ARTICLE

Modeling the risk of ship grounding—a literature reviewfrom a risk management perspective

Arsham Mazaheri & Jakub Montewka & Pentti Kujala

Received: 1 March 2013 /Accepted: 27 November 2013# World Maritime University 2013

Abstract Ship grounding accidents, being one of the major types of maritime acci-dents, are significant failures putting in danger maritime transportation systems.Moreover, the risks associated with those failures can be catastrophic for the system,society, and the environment. This highlights the importance of appropriate methodol-ogy for assessing and managing the associated risk. Many scholars have introduced awide range of methods for modeling the risk, utilizing the concept of the probabilityand the consequence of an accident; however, those models very often employ criticalassumptions on the behavior of maritime transportation systems, which may seem notto be supported by evidences. This in turn limits models' ability to mitigate the risks, asthose simply remain unknown. Therefore, this article has three aims. First, it proposes amethodological framework suitable for knowledge-based risk modeling, fulfilling therecommendations given by the Formal Safety Assessment issued by the InternationalMaritime Organization. Secondly, it thoroughly reviews and discusses all the existingrisk models available in the literature developed for ship grounding risk analysis in lightof the proposed risk perspective. Third, the models that are more appropriate for riskmanagement and decision making are highlighted and the recommendations are givento future model developments.

Keywords Ship grounding . Accident probability . Risk modeling . Riskmanagement .

Decisionmaking

1 Introduction

Ship grounding accident is a type of marine accident that involves the impact of a shipon seabed or waterway side. It may result in the damage of the submerged part of theship's hull and in particularly the bottom structure, potentially leading to water ingress,which may at the end compromise the ship's structural integrity, stability, and finally

WMU J Marit AffairsDOI 10.1007/s13437-013-0056-3

A. Mazaheri (*) : J. Montewka : P. KujalaSchool of Engineering, Department of Applied Mechanics, Marine Technology, Aalto University,P.O. Box 15300, 00076 Aalto, Espoo, Finlande-mail: arsham.mazaheri@aalto.fi

safety. Severe grounding applies extreme loads onto ship structures. In less graveaccidents, it might result in merely some damages to the hull; however, in most seriousaccidents, it might lead to hull breach, cargo spills, total loss of the vessel, and in theworst case, human casualties. In global perspective grounding accounts for about onethird of commercial ship accidents all over the world (Kite-Powell et al. 1999; Jebsenand Papakonstantinou 1997), and it has the second rank in frequency, after ship–shipcollision (Samuelides et al. 2009).

Many scholars (e.g. Fujii et al. 1974; Macduff 1974; Pedersen 1995; Simonsen1997; Fowler and Sørgård 2000; Amrozowicz 1996b; Amrozowicz et al. 1997) havetried to model this type of ship accident in order to predict the likelihood of the accidentgiven certain criteria, which then allows risk estimation as specified in the InternationalMarine Organization (IMO) guideline (IMO 2002). One of the matters one shouldconsider when modeling a complex phenomenon, like ship grounding, is the tradeoffbetween the details and the accuracy of the model, and the cost of the model in terms ofthe required time and data; therefore, “elegant simplicity instead of unnecessarycomplexity” (Amrozowicz et al. 1997) is highly appreciated. Moreover, since theultimate goal of risk modeling and risk assessment is to provide information requiredfor decision making to mitigate the risk (IMO 2002), merely being aware of theaccident risk, as a single number, is not crucial. Thus, a suitable model for riskmanagement purposes should, firstly, reflect the knowledge on the analyzed systemwith satisfying accuracy (Aven 2013), secondly, be able to suggest the feasible andmeaningful measures for lessening the involved risk, and, thirdly, make a comparisonamong the measures based on predefined objectives and constraints that leads toselecting the optimal solutions at the end.

The existing reviews on the risk models of grounding accidents do not deeplydiscuss the weakness and strength of the models and the applied methods within a riskmanagement framework; see for example (Li et al. 2012; Przywarty 2008; Nyman2009; Mazaheri 2009; Pedersen 2010). Therefore, the aim of this paper is to provide acomprehensive and critical review of the available literature related to modeling the riskin maritime transportation systems (MTS) with the focus on ship grounding, within aframework of risk management for MTS.

For this purpose, Section 2 proposes a methodological framework suitable forknowledge-based risk modeling, fulfilling the recommendations issued by the IMOin the guidelines for Formal Safety Assessment. Section 3 thoroughly reviews anddiscusses all existing risk models available in the literature developed for ship ground-ing risk analysis. Section 4 highlights the existing models that are more appropriate forrisk management and decision making and provides the recommendations to futuremodel developments. The paper is summarized in Section 5.

2 Methodological framework

In the context of risk analysis, presented in Chapter 6 of the FSA guidelines (IMO2012), risk is defined as a product of the probability (P) and the consequences (C) of agiven action:

R ¼ P � C ð2:1Þ

A. Mazaheri et al.

whereas in the context of Chapter 7 (ibid), called “Risk control options”—aiming todetermine the areas needing control, the risk is decomposed and the uncertainty aspectof two risk components is added as an important element of the decision process.Moreover, for the identification of risk control measures, Chapter 7.2.2 (ibid) suggestsdeveloping the causal chains of events leading to an accident, which means that thedefinition of risk includes an insight in certain scenarios leading to the undesiredsituations. Finally, in the context of the recommendations, called “Presentation ofFSA results,” discussion about the assumptions, limitations, and uncertainties of therisk model is recommended (ibid).

To make sure that all these recommendations can be addressed at the last stage of theanalysis, the initial definition of risk must allow for the knowledge-based scenariobuilding, uncertainty analysis, and model validation (see Rosqvist and Tuominen 2004;Rosqvist 2010; Aven and Heide 2009). The most common definition of risk as theproduct of the probability of an accident and its consequences (Eq. 2.1) may thus leadto confusion, especially when comparing the risks associated with the following twosituations: A, frequent events resulting in low consequences with B rare events of highconsequence. Even though the products of P and C in both cases can be the same, thesetwo situations differ substantially. The background knowledge on A is most probablybetter than in the case of B, as A occurs frequent and B occurs rare. This knowledgeaffects the amount of uncertainty associated with the descriptions of A and B.Moreover, the measures to mitigate the risks are completely different.

Therefore, describing risk as the above combination, expressed as a single number,leads to the situation where much of the relevant information needed for knowledge-based decision making is not properly reflected. Thereby, the wider concept of riskshould be applied, allowing systematic reasoning.

2.1 Definition

Considering maritime traffic as a system, a well-founded approach to risk can befollowed (Haimes 2009; Aven 2011b), where the risk existing within the system canbe defined as a complete set of triplets (Kaplan and Garrick 1981):

R ¼ S; L;Cf gC ð2:2Þ

where this triplet attempts to answer the following questions: What can go wrong in thesystem (scenario—S), how likely is it that it goes wrong (likelihood—L), and what arethe consequences if the assumed scenario happens (consequence—C)? However,describing the risk as a complete set of triplets is unattainable, simply because ourknowledge on the system is never complete, thereby the system cannot be characterizedexactly (Aven and Zio 2011). Therefore, what we actually attempt to describe is anincomplete set of triplets, called “a set of answers” (Kaplan 1997), which reflects thedefined risk for the given system according to our best knowledge and anticipation.This incompleteness, which may result from lack of background knowledge on thegiven system, should be recognized.

To define a set of outcomes, knowledge and proper understanding of the system orphenomena being analyzed is a prerequisite; this is referred to as background knowl-edge (BK) in this paper. Therefore, risk perspective should account for the amount of

Modeling the risk of ship grounding - a risk management perspective

available BK. Thus, the description of risk perspective for the given system can yield asfollows:

R∼ S; L;CjBKf g ð2:3Þ

where S stands for a set of explanatory variables for a given scenario, where thevariables and their relations can take different values due to the stochastic nature ofthe phenomena being analyzed or by applying different assumptions, which depends onour background knowledge (BK) of the process being analyzed; L is a set of likelihoodscorresponding to the set of consequences C, for a given scenario and the givencombination of assumptions governing the input variables.

If the results of the risk analysis are utilized for the risk management, the measures tocontrol or mitigate the risk [risk control options (RCO)] are determined and their effectson the risk are studied. The risk control options can address the likelihood or theconsequence part of the risk, but they should be demonstrated in the context of theanalyzed scenario, adopted assumptions, and the available BK. Thus, an answer to thefourth question is sought: What can be done to efficiently mitigate the risk, meaningpreventing the accident from happening (proactive approach) or reducing the conse-quences given the accident happens (reactive approach), and which option is the mosteffective and economically justified?

