship trip
data (18). Weng (2012) estimated vessel collision frequency in the Singapore Strait
using Automatic Identification System (AIS) data (19). Huang et al. (2013) analyzed
the spatial distribution of maritime accidents using GIS (20). As for piracy, there are
reports about the number of piracy while it is difficult to get the data about trips in
each area. So it is difficult to calculate the occurring probability of piracy.
Without the traffic flow data in each shipping lane, this paper tries to estimate the
probability of piracy using a tangible method. At first, it is assumed that there is equal
probability of piracy everywhere in the sea. In this way, the average probability of
piracy in the whole sea is calculated. But it is obvious that different areas have
different probability of piracy. In order to solve this problem, a coefficient is
calculated by the number of piracy occurred in the areas the trip comes across to
adjust the result. The remainder of the paper is structured as follows: Section 2
describes the piracy statistic data and seaborne trade data. Next, the probability
estimation and implication model is presented in Section 3. Section 4 carries out a
numerical example to illustrate the application of the proposed method. Finally,
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discussions and conclusions are provided in Section 5.
2. PIRACY STATISTIC DATA AND SEABORNE TRADE DATA
The ICC International Maritime Bureau Piracy Reporting Centre
The ICC International Maritime Bureau (IMB) is a specialized division of the
International Chamber Of Commerce (ICC). The IMB is a non-profit organization,
established in 1981 to act as a focal point in the fight against all types of maritime
crime and malpractice. IMB’s main task is to protect the integrity of international
trade by seeking out fraud and malpractice. For over 25 years, it has used industry
knowledge, experience and access to a large number of well-placed contacts around
the world to do this: identifying and investigating frauds, spotting new criminal
methods and trends, and highlighting other threats to trade.
One of the IMB’s principal areas of expertise is in the suppression of piracy.
Concerned at the alarming growth in the phenomenon, this led to the creation of the
IMB Piracy Reporting Centre in 1992. The Centre is based in Kuala Lumpur,
Malaysia. It maintains a round-the-clock watch on the world’s shipping lanes,
reporting pirate attacks to local law enforcement and issuing warnings about piracy
hotspots to shipping. IMB Piracy Reporting Centre writes a report about pirate attacks
every year. Its annual report has been regarded as the most reliable report about pirate
attacks. According to ICC-IMB annual report, piracy is divided into four categories as
shown in Table 1. Figure 2 shows the percentage of different types of piracy in 2012.
Among the four kinds of piracy, hijack is the only one which causes huge loss to ship
owners.
It is assumed that:
Rate of Hijack (ROH) = The number of hijack/ total piracy cases.
It can be calculated from Table 2 that ROH is around 10% from year 2009 to
2012. This means pirates don’t have dominate advantages over ships. Many piracy
attempts are failed. If the ship owners remain on their guard, piracy cases of hijack
can be decreased.
According to data from IMB Piracy Reporting Center, Coggins (2012) introduced
Maritime Piracy Data (MPD), a dataset dedicated to understanding the nature,
dynamics, and causes of contemporary piracy and armed robbery against ships (21).
He summarized the piracy data with coordinate data from 2000 to 2009.
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TABLE 1 Category of Piracy Cases
Type
Hijack
Boarded
Fired upon
Attempted
boarding
Meaning
Pirates boarded and
taken control of a vessel against the crews will
Pirates boarded but failed to take control of a
vessel against the crews will
Pirates fired upon the ship but failed to board the ship
Pirates attempted to board the ship
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9%
23%
9%
59%
Hijack
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Fired upon
Attempted boarding
FIGURE 2 Pie chart of different types of piracy cases in 2012.
TABLE 2 Rate of Hijack in all the Piracy Cases from 2009 to 2012
Type
Year 2009
Total attacks
Hijacked ships
Ratio of Hijacked
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Boarded
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12%
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2011
2012
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12%
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10%
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9%
United Nations Conference on Trade and Development:
Review of Maritime Transportation 2012
The Review of Maritime Transportation is a recurrent publication prepared by the
United Nations Conference on Trade and Development (UNCTAD) secretariat since
1968 with the aim of fostering the transparency of maritime markets and analyzing
relevant development. The review would include the international seaborne trade, the
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world fleet, freight rates and maritime transport costs, port, and legal issues and
regulations. Review of Maritime Transportation 2012 gives a comprehensive
overview of the situation of maritime transportation. It shows the number of ships in
the market, the total deadweight tons of these ships and the total ton miles of seaborne
trade (22). Specific data needed in this paper is extracted and shown in Table 3.