Therefore, from the risk management perspective, it is important that the formaldefinition of risk, which is adopted, enables the reliability check of the model togetherwith the model validation (Aven and Heide 2009).

2.2 Background knowledge

A clear representation of BK that is available about the given system is relevant for anymodel, which is intended for practical use; see (Aven 2013). Since the lack ofknowledge about the underlying phenomena governing the behavior of the analyzedsystem leads to uncertainty in the model parameters and on the hypotheses supportingthe model structure (Aven and Zio 2011), it is desirable for a risk framework tocommunicate the BK level and the involved uncertainties (IMO 2002; Aven 2010;Rosqvist and Tuominen 2004), in order to determine whether the risk results areinformative and can be used for decision making, or should be used with great caution.The latter may be the case if the uncertainties are greater than the margin between theestimated risk and the risk limit.

2.3 Scenario

A fundamental and most probably the most important stage of any risk analysis, whichin turn affects all the steps following the analysis, is scenario identification, meaning theproper description of the knowledge on a system and its behavior. Intuitively, theimportance of this step seems obvious, while it does not always receive due credits (seeApostolakis 1990; Rae et al. 2012). A scenario can be defined as a realization of a chainof events triggered by an initiating event (IE). The IE may cause the system to movefrom its predefined safe and efficient trajectory (S0) towards the set of trajectories (Si),which are not as safe and effective as S0, but it does not mean they are all unsafe. The

A. Mazaheri et al.

system being on its trajectory Si travels through various mid-states (MS) at whichtransitions take place, redirecting the system towards the end states (ES). The latter canbe either an undesired event, like an accident, or safe operation of MTS, which meansthat the system may return at some point to S0; for a thorough discussion on this, areader is referred to the original work of Kaplan (1997).

Different trajectories of the system, each deviated from the predefined safe trajectorywith an IE, may share some MSs and end up in a common ES; see Fig. 1. Therefore, ascenario over the space state of the system can be formulated as:

s ¼ IEi;∪j¼1

n

MS j;ESk

� �ð2:4Þ

Taking MTS and ships operating there as an example, the S0 means the safe andefficient transitions of the system within predefined space state, as depicted in Fig. 1.Any event requiring an action of the system agents, like ship heading shallow water,can be considered as an IEi. Depending on the action taken (e.g., grounding evasivemaneuver) referred to as MSj, the system can continue along S0 towards ES0 (safeoperation) or goes through Si, heading to ESk meaning accident or other failure insystem operation. From the ship perspective, where the risk analysis is performed in thetime domain, the S0 can be tantamount to safe and undisturbed arrival to harbor,whereas all other scenarios leading to nonsafe arrivals or nonarrivals would belong toSi. When describing risk in a MTS, the main focus should be on understanding thesescenarios that ultimately lead to undesired events, as those govern the remainingelements of the risk equation (Eq. 2.3). Scenario identification can be tantamount withdiscovering causality, which seems to be the natural way of understanding, analyzing,and finally mitigating the hazardous situations which produce risks (see Roelen 2008;Ale et al. 2009; Roelen et al. 2011). In the maritime transportation, this approach is notcommonly adopted; however, in the recent years, some researchers made attempts tofollow this way of describing and analyzing maritime accidents (e.g., Mullai andPaulsson 2011; Kristiansen 2010).

When it comes to risk management, the accident scenario can be divided into twophases: pre- and postaccident (Fig. 1). Therefore, two different approaches of mitigat-ing the risk can be studied, namely, proactive and reactive. The former can focus on

Stat

e of

the

Syst

em

Time (t)

S0 or Success

IE2

e.g. “Black Out”

IE1

IEi

MS1

MS2

MSj

ES1

ES2

ESk

e.g. “Loss of Control”

e.g. “Emg. Anchoring”

e.g. “Self-repair”

Undesired Event

RCO2

RCO1

Pre-Accident Accident (Undesired Event)

Post-Accident

IEi

MS1

ESk

ES1

IE1

MS2

ES2

e.g. “Engine Failure”

Safe Arrival

e.g. “Laying Booms”

e.g. “Oil Spill”

e.g. “Coastal Contamination”

e.g. “Oil-Combat Vessels”

Fig. 1 The trajectory of a “success” or safe scenario in the state space of a system is called S0. Deviation ofthe system's trajectory from S0 by an initiating event (IE) goes through some mid-states (MS) and ends to anend state (ES). Deviated trajectories from S0 may share MSs and ESs. Risk control option (RCO) diverts thetrajectory of the system from some undesired MSs and ESs by breaking the chain of hazardous events. An ESof the preaccident stage can act as an IE for the postaccident stage

Modeling the risk of ship grounding - a risk management perspective

actions to reduce the likelihood of an accident, whereas the latter focuses on lesseningthe consequences of an accident. Such a division is easy to understand andclear to perform if the formal definition of risk is adopted, as given in Eq. 2.3.Both phases (pre- and postaccident) require the same steps to be taken(S,L,C|BK), in order to evaluate and mitigate the risk.

2.4 Likelihood

To quantify the second component of risk, namely, the likelihood of an accident, a well-founded mathematical concept of probability can be adopted. However, this requires ananswer to a question on the meaning of the probability, which in turn depends on aninterpretation of the probability adopted (for discussion about this topic, see Aven andReniers 2013; Apostolakis 1990; 1988; Kaplan 1997). In the engineered systems, thefollowing three interpretations are often in use:

1. The relative-frequency interpretation of probability defines the probability of anevent in terms of the proportion of times the event occurs in a long series ofidentical trials (Winkler 1996).

2. The subjective interpretation of probability views the probability as a degree ofbelief, and this notion can be defined operationally by having an individual makecertain comparisons among lotteries. This implies, of course, that different peoplecan have different probabilities for the same event (see Winkler 1996).

3. The probability of frequency applies when there is a repetitive situation or canimagine one as a thought experiment. However, since the experiment has not beenconducted, we are uncertain about the frequency. Therefore, our knowledge aboutthe frequency is expressed with the probability curve (Kaplan 1997). However, thiskind of interpretation can be seen as subjective.

All those interpretations are rooted in the concepts of probability, which are based onsolid mathematical foundations; however, the proper implementation and interpretationare challenging. The probabilities, as the mathematical concepts, follow certain axiomsthat in some real-life cases may not hold the true.

2.5 Consequence

The consequences are considered as the negative outcomes of a scenario; there-fore, their interpretation may depend on the adopted approach of risk manage-ment (proactive or reactive). In the case where the proactive measures aresought, since the aim of risk management is to actively influence the way theships are navigated to minimize the chances of accidents, the ultimate conse-quences can be understood as the negative outcome of ship navigation, meaningthe accident itself. However, if the reactive measures are involved, then theconsequences can be seen as the negative outcome of an accident, meaning theenvironmental pollution resulting from an oil spill in case of accidents wheretankers are involved, or human loss in case of ships carrying passengers.

The existing models for ship consequences analysis are capable of evaluating thedamages to a ship given an accidental scenario, in a very detailed and accurate way(e.g., Ehlers and Tabri 2012; Hogström and Ringsberg 2012). However, in order to

A. Mazaheri et al.

obtain these estimates, the detailed input data on the scenario path leading to anaccident with all relevant IEs and MSs are the prerequisite (e.g., masses of ships andtheir speed, loading conditions, etc.). The major problem that most of the modelssimulating maritime traffic and the resulting accidents are facing is the lack ofsupporting evidences for the assumed relations between IE, MS, and ES, meaning thatthere are gaps in the scenarios. Moreover, the gaps exist in very sensitive part of thescenarios (Goerlandt et al. 2012), meaning that there is a need for a proper, reliable, andevidence-based definition of the parameters involved in the accident. This shows andproves that if the accidental scenario cannot be determined in a sound and reliablefashion, then the consequences cannot be expected to be evaluated reliably (Goerlandtet al. 2012), since a combination of uncertain factors can only increase the associateduncertainties (Rae et al. 2012).

2.6 Risk control option

Referring to the way that a scenario is defined in Eq. 2.4, an RCO prevents the transitionof the system from an IE to specific MS or ES, or from a MS to a specific MS or ES.Therefore, an RCO can mitigate the risk by breaking or redirecting the chains of thehazardous events and therefore protects the system from transition to an undesired state(Fig. 1). Kaplan and Garrick (1981) have hypothetically stated that to eliminate risk oneneeds to eliminate hazards. However, in reality, we are not able to eliminate risk but tochoose between them. This creates the question of the best decision options for the givensituation. These options cannot be efficiently selected without proper understanding of asystem, its behavior, relationships among its elements, and mutual interactions. Thismeans that the RCO cannot be effective nor be properly implemented if the uncertaintiesassociated with their type and location in the state space (see Fig. 1) and their impacts onthe system are not identified and, preferably, quantified if possible. Otherwise the choiceof RCOs may be just selection between the sets of options suitable for a model, whichdoes not reflect the reality and explains nothing but itself.

3 Review of the existing models

3.1 Scope of the Review

As mentioned, the fundamental phase of a risk modeling, having in mind the riskmanagement perspective, is a process of scenario identification along with evalu-ation of background knowledge about the analyzed system, in order to determinethe appropriate risk control options. In the context of this paper, the maritimetransportation is defined as a system, and the scenarios of the reviewed modelsare assessed as they all share the same ES referred as ship grounding accident. Theapproaches that each model follows for building the scenarios, meaning whether thescenarios are knowledge-based or imaginary, are reviewed and discussed.Moreover, the ways that BK is incorporated in the models are discussed. Theultimate aim of this analysis is to highlight those models, which allow for riskperspective as given by Eq. 2.3, which reflects the best the IMO recommendationgiven in FSA and meet the formal definition of risk, as per Stirling and Gee (2002).

Modeling the risk of ship grounding - a risk management perspective

The models in the literature have also been reviewed to detect whether the models arecapable of detecting the plausible RCOs as an important stage of a risk managementprocess. Currently, the risk is mostly mitigated by applying RCOs, which are suggestedby the domain experts (see Amrozowicz 1996b; Briggs et al. 2003; DNV 2003), whichmainly relate to their knowledge on the way that the system works, meaning that theeffective RCOs cannot be defined based on the model. Therefore, in order to assess thepracticality of the existing grounding models for risk management, the ability of themodels for showing and testing the RCOs on the current associated risk as well as thefuture scenarios before the implementations of the RCOs (Haimes 2009) should beinvestigated. It is believed by the authors that setting the ES of a system at a desired statein a risk model and then reverse analyzing the scenarios to the possible IEs throughdifferent MSs will reveal the feasible RCOs for mitigating the risk of the modeledsystem and achieving the desired ES. Hence, the reviewed models and their keyelements have been also analyzed from this perspective. Moreover, the key elementsof each model that are playing the role of the inputs for the model are reviewed andpresented, and the ways each model quantifies its key elements are discussed.

To extract the existing models, more than 90 relevant articles, reports, and disserta-tions all written in English have been reviewed. However, not all of the reviewedliteratures were presenting a genuine model for grounding accident risk analysis; someof them have studied the different causality of grounding accidents in qualitative andquantitative manners (e.g., Jebsen and Papakonstantinou 1997; Lin et al. 1998; Martinsand Maturana 2010; Samuelides et al. 2009; Quy et al. 2006; Briggs et al. 2003; Laxand Kujala 2001; Amrozowicz 1996a; Brown and Haugene 1998; Kite-Powell et al.1999), and some have implemented the models of the others (e.g., Friis-Hansen andSimonsen 2002; Gucma 2002; Chen and Zhang 2002).

In order to have a more organized discussion, the reviewed models are categorizedinto two groups based on the kernel of the implemented method: group 1, analyticalmodels, where the scenarios of ship grounding are obtained based on a geometricaldescription of the event; and group 2, probabilistic models, where techniques such asFault Tree and Bayesian Network are used for modeling.

3.2 Analytical models

3.2.1 Macduff (1974) and Fujii et al. (1974)

The idea of analyzing the ship accidents by the way of modeling was traced back toMacduff (1974) and Fujii et al. (1974) and Fujii and Shiobara (1971), when theyexpressed the idea of causation probability. Macduff mentioned that the probability of agrounding accident should be estimated as a combination of two probabilities, so-calledgeometrical (PG) and causation (PC). Geometrical probability of grounding gives thelikelihood or the number of the ships that are grounding candidates, assuming the blindnavigation, which is defined as no grounding evasive maneuvers are performed.Causation probability expresses the likelihood that the ship heading a ground will notevade it due to variety of reasons.

Fujii expresses the expected number of groundings (NG) (Eq. 3.2.1) as a function ofthe ship's speed (V), the traffic density (ρ), and the width of the shoal (D) in addition tothe causation probability (PC), while Macduff implemented Buffon's needle problem

A. Mazaheri et al.

(Fig. 2) to estimate the geometrical probability of grounding (PG) (Eq. 3.2.2), meaninga ship hits the wall of a waterway, as a function of two parameters, namely, the width ofthe waterway (C) and the stopping distance (T). The latter is defined as a function of theship's length and the speed.

NG ¼ PCDρV ð3:2:1Þ

PG ¼ 4T

πCð3:2:2Þ

From among the key elements of Macduff and Fujii's models, one may be able toalter the associated risk only by affecting the ship particulars, since the rest of theinvolved elements are location-related and are practically unchangeable. Thus, owingto the fact that the factors affecting the causation probabilities implemented in themodels are unknown, the models cannot recommend any feasible RCOs. The modelsassume ship navigation as a random process, which cannot find support in the practice.Moreover, since the models are not scenario oriented, they do not provide anyknowledge regarding the possible triggering causes of the accident. The ships areassumed to be in a grounding course without providing any prior knowledge of therationale. Thus, IEs and possible MSs for a grounding accident cannot be identified,which makes the followed approach improper from a risk management perspective.Besides, the models present the number of the grounding candidates as a singlenumber, which is then calibrated with the causation probability that comes from theaccident history in the location. The method of calibration by merely using historicalaccident data introduces uncertainty to the modeling, which is irreducible as it is relatedto the unknown causes in the past state of the system (Rowe 1994). Additionally, usingtraffic density, especially when the traffic is assumed as uniformly distributed, isanother source of uncertainty. However, this can be resolved to some extent by

Fig. 2 Macduff (1974) implemented Buffon's needle problem to estimate the geometrical probability ofgrounding [reference: adapted from Macduff (1974)]

Modeling the risk of ship grounding - a risk management perspective

replacing the traffic density with the actual pattern of the traffic in the area (Mazaheriand Ylitalo 2010). Therefore, from a risk management perspective, the models cannotbe validated as they are not presenting the measures for controlling the risk. Besides,the models cannot be verified as the causation probability, which acts as a black box,keeps most of the affecting parameters hidden. Moreover, the models do not cover theconsequence of a grounding accident nor provide any knowledge that can be used forconsequence analysis. Although this is not an issue as such, it makes the validation ofthe model hard when it comes to a postaccident risk analysis.

Despite the above argument, the method has been widely accepted by other scholarsfor modeling the ship grounding accident (e.g., Pedersen 1995; Simonsen 1997; COWI2008; Rambøll 2006). The general idea of the method was to use the trajectory of thevessel's current heading to find if it will have any intersection with nearby shoals orgrounds given certain sets of conditions, e.g., meteorological conditions. The differ-ences between various models are on utilizing the available knowledge to model thefactors that can affect on the prediction of the ship's heading, which in Macduff andFujii's models are only the function of the width of the waterway and speed and lengthof the ship. Thus, the other possible contributing factors like human elements, ship'smaneuverability, and the environmental aspects were all neglected by the way that theydefined the causation probability.

3.2.2 Pedersen (1995) and Simonsen (1997)

In spite of its limitations, the methodology presented in Section 3.2.1 has been adoptedby Pedersen (1995) and, later on, Simonsen (1997) to develop their models (Eq. 3.2.3).This helped the widespread use of the method (see for example IWRAP 2009;Kristiansen 2005; Otto et al. 2002; Rambøll 2006; Fowler and Sørgård 2000;Karlsson et al. 1998). They estimated the expected annual number of groundings(NG) as:

NG ¼Xn class

Ship class i

PC;iQie−d=ai∫

Zmax

Zminf i zð Þdz ð3:2:3Þ

Similar to Fujii's, the models of Pedersen and Simonsen estimate the potentialnumber of groundings (NG), where PC represents the causation probability. However,the key elements of the models were extended to the ship type and the deadweighttonnage (ship class, i), the annual number of transshipment (Q), the average timeinterval between the position checks by the navigator (a), and the width of thewaterway (d). Additionally, instead of traffic density, the actual traffic distribution ofships (f) through the transverse coordinates of the obstacle (z) is used (see Fig. 3).Nowadays, one can use AIS-data to accurately extract the real traffic properties likedistribution of the ships in a certain path (see IWRAP 2009; Goerlandt and Kujala2011; Montewka et al. 2011; Montewka et al. 2010a; Talavera et al. 2013).Nevertheless, using only the traffic distribution of ships means that the event is beinginvestigated in deductive manner, which means neglecting the role of the individualship's maneuverability for avoiding the accident. This has been pointed out by Kaneko(2010), where he used an inductive approach to address the problem. Nonetheless, for

A. Mazaheri et al.

more accurately modeling the ship grounding accident, both approaches should be usedand the event should be modeled by simultaneously taking the role of the whole traffic,if there is any, and the individual ships into account.