TABLE 3 World Fleet and Seaborne Trade Data in 2012
World total capacity (dwt)
The number of vessels
The world seaborne trade
in cargo millions of ton-miles
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1,518,109,503
46,901
44,540,000
3. PROBABILITY ESTIMATION AND IMPLICATION MODEL
In this section, the probability estimation and implication model is built based on the
frequency probability theory. At first, the number of piracy is acquired. Then, the
number of piracy is divided by the traffic flow in each shipping lane. Because the
traffic flow in each shipping lane is unknown, we propose a tangible method to
estimate the probability of piracy in each shipping trip under conditions without
traffic flow data. The tangible method consists of two steps. The first step is to
calculate the average probability of piracy in a thousand ship-miles assuming that the
probability of encountering piracy is equal everywhere in the sea. The other step is to
adjust the average probability using a coefficient. The coefficient is determined by the
spatial distribution of historical piracy and calculated with the aid of GIS.
As the premise of estimation, some assumptions are made.
(1) The number of piracy reported by IMB is considered to be the actual number
of piracy.
(2) Every ship travels the same shipping miles.
(3) The probability of encountering piracy is equal everywhere in the sea.
The procedure of estimating the probability of piracy is presented as follows:
Step 1: estimate the number of piracy in the studied time period;
Step 2: estimate the average size of ships in this period;
Step 3: count the ship-miles all the ships traveled in this period;
Step 4: calculate the average probability of piracy in a thousand ship-miles;
Step 5: calculate the adjusting coefficient of a trip;
Step 6: calculate the probability of the trip.
3.1. The Number of Piracy
The first step of probability estimation is to acquire the number of piracy served as the
nominator. The number of piracy from ICC IMB is used. As stated in the annual
report of IMB in 2012, the number of piracy in 2012 is 297. The ICC IMB reports on
Somali piracy have been criticized in different opinions (14); one view states that
there is a certain amount of over reporting of piracy incidents due to the Best
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Management Practice (BMP) developed by the shipping industry (11), which
recommends that seafarers report any suspicious approaches in the vicinity. The other
view claims of underreporting in the ICC IMB statistics because some ship operators
fear that their illegal activity will be disclosed if they report piracy activity (23).
However, the data reported by the IMB are consistent with other global reports and
have been widely adopted by international institutions like the IMO because no
alternative source can resolve the potential underreporting problem (24)
3.2. Estimation of Average Probability in Certain Ship-Miles
For the convenience of estimation, it is supposed that there are N ships in the market
and notations are given as follows.
Notations:
i:
ship i. 1  i  N ;
:
the distance in miles that ship i travels;
:
the size of ship i in dwt;
:
the average size of ships in dwt taking travel distance of ships as the weight;
Q:
true demand for shipping service taking distance into consideration in ton miles.
M:
the number of piracy;
P a:
the average probability of encountering piracy in a thousand ship miles;
: if there were only one ship in the market, how many miles the ship travels to
have the same effect of all the present ships;
Q is the total transportation volume of all ships. It is calculated in Eq. (1) below:
N
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Q
S D
i
(1)
i
i 1
is calculated as the following equation.
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N
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S=
S D
i
i 1
i
N
D
i
i 1
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Q
(2)
N
D
i 1
In Eq. (2), it is difficult to get the data of
ship travels the same shipping miles.
i
. According to assumption 2, every
Di  D j , 1  i  N , 1  j  N
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
Then,
(3)
can be estimated using the following formulation:
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S=
S
i 1
i
(4)
N
is the miles that if there were only one ship in the market, the ship
travels to have the same effect of all the present ships. The average probability Pa can
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be calculated as follows:
Pa 
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M
Q/S
(5)
3.3. Adjusting Coefficient
In chapter 3.2, in order to be convenient to calculate the probability of piracy, it is
assumed that the probability of encountering piracy is equal everywhere in the sea.
However, in reality, it is not always the case. In order to solve this problem, a
coefficient is advised to adjust the probability calculated by the model in 3.2. This
coefficient is determined by the number of piracy occurred along the trip.
In order to calculate the coefficient, GIS is used as a technical tool. It is an
effective and unique tool for spatial analysis and provides visualization of geographic
data. The aim of GIS is to provide a spatial framework in which we can model our
world, make reasonable usage of our resources, and support our decision for
sustainable development of the environment. Generally, GIS comprises three
components. Firstly, GIS has a spatial database which contains data models (like
features, grid, and topology) used to describe the physical world. Similar objects are
grouped into layers and information about each object is maintained in a relational
database or file. Objects are typically represented in vector format, such as points,
lines or polygons. Aerial images, such as satellite photos, can also be used in most
GIS packages and included in the database. Secondly, a GIS presents its data via an
intelligent map. This map can also be regarded as a visualization of the database.