Pedersen and Simonsen's models also present the grounding candidates as a singlenumber; however, their models additionally provide the information that is helpful forconsequence analysis, like the type and size of the ship that is involved in the accident.Pedersen and Simonsen's models are scenario-based models, where four predefinedgeneral scenarios are (1) when the ships are following the ordinary and direct route atnormal speed, and accidents happen mainly due to human error, or unexpectedproblems with the propulsion/steering system which occur in the vicinity of a shoal;(2) the ships which fail to change the course at a given turning point near the obstacle;(3) the ships which take evasive action in the vicinity of an obstacle and as a resultground on a shoal; and (4) the ships are off-course or drifting ships. Thus, themodels introduce four quite general IEs that scenario analysis process can bestart from. Although the presented scenarios are quite useful for risk assess-ment, the question about being useful for decision making process and thus forrisk management is still open.

For estimating the causation probability (PC), Pedersen and Simonsen have usedfault tree analysis (FTA), where the required data has been extracted from eitherhistorical accident databases or through expert opinions. Nevertheless, their modelsare still quite sensitive to the value of causation probability (Mazaheri and Ylitalo2010), as it is assumed that the ships are being navigated blindly in the waterway and,consequently, some important factors like the maneuverability of the ship and thehuman role to navigate the ship have still been neglected. Implementing FTA toestimate the causation probability, where the utilized knowledge can be closelyassessed by looking at the contributing elements, is more logical than restoringhistorical accident data to calibrate the causation probability. This procedure can reduce

Fig. 3 General scenarios for grounding defined by Pedersen (1995) [reference: Pedersen (1995)]

Modeling the risk of ship grounding - a risk management perspective

the involved uncertainties and has actually been recommended for risk assessment forpractical decision making (Aven and Zio 2011). However, some elements of knowledgethat is implemented into the model by Pedersen and Simonsen, like the effect of traffic(Q) and ship class (i) on a grounding accident, are not evidence-based and comes fromsome general assumption (Mazaheri et al. 2013a).

3.2.3 Fowler and Sørgård (2000)

Fowler and Sørgård (2000) have also used the same methodology as Pedersento estimate the frequency of powered (fpg) (Eq. 3.2.4) and drift (fdg) (Eq. 3.2.5)groundings as:

f pg ¼ npg Pcppg;c þ P fppg; f

� �ð3:2:4Þ

f dg ¼X

lf p;lpd

Xwpw 1−psr;w

� �1−pt;w� �

1−pa;w� �� ð3:2:5Þ

They have also utilized FTA to estimate the causation probability of grounding ingood (Pc) and bad (Pf) visibilities. However, they have defined the grounding candi-dates differently. Instead of integrating the probability density function of the shiptraffic over the transverse coordinates of an obstacle, they have defined two criticalsituations, where the grounding candidates in powered and drift groundings can berecognized. In order to define the critical situations, they have consulted experts. Forpowered grounding, the critical situation (npg) is defined as when the vessel is in agrounding course within 20 min of a depth contour less than the vessel's draft. For driftgrounding, the critical situation is defined as the product of the number of ship hoursthat are spent within 50 nautical miles of a shoreline and the probability that the vesselis drifted toward the shore (pd) within different wind speed categories (pw). Theprobability and the location of drifting are defined by combining the frequency andlocation of breakdown situations (fp) with three ways of regaining the control of adrifting ship as emergency anchoring (pa), self-repair (ps), and tug assistance (pt). Thedata that are used for the frequency analysis of different elements of the model arebased on some assumptions and simplifications that are not explicitly mentioned. Thisintroduces unknown levels of uncertainties to the model, which is thus irreducible.However, the authors have tried to address the uncertainty matters in the discussionpart, where they have discussed about the accuracy of the used databases. Nevertheless,since one of the matters that make a model useful for decision makers is the clarifica-tion of all the assumptions behind the actual model and its elements, the verification ofthe model cannot be done flawlessly when it comes to the involved uncertainty.Moreover, the model estimates the grounding frequency associated to an area, withoutassessing the possible consequences or having the potential to deliver the knowledgerequired for a post-accident consequence assessment.

3.2.4 Eide et al. (2007)

Eide et al. (2007) have used the same procedure as Fowler and Sørgård (2000) formodeling the drift grounding, though omitting the emergency anchoring from the

A. Mazaheri et al.

possible control regaining options, which is acceptable as the model is aimed for thedeep coastal waters of the Norwegian Sea. However, this needs to be reconsidered if themodel is used in more shallow water areas with possibility of emergency anchoring.The advantage of the model over the model of Fowler and Sørgård (2000) is theutilization of the dynamic meteorological data as wind, current, and wave and theacknowledgment of the dynamic nature of ship related conditions as position andspeed, which are affecting both the frequency (F) and consequence (C) of driftgrounding (Eqs. 3.2.6 and 3.2.7).

Risk x; y; tð Þ ¼ F x; y; tð Þ � C x; y; tð Þ ð3:2:6Þ

F x; y; tð Þ ¼ Fdrift � Pgroundingjdrift x; y; tð Þ ð3:2:7Þ

The frequency of drifting is estimated based on the available statistics on the failurerates of steering and propulsion for different ship types as well as some modificationfrom experts' judgment. The probability of a grounding accident given a drifted vesselis estimated given the control regaining options as self-repair and tug assistance as wellas the dynamical surrounding conditions. The required probability density functions arebased on statistics and are modified from the previous studies.

Eide et al. have modeled the consequence of the tankers drift groundings in two partsas size of oil spill, which depends on the ship size, loading condition, and the hullstructure as double or single hull; and as the impact of one tone of spilled oil on theenvironment, which depends on the sensitivity of the location of the spill and on thetype of the spilled oil. Therefore, their model is basically capable of providing therequired knowledge for postaccident consequence analysis, which makes it moresuitable for risk management than what is previously presented for the purpose of riskanalysis. However, the oil outflow model used by Eide et al. is rather a simplemodel that is based on the statistics of the previous tanker accidents. In this regardand in order to be more comply with the dynamic nature of the presented risk modeland decrease the level of the involved uncertainties, dynamical oil outflow models(e.g. Sergejeva et al. 2013; Tavakoli et al. 2010) that more accurately estimate theoil outflow as a result of a grounding accident should be used instead. Additionally,the consequence analysis of their model can be greatly enhanced if a more detailedmodel (e.g., Lecklin et al. 2011) is used for impact analysis of the spilled oil on theenvironment.

Nevertheless, the presented approach encompasses uncertainty description. Thediscussion is quite detailed and outstanding, and the uncertainty analysis has beenperformed qualitatively. This allows the comparison between the risk levels of differenttanker accidents. Therefore, from a risk management perspective, this approach mayseem to be useful.

3.2.5 COWI (2008)

COWI (2008) has performed FSA by implementing Pedersen's approach, as presentedin Section 3.2.2. Therefore, COWI's model is another revision of Pedersen's modelwhile using the distribution of the course over ground (COG) of the ships in the vicinity

Modeling the risk of ship grounding - a risk management perspective

of shoals (Fig. 4). In addition to Pedersen's expression of probability of grounding,COWI expresses the probability of grounding (PG) as:

PG ¼ F α1ð Þ−F α2ð Þ ð3:2:8Þ

where F is the Gaussian distribution of the ship's COG in the vicinity of the shoals thatits parameters are extracted from the AIS data; α1 and α2 are the COG angles that thetrajectory of the ship has intersection with the nearby shoal (see Fig. 4).

Perhaps, implementing the distribution of COG in the vicinity of shoals can be seen astaking the ship's maneuverability into account since quite the same approachwas followedby Kaneko (2010), who believed that Pedersen neglected the role of the individual ship'smaneuverability in accident avoidance. Nonetheless, the question is whether the distribu-tion of the COGs of the ships from the historical data (here AIS or radar) can necessarilyreveal the individual ship's maneuverability. Excluding the COG distribution of the ship,the COWI's analytical model is the same as Pedersen's model, which identifies thescenarios from the four general IEs, as described in Section 3.2.2. Nevertheless, insteadof applying FTA, COWI has borrowed and calibrated the causation probability fromFujii's model. This keeps the concerns explained above for both Fujii and Pedersen'smodels still valid for COWI's model.

3.2.6 Montewka et al. (2011)

Montewka et al. (2011) have also considered the maneuverability of an individual shipin their model, where the interaction between the ship and the shoal is evaluated in

Fig. 4 Ship maneuverability based on the course over grounds of the ships [reference: COWI (2008)]

A. Mazaheri et al.

different locations. For this purpose, a utility function is defined, which encompasses aset of variables as the characteristics of the vessel together with the spatial properties ofthe waterway and the traffic. The characteristics of the vessel are modeled by themaximum draught, the turning circle, and two coefficients that one describes thedistance at which a hazard to the vessel can be detected and one represents the technicalequipment possessed by the ship. The spatial properties of the waterway are modeledtaking into account the depth of the channel by coefficients that represent the soundingaccuracy of the depth and the seabed composition. In contrary to COWI (2008) andKaneko (2010), Montewka et al. (2011) have taken into account the maneuverability ofindividual ships based on indices like the maximum draft of the ship and the resultingradius of the turning circle; and have estimated the consequence of the accidentexpressed in the amount of oil spilled using the generic methodology proposed byIMO. However, the concern about the disability of providing the RCOs for riskmanagers by reverse analysis of the scenarios is valid for this model. Montewkaet al. have utilized the physical description of the event (grounding accident) that madethem able to validate the model within its defined aim, which is determining the mostnavigable, i.e. safest route, for a single vessel. Nevertheless, since the physics of theevent is considered the only cause of the accident, the model lacks an evidence-basedapproach, which makes it hard to validate the model in the framework of knowledge-based risk management.

3.3 Probabilistic models

Probabilistic models can be seen as a tier above the analytical models. As complemen-tary to analytical models, probabilistic models analyze the grounding accident from amore holistic and systematic view, utilizing different methods like FTA or Bayesianapproach. By a FTA, the grounding accident as the top event is broken down into itsinitiating factors, and by the Bayesian approach, the key factors that contribute to theaccident are recognized together with the degree of belief associated with the states ofeach factor, and they are taken into account as a Bayesian Belief Network (BBN). BBNhas been suggested as a suitable tool for analyzing the complex phenomena underuncertainty with deterministic and stochastic data allowing the causality discovery(Kristiansen 2010; Kaplan 1997). Moreover, the Bayesian probability theory has beenspecifically mentioned as a suitable method to handle the uncertainty as it allows themeasurement and combination of different types of uncertainty (Paté-Cornell 1996).

There are some issues that makes using BBN more suitable than FTA for riskanalysis purposes in probabilistic models (Kristiansen 2010). From among them, twoissues can be highlighted; in FTA the events can have only two states (binary events);otherwise, since the failures in FTA need to always be sequentially dependent, theprocess would become complicated for multistate events, as the size of the tree growsexponentially by the number of the involved parameters. The other issue is that, inFTA, the events need to be statistically independent (Bobbio et al. 1999), and it iscomputationally difficult to use common mode failures in FTA (Kristiansen 2010).However, in BBN, for the nodes (failure elements) that the parents are uncertain orunknown, the incomplete Conditional Probability Tables (CPT) can be neglected byimplementing so-called noisy-or model (Bobbio et al. 1999). Additionally, from riskmanagement perspective, a unique inherent ability of a BBN is the possibility to

Modeling the risk of ship grounding - a risk management perspective

perform backwards reasoning on the model to find the most probable causes of thesystem failure, which is essential for determining RCOs (Bobbio et al. 1999). BBNs arecapable of handling multistates scenarios burden with uncertainty and lacking knowl-edge. Finally, such models allow introducing decision and utility nodes, which makesthem suitable for fast decision-making processes.

3.3.1 Amrozowicz (1996)

With this being said, Amrozowicz performed a FTA on tankers grounding. He analyzedthe scenarios by defining two ESs as powered and drift groundings, knowing the factthat they are mutually exclusive events (Eq. 3.3.1) (see Amrozowicz et al. 1997;Amrozowicz 1996b,a). Each type of grounding has been put in a FT as the top eventand has been broken down to its basic events. By taking a system analysis approach,Amrozowicz (1996a) has used expert knowledge to develop the FTs. To estimate theprobabilities, historical data was used in addition to expert judgment. For analyzing thehuman errors and estimating their probabilities, he applied the Technique for HumanError Rate Prediction method, which is recommended by IMO (2002) for humanelement analysis in FSA, while consulting the Handbook of Human Reliability thatis written mainly for nuclear industry. For drift grounding, Amrozowicz (1996a)considered two rescue options as the tug assistance and the emergency anchoring, yetneglected the chance of the self-repair for avoiding the drift grounding.

P groundingð Þ ¼ P poweredgroundingð Þ þ P drift groundingð Þ ð3:3:1Þ

In order to tackle the uncertainty due to using expert opinion, Chen and Zhang(2002) added fuzzy concept to Amrozowicz et al. (1997) FTA for powered groundingby applying the theory of Fuzzy Fault Tree (Singer 1990). Therefore, the final resultswill contain the uncertainty associated with the accident probability estimation, whichwill be also present while making decisions based on the model outcomes.

3.3.2 Rambøll (2006)

Rambøll (2006) incorporates the analytical model of Pedersen as part of its probabilisticmodel (Fig. 5). Similar to COWI (2008), Rambøll has applied a scenario-basedapproach following the framework of FSA in the modeling process. The causationprobability has been defined using BBN, while the geometrical probability of a shipbeing a grounding candidate is added to the network by nodes expressing the elementsof Pedersen's analytical model. Thus, Rambøll has replaced the FTA in Pedersen modelby a BBN keeping the same elements; thereby from the conceptual point of view, thetwo models do not differ much. Similar to Pedersen, Rambøll has tried to bring theenvironmental condition into account by merely adding the node “visibility.”Moreover, the technical failure only includes failure from radar and not steering orpropulsion; thus, it limits some plausible IEs for a grounding scenario. In addition, aBBN has been utilized to model the postaccident consequence, which is fed by theoutputs from the frequency network, such as the ship type, ship size, and the speed thatall are actually the outputs from Pedersen's analytical model. The consequence modelthen combines these outputs with the other nodes that give the amount of cargo and

A. Mazaheri et al.

bunker oils and the number of passengers onboard. It then gives the amount of oil spillor human casualties as the result of the grounding accident. Nevertheless, all theassumptions behind the BBN model by Rambøll, which some come from Pedersen'smodel and some from experts' opinions, make the model a nonevidence-based modelthat does not fit to knowledge-based risk management.

3.3.3 DNV (2003)

Another BBN model for collision and grounding accident analysis has been proposedby DNV (2003). The main network has two subnetworks on operator's behavior andthe situation of the vessel (see Fig. 6). The study is made in FSA framework and byhaving cruise vessels in mind. The structure of the model has been defined by a groupof experts, and statistical data have later been used to calibrate the model. The CPTs ofthe nodes were also estimated using expert judgment and historical accident data. The

Fig. 5 The geometrical model to estimate the grounding candidate on a route with a bend [reference: Rambøll(2006)]

Modeling the risk of ship grounding - a risk management perspective

uncertainties associated on the system behavior are also discussed, though how theuncertainties affect the output of the model is not addressed.

The geometrical part of the model has five IEs, which creates five different scenariosfor a ship to be a grounding candidate. They are defined as when the ship is: (1) in acourse towards a shoal, supposed to change the course, does not; (2) in a course alongthe shore, not supposed to change the course, turns towards the shore; (3) in a coursealong the shore, she drifts-off the course, should correct the course, does not; (4) in awrong position towards an obstacle, should steer away, does not; and (5) in meeting/crossing traffic, gives way, steer towards a shoal (see Fig. 7). Thereby, the scenarios aremainly defined based on the experts’ knowledge about the system.

In addition to the human and the environmental factors, the model contains thecausality from the technical, organizational, and managerial factors. Notwithstandingthe model's ability for backwards reasoning, the RCOs have not been determined as thedirect outcome of the model and they have been suggested by domain experts whilethey have focused on reducing the frequency of grounding accidents.

Fig. 7 Five grounding scenarios defined by experts [reference: DNV (2003)]

Safety Culture

Fatalities

GROUNDING

Vessel damage

Course towardsshore

Vigilance

Work Conditions Managementfactors

TechnicalVessel loose

control

Humanperformance

Personnel factors

15

4

32

Situation of the vessel

Operator’s behaviour

Fig. 6 Overview of the Bayesian grounding model for passenger ships [reference: DNV (2003)]

A. Mazaheri et al.

3.3.4 Kristiansen (2010)

The only model that determines the causality in the system behavior having in mind theship grounding accident as an ES has been developed recently by Kristiansen (2010),who has analyzed the powered grounding accident utilizing accident reports andstructured the obtained knowledge into a BBN. Kristiansen was inspired by anapproach taken in the aviation industry (Luxhøj and Coit 2006) together with thefrustration from the lack of supporting empirical data on the maritime accident model-ing. The way that Kristiansen coded the data ends to have three major causes for apowered grounding accident as human factors, unsafe acts, and external factors (seeFig. 8). The study shows that the coding procedure of the data has influence on the finalstructure of the model by delivering the different relative frequencies for the casualfactors. Additionally, the Greedy Thick Thinning algorithm as a Bayesian searchlearning algorithm (Dash and Druzdzel 2003) that was used for structuring the BBNallowed the inputs from human experts as well as from the accident data (Mazaheriet al. 2013b). Therefore, one may question the level of experts' knowledge contributionto the learning process in order not to expose the contribution of the empirical data asan evidence-based approach.

Although the model is still in the initial stages and is not ready to be used for riskanalysis objectives, and the learning data on grounding accidents used for constructingthe model is limited to the Norwegian waters, it is an important step forward in the fieldof risk analysis and management of MTS. The model that is constructed evidence-based and based on the real scenarios—as opposed to imaginary—reflects the reality.This gives the opportunity to learn from the real data, thus showing the areas to beimproved in order to reduce the number of accidents.

3.3.5 Uluscu et al. (2009) and van Dorp and Merrick (2009)

All of the reviewed models till now, except Eide et al. (2007), are stochastic but staticmodels that are not considering the time issue into account. Nowadays, the widespreaduse of computers makes easier to address the time dependent factors by modeling thestochastic scenarios based on the historical data of time dependent elements to estimatethe frequency of an accident (van Dorp and Merrick 2009; Gucma 2006; Uluscu et al.2009; Goerlandt and Kujala 2011). For this purpose, either PC-based models or full-mission bridge simulators are utilized (Briggs et al. 2003; Gucma 2002).

Fig. 8 Powered grounding risk model by Kristiansen (2010) [reference: adapted from Kristiansen (2010)]

Modeling the risk of ship grounding - a risk management perspective

The power of PC-based simulation models is in the number of scenarios that theycan generate and analyze in a reasonable time. In this regard, using methods like MonteCarlo (MC), the models generate variety of IEs and MSs of traffic scenarios based onthe distribution of the input elements. Thereafter, by implementing different algorithms,the models analyze the likelihood of the various ESs of each scenario. Thus, the modelsestimate the frequency of the ESs that are grounding accidents and output them togetherwith the knowledge about the traffic scenario that can be fed to the consequence modelsfor postaccident analysis. Besides, by utilizing techniques like MC, PC-based simula-tion models have the ability to propagate the uncertainty of the input variables into theoutputs for further consideration of the decision makers, which is accepted as a way tohandle the uncertainty issues (Pedronia et al. 2012; Merrick and van Dorp 2006).

Using computer simulation, Uluscu et al. (2009) have randomly generated accidentscenarios. They estimated the frequency of powered grounding accidents in the Strait ofIstanbul using the proportional hazards model proposed by Cox (1972), which is madeon the assumption that the accident probability behaves exponentially with changes inthe related covariate values. This is the same method that has been used by van Dorpand Merrick (2009) [see also (Merrick et al. 2005a)] for simulating powered and driftgroundings in Puget Sound and surrounding waters. van Dorp and Merrick (2009) haveused computer simulation to predict the ship's position, course, and speed in a limitedtime frame, given certain conditions as covariate values, like meteorological conditionsas wind, current, and visibility. The ship and the route-related information for gener-ating the scenarios were extracted from the AIS data. The simulation for drift groundingscenarios runs till the drifting path of the vessel, which is predicted in a 5-h timeframeconsidering the effect of future wind speed and current, has its first intersection with adepth contour shallower than the draft of the vessel; however, no barrier options liketug assistance or emergency anchoring has been considered. The powered groundinglocations are defined as the most frequent depth contours that ships' trajectoriesintersect with within 5-h timeframe, conditioned to the constant speed of the vessel.The likelihood of the scenarios in both types of grounding was calibrated based on theexpert opinions. At the end, the model is able to produce a risk map based on thefrequency of the occurred grounding in the simulation timeframe. The same holds truefor the model by Uluscu et al. (2009), too. The strength of the simulation modelsfollowing the methodology presented in the literature (Goerlandt and Kujala 2011;Uluscu et al. 2009; van Dorp and Merrick 2009) lies on their abilities to feed theconsequence models with detailed and location dependent outputs. Simple conse-quence models for tanker grounding will use the particulars of the ships (e.g., dimen-sion and mass) that are involved in the accidents, to predict the size of the hole in abreached tank and then oil outflow after a tanker grounding accident (van de Wiel andvan Dorp 2009; Tavakoli et al. 2010; Montewka et al. 2010b). This approach has beenimplemented by van Dorp and Merrick using the consequence model of van de Wieland van Dorp (2009). van Dorp and Merrick (2009), however, have relied onexpert opinions for estimating the consequence of the accidents, using question-naires. Nonetheless, none of the simulation-based models presented here have theability of reverse analysis, in which the ES of a scenario is set at a desiredcondition and the possible option to reach the ES is obtained by a reverse scenarioanalysis. This can be generalized as the weak point of the simulation models thatdo not have a BBN kernel. Therefore, the RCOs in the simulation models as such

A. Mazaheri et al.

are not the outcome of the modeling process, rather they are generally recom-mended by the experts.

4 Discussion and recommendations

The above review of the available models for risk analysis of ship grounding shows thatthere is no single systematic and holistic method that can satisfy all the existingconcerns about the modeling process, such as the ability to provide and evaluatefeasible RCOs, inherent uncertainty of the data and the outcomes, possibility to easilyupdate the model when new information is acquired, possibility to generalize the modelover other locations and vessel types, the clarity of the affecting factors, and the abilityto handle dynamic variables.

Decision making is one of the critical parts of a risk management process. Fordecision making, three items are indispensable: (1) a set of the available options, (2) aset of the evaluated outcomes of each option, and (3) the value judgment on eachoutcome (Kaplan 1997). The value judgment should only be done by the decisionmakers provided with the set of the options. The RCOs in the reviewed papers have allbeen recommended by domain experts and not as the direct result of the modeling (seeTable 1). However, for a systematic and reliable decision making, the RCOs should bethe direct result of the knowledge-based modeling process, and the expert opinionshould be supplementary to the model's output. As if otherwise, the outcomes of theRCOs cannot be evaluated with the utilized risk model, and the final state of the systemafter the implementation of the control options will remain unpredictable. Besides,relying on only expert opinion for all three essential parts of decision making will pushsubjectivity into the risk management process. With that being said, neither of thepossible outcomes of the RCOs recommended for controlling the risk was actuallyevaluated in the reviewed papers. There are two major features that elevate a modelfrom the level of risk analysis to the level of risk management: (1) the reverse analysisof the scenarios that enables the model to identify the RCOs and (2) the ability of themodel to handle the decision nodes that can measure the effect of various RCOs anddetermine the optimal solution for an analyzed scenario (Hänninen et al. 2012,Hänninen et al. 2013; Helle et al. 2011; Lecklin et al. 2011). From among the reviewedmodels, only the models of DNV, Rambøll, and Kristiansen that are BBN-based modelsand have the ability of the reverse analyzing of the scenarios may have the above twofeatures and thus have the better potential to be used for risk management and decisionmaking purposes (see Table 1).

Another key issue is how a model addresses the involved uncertainty. Due to thelimited available background knowledge on the modeled system, always some level ofuncertainty is involved in the models used for risk assessment (Amrozowicz et al.1997), either in the way that the models are structured or in the way that the likelihoodof each element is quantified. In all the reviewed models, the historical data have beenused for quantifying the likelihood of the IEs and the MSs in the analyzed scenarios,which was unavoidable as the only way to understand a phenomenon is to look at whathappened in the past. However, since there are doubts on the ability of the historicaldata to predict the future state of a system (Paté-Cornell 2007), using the data from thepast state of a system will introduce (aleatory) uncertainty into the modeling (Rowe

Modeling the risk of ship grounding - a risk management perspective

Tab

le1

Com

parisonof

themodelswith

noticeablecontributio

nin

therisk

modelingof

thegroundingaccident

Nam

eYear

The

implem

entedmethods

Source

oftheused

data

Inputs

Geometrical

scenarios

FTA

BBN

Sim

ulation

Historical

data

Expert

opinion

Analytical

model

Evidence-

baseda

Fujji

etal.

1974

√–

––

√–

√–

f(C,Z

,v)

Macduff

1974

√–

––

√–

√–

f(L,

v,C)

Pedersen

1995

√√

––

√√

√–

f(type,d

wt,L,T

,C,Z,

a)

Amrozowicz

1996

–√

––

√√

––

f(a,

F)

Fow

leretal.2000

√√

––

√√

√–

f(C,F

,w)

DNV

2003

––

√–

√√

––

f(C,a

,F,w

)

RAMBØLL

2006

√–

√–

√√

√–

f(C,Z

,T,F

,v,a

,w)

Eideetal.

2007

√√

––

√√

√–

f(w,t,F)

COWI

2008

√–

––

√√

√–

f(C,T

,Z,a

,v)

Uluscuetal.2009

√–

–√

√√

––

f(a,F,C,w

,L,type,age,flag,t)

vanDorp

etal.

2009

√–

–√

√√

––

f(a,

F,C,w

,L,type,t)

Kristiansen

2010

––

√–

√√

–√

Dictatedby

therealaccident

cases

Montewka

etal.

2011

√–

––

√–

√–

f(T,

a,C,F,

L,v)

Nam

eOutputs

Causatio

nprobability

Consequence

assessment

Dynam

icelem

ents

RCOs

Uncertainty

discussion

Reverse

analysis

ability

Decisionmaking

potential

Fujjietal.

NG

1.55E−0

4–

––

––

L

Macduff

PG

3.70E−0

4–

––

––

L

A. Mazaheri et al.

Tab

le1

(contin

ued)

Nam

eOutputs

Causatio

nprobability

Consequence

assessment

Dynam

icelem

ents

RCOs

Uncertainty

discussion

Reverse

analysis

ability

Decisionmaking

potential

Pedersen

NG,type,dw

t,L,T

1.59E−0

4–

––

––

L

Amrozowicz

PG

––

–Byexperts

√–

M

Fow

leretal.

PG

3.70E−0

4–

––

√–

L

DNV

RG

–√

–Byexperts

–√

M/H

RAMBØLL

PG,type,d

wt,L,T

–√

–Byexperts

–√

M

Eideetal.

PG

–√

√–

√–

M

COWI

PG,type,d

wt,L,T

3.00E−0

4–

–Byexperts

––

L

Uluscuetal.

RG

–√

√Byexperts

––

M/H

vanDorp

etal.

RG

–√

√–

√–

M/H

Kristiansen

PG

––

––

–√

M/H

Montewka

etal.

PG

–√

––

––

L

aBased

ontherealaccident

andincident

cases

ahuman

or/and

organizationalfactors,Cwidth/geometry

ofthewaterway,F

technicalreliability,Lship'slength,T

ship'sdraft,ttim

e,vship'sspeed,

wmeteorologicalconditions,Z

trafficdensity

ordistributio

n,dw

tdead

weighttonnage,NGannualnumberof

grounding,

PGprobability/frequency

ofgrounding,

RGrisk

ofgrounding,

Hhigh,M

medium,L

low

Modeling the risk of ship grounding - a risk management perspective

1994). Therefore, all the reviewed models have used at least one other source of data asanalytical model or expert opinion. When it comes to the use of analytical models, thequestion is how accurately the models are mimicking the reality. Thus, depending onthe knowledge that is utilized into the model, some level of (epistemic) uncertainty isinvolved. From among the ones that have used such method, only Rambøll (2006) hasdiscussed the involved uncertainty, which then increases its potential to be used fordecision-making purposes (see Table 1). When the expert opinion is used either formodel construction or for likelihood quantification, the involved uncertainty becomeseven more highlighted. Typically, the largest source of uncertainty is human elementsin the forms of expert judgment and human failures quantification (Amrozowicz1996b). Although there are some methods that can somehow decrease the effects ofhuman elements uncertainty (Pyy 2000; Rosqvist 2003), they are very often not utilizedand the uncertainty of this type is not addressed nor discussed in the reviewed papers.Although involved uncertainty in the model construction may be eased using themethod adopted by Kristiansen (2010) (i.e., knowledge-based model construction),from a risk management point of view, the remaining uncertainty should besomehow exposed to the decision makers for further precautions. The possibleways to visualize the involved uncertainties, when quantifying the key elementsof the risk models, are the probability of frequencies, risk curves, the impreciseprobability, fuzzy logic, and the theories of possibility and evidence (see Avenand Zio 2011; Aven 2011a; Kaplan 1997). The visualization of the uncertaintieshas only been addressed in few of the reviewed papers (Merrick and van Dorp2006; Merrick et al. 2005b; Chen and Zhang 2002), while the rest were eithersilent or have merely presented a general discussion on the topic.

The other concern about a risk model is how the model reflects the current reality ofthe phenomena that the model is being used for. Idealistically, a model only representsthe phenomenon that is designed for, and merely based on the available knowledge ofthe time that is developed. With the fast forwarding advancement in the humanunderstanding about the physical phenomena, the possibility that a model becomesobsolete in a short time is high. Thus, the possibility to easily update the model whennew knowledge is acquired seems important. To do so, the affecting factors of themodel should be clear in order to make the developers able to understand the way andthe situation that the model works, and possibly alter the elements according to the newstate of the knowledge. From among the reviewed models, those that are only based onpredefined scenarios (i.e., Fujii's, Macduff's, Pedersen's, and COWI) do not have thisability (see Table 1). They only represent the scenarios that they are designed for, andthe validity of the model is questionable if the scenarios are changed. Besides, themodels that have implemented causation probability (i.e., Fujii et al., Macduff,Pedersen, Fowler et al., and COWI) have also made some of their affecting factorsunknown and unclear to the user, which then makes the model hard to be updated andthus less reliable to use in a different situation. On the contrary, the tree-based and BBNmodels do not have such flaw. Since they clearly exposed their elements to the user, themodels can be updated, and they do not need a total restructure when newknowledge is acquired. However, since BBN models do not have the hierar-chical structure of the tree-based models, and the elements do not need to besequentially dependent (Bobbio et al. 1999), they can be updated more easilywhen new knowledge is acquired or when the situation is changed.

A. Mazaheri et al.

Moreover, the grounding accident is a dynamic-by-nature phenomenon as it has time-dependent affecting factors. Thus, ability to handle dynamic variables will certainlyincrease the reliability of a model that is designed for assessing the risk of groundingaccidents. From among the reviewed models, models of Eide et al., Uluscu et al., andvan Dorp and Merrick have considered the dynamic nature of the phenomenon.

Thus far and based on the reviewed models and from the risk management perspec-tive, it can be argued that a BBN model that has decision and utility nodes and iserected on the real data of grounding incidents/accidents (i.e., evidence-based) withmodification from the knowledge of the domain experts can satisfy the requirements ofthe knowledge-based decision-making process. Although a BBN core can address theinvolved uncertainties (Merrick and van Dorp 2006; Paté-Cornell 1996), the remaininguncertainty of the modeling process should be clearly presented and visualized in thefinal results, in order to make the different decision makers able to optimally choose thebest possible RCOs for decreasing the risk and at the same time maximize the utilityvalue of each stakeholder (Grabowski et al. 2000; Merrick and van Dorp 2006).Undoubtedly, not all of the decision makers have the same priorities, and not evenhave the same degree of feeling about the risk. Therefore, the risk and the RCOs shouldbe estimated under the doctrine of utilitarianism (Kaplan 1997), in order to maximizethe utility of the stakeholders that the risk is defined for. Besides, integrating such BBNmodel with PC-simulation techniques gives the model the ability to easily handle thedynamic elements of the model, and thus make the output of the model more reliable.

5 Conclusion

The aims of this paper were, first, to propose a methodological framework suitable forknowledge-based risk modeling, fulfilling the recommendations given by the FormalSafety Assessment issued by the IMO; second, thoroughly review and discuss all theexisting risk models available in the literature developed for ship grounding riskanalysis in light of the risk perspective provided; and third, to highlight the modelsthat are more appropriate for risk management and decision making and to provide therecommendations to future model developments.

As the result of the reviewing process and the comparisons between the reviewedmodels, we have found some of the models to be more proper for decision makingpurposes in compare with the others (see Table 1). What we have also found, which canbe considered as a recommendation for risk management process, is to use a model thatallows the discovering causal relations existing in the modeled system. This can bedone by mixing various methodologies, for instance, a simulation-based model with aBBN core, which has the ability to address the dynamic nature of the event; moreover,such a model has the ability of reverse analysis of scenarios that is indispensable for theRCOs recognition by the model itself. Besides, using analytical models to identify thepossible scenarios in the specific situations is recommended. The conditional proba-bility of the different nodes and their states in the BBN could be addressed usingdifferent statistical and time-series models. Additionally, the involved uncertainty in allsources of data should be clearly visualized and presented in the final results, in order tomake the different decision makers able to optimally choose the best possible RCOsthat maximize the utility function of the stakeholders that the risk is defined for.

Modeling the risk of ship grounding - a risk management perspective

In this paper, more than 90 articles, reports, and dissertations all written in Englishhave been reviewed. From among the reviewed literature, 13 genuine models that madecontribution to the risk modeling, focusing on the ship grounding accident, have beenclosely assessed from a risk management perspective. Thus, the scope of the reviewwas limited only to those models that have been published in English and for shipgrounding risk assessment.

Acknowledgments This study was conducted as a part of “Minimizing risks of maritime oil transport byholistic safety strategies” (MIMIC) project. The MIMIC project is funded by the European Union and thefinancing comes from the European Regional Development Fund, The Central Baltic INTERREG IV AProgramme 2007–2013; the City of Kotka; Kotka-Hamina Regional Development Company (Cursor Oy);Centre for Economic Development, and Transport and the Environment of Southwest Finland (VARELY).Our colleagues, Floris Goerlandt, Kaarle Ståhlberg, and Otto Sormunen are greatly appreciated for theinspiring conversations and their comments on the manuscript. The authors are also grateful towards thetwo anonymous reviewers that their useful comments and suggestions help us to improve the first version ofthe manuscript.

References

Ale BJM, Bellamy LJ, Boom R, Cooper J, Cooke RM, Goossens LHJ, Hale AR, Kurowicka D, Morales O,Roelen ALC, Spouge J (2009) Further development of a causal model for air transport safety (CATS):building the mathematical heart. Reliab Eng Syst Saf 94(9):1433–1441

Amrozowicz MD (1996a) The need for a probabilistic risk assessment of the oil tanker industry and a qualitativeassessment of oil tanker groundings. Massachusetts Institute of Technology, Cambridge

Amrozowicz MD (1996b) The quantitative risk of oil tanker groundings. Massachusetts Institute of Technology,Cambridge

Amrozowicz MD, Brown A, Golay M (1997) A probabilistic analysis of tanker groundings. Paper presented atthe 7th International Offshore and Polar Engineering Conference, Honolulu

Apostolakis GE (1988) The interpretation of probability in probabilistic safety assessments. Reliab Eng SystSaf 23(4):247–252

Apostolakis GE (1990) The concept of probability in safety assessment of technological systems. Science250(4986):1359–1364

Aven T (2010) On how to define, understand and describe risk. Reliab Eng Syst Saf 95(6):623–631Aven T (2011a) Interpretations of alternative uncertainty representations in a reliability and risk analysis

context. Reliab Eng Syst Saf 96:353–360Aven T (2011b) On some recent definitions and analysis frameworks for risk, vulnerability, and resilience.

Risk Anal 31(4):515–522Aven T (2013) A conceptual framework for linking risk and the elements of the data-information-knowledge-

wisdom (DIKW) hierarchy. Reliab Eng Syst Saf 111:30–36Aven T, Heide B (2009) Reliability and validity of risk analysis. Reliab Eng Syst Saf 94(11):1862–1868Aven T, Reniers G (2013) How to define and interpret a probability in a risk and safety setting. Saf Sci 51(1):

223–231Aven T, Zio E (2011) Some considerations on the treatment of uncertainties in risk assessment for practical

decision making. Reliab Eng Syst Saf 96:64–74Bobbio A, Portinale L, Minichino M, Ciancamerla E (1999) Comparing fault tree and Bayesian networks for

dependability analysis. In: Kanoun K (ed) Computer safety, reliability and security, vol 1698. Springer,Berlin/Heidelberg. doi:10.1007/3-540-48249-0_27

Briggs MJ, Borgman LE, Bratteland E (2003) Probability assessment for deep-draft navigation channeldesign. Coast Eng 48:29–50

BrownA, Haugene B (1998) Assessing the impact of management and organizational factors on the risk of tankergrounding. Paper presented at the 8th International Offshore and Polar Engineering Conference

Chen G, Zhang S-K (2002) Fuzzy probability calculation of ship grounding. J Ship Mech 6(3):69–75

A. Mazaheri et al.

COWI (2008) Risk analysis for Sea traffic in the area around Bornholm. Danish Maritime Authority, KongensLyngby

Cox D (1972) Regression models and life tables (with discussion). J R Stat Soc Ser B 34:187–220Dash D, Druzdzel MJ (2003) Robust independence testing for constraint-based learning of causal structure. In:

Kaufman M (ed) 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI-03). pp 167–174DNV (2003) FSA navigation large passenger ships. Technical Report No. 2003-0277 by Det Norske VeritasEhlers S, Tabri K (2012) A combined numerical and semi-analytical collision damage assessment procedure.

Mar Struct 28(1):101–119Eide MS, Endresen O, Breivik O, Brude OW, Ellingsen IH, Roang K, Hauge J, Brett PO (2007) Prevention of

oil spill from shipping by modelling of dynamic risk. Mar Pollut Bull 54:1619–1633Fowler TG, Sørgård E (2000) Modeling ship transportation risk. Risk Anal 20(2):225–244Friis-Hansen P, Simonsen BC (2002) GRACAT: software for grounding and collision risk analysis. Mar Struct

15:383–401Fujii Y, Oshima R, Yamanouchi H, Mizuki N (1974) Some factors affecting the frequency of accidents in

marine traffic: I—the diameter of evasion for crossing encounters, II—the probability of stranding, III—the effect of darkness of the probability of collision and stranding. J Navig 27(2):239–247

Fujii Y, Shiobara R (1971) The analysis of traffic accidents. J Navig 24(4):534–543Goerlandt F, Kujala P (2011) Traffic simulation based ship collision probability modeling. Reliab Eng Syst Saf

96(1):91–107Goerlandt F, Ståhlberg K, Kujala P (2012) Influence of impact scenario models on collision risk analysis.

Ocean Eng 47:74–87Grabowski M, Merrick JRW, Harrald JR, Mazzuchi TA, Drop JRv (2000) Risk modeling in distributed, large-

scale systems. IEEE Trans Syst Man Cybern Part A: Syst Hum 30(6):651–660Gucma L (2002) Navigation risk assessment for vessels maneuvering in various conditions. Paper presented at

the Risk Analysis III, Southampton, BostonGucma L (2006) The method of navigational risk assessment on waterways based on generalised real time

simulation data. In: International conference on marine simulation and ship maneuverability, TerschellingHaimes YY (2009) On the complex definition of risk: a system-based approach. Risk Anal 29(12):1647–1654Hänninen M, Mazaheri A, Kujala P, Laaksonen P, Salmiovirta M (2012) The Effects of an Enhanced

Navigation Support Information Service on Maritime Traffic Risks in the Gulf of Finland. Paper presentedat the 11th Probabilistic Safety Assessment and Management Conference (PSAM) and the AnnualEuropean Safety and Reliability Conference (ESREL), Espoo, Finland, June 25th–29th

Hänninen M, Mazaheri A, Kujala P, Montewka J, Laaksonen P, Salmiovirta M (2013) Expert elicitation of anavigation service implementation effects on ship groundings and collisions in the Gulf of Finland. ProcIME O J Risk Reliab. doi:10.1177/1748006X13494533

Helle I, Lecklin T, Jolma A, Kuikka S (2011) Modeling the effectiveness of oil combating from an ecologicalperspective