Finally, GIS typically provides a spatial process toolbox that enables complex
analysis of database objects based on their spatial locations using the current analysis
module or through software written by the user or third parties. GIS has been widely
used in highway planning, network analysis, and other applications.
Arcgis 10 is used as our software platform. In Arcgis 10, the world map is
divided into 18*36 (648) grids. Then the number of piracy in each grid can be
calculated. A map was divided into 18*36 fishnets by the creating fishnet tool in
ArcToolbox. A new layer named fishnet was created. Then, the piracy layer was
connected to the fishnet layer, creating a new layer named fishnet_SpatialJoin. In the
layer fishnet_SpatialJoin, there was a data field named Joined_Count, which
represented the number of piracy in a particular fishnet. Finally, the number of piracy
in each grid is shown in Figure 3, which is the basis of calculating coefficient.
The coefficient of each trip is calculated according to the number of historical
piracy in the grids the trip comes across. Here, the piracy data from 2000 to 2009 is
used to calculate the coefficient.
According to the piracy data from 2000 to 2009, the average number in a grid is
3413/648=5.3.
As for a trip j, the grid it comes across can be found. Then the average number of
piracy in each grid it comes across is calculated, regarded as .
If kj stands for the coefficient of trip j, it is define:
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Kj 
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Then, the adjusted P of trip j,
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can be calculated as
(7)
As for trip j, the real probability of this trip, Pj, can be calculated as:
Pj  Pa , j  L j
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(6)
Pa, j  Pa  K j
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N
5.3
(8)
Where Lj represents the length of the trip.
FIGURE 3 The number of piracy in each grid.
4. CASE STUDY
In order to illustrate the application of the proposed method, a trip from Shanghai to
the Republic of Kenya is taken as an example, labeled as tripsh-k. The year 2012 is
selected as calculation time period. According to ICC IMB Piracy and Armed
Robbery Against Ships-2012 Annual Report, the number of piracy in 2012 is 297. As
recorded in Review of Maritime Transportation, the number of ships in the market is
46901, the total deadweight tonnage is 1,518,109,503 and the world seaborne trade in
cargo ton-miles is estimated as 44,540,000,000 thousand of ton-miles. Then, the
average size of all ships is calculated according to Eq. (4).
n
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S
S
i 1
N
i
 32368 dwt
Q 44,540, 000, 000

 1,376,000 thousand miles
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Pa 
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M
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
 2.16104 (thousand miles)1
Q / S 1,376, 000
It means if a ship travels one thousand miles, the probability of encountering
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piracy is 2.16104 .
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It is 5536 miles from Shanghai to the Republic of Kenya. Based on the result in
Figure 3, by calculating the number of piracy in the grids come across by this trip in
Figure 4, the average number of piracy occurred in each grid of the trip is 71.5.
From Eq. (6), the coefficient of the trip is calculated.
71.5
K sh k 
 13.6
5.3
Combining Eq. (7) and (8), the probability of this trip, Psh-k , is estimated.
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Pshk  Pa  Kshk  Lshk  2.16 104 13.6  5536 103  1.62%
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This trip comes across the Somali area and the Malacca Strait, which are two hot
spots of piracy. So the probability seems a little big. Probability of other trips can be
calculated in the same way.
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FIGURE 4 Example of a trip from Shanghai to the Republic of Kenya.
5. CONCLUSIONS
This paper proposes a tangible method to estimate the probability of piracy under the
condition without the traffic flow data in each shipping lane. Even though it is not
precise, it is a meaningful foundation to quantify the probability of piracy, especially
when the exact data is difficult to get. From the result, it can be seen that piracy is a
threat with small probability. It could be a meaningful step for shipping companies to
assess risk of piracy.
This paper may have some limitations. For example, the number of piracy may be
underreported or overreported. Furthermore, the data used to calculate the adjusted
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coefficient should be renewed to the year 2013. Because of lack of time, this renewing
work is delayed. Other factors, influencing the probability of a ship encountering
pirates, for example, the velocity of ship, the height of ship, safeguard of the ship, are
not considered in this research.
Future work can be done in three aspects. One is looking for the traffic flow data
in each shipping lane. If the traffic flow data can be found, the probability of piracy
can be calculated more easily and more precisely. Then, the consequence of piracy
incidents can be considered to make a comprehensive risk analysis. Finally, the
method needs to be verified in practice.
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TRB 2014 Annual Meeting
Paper revised from original submittal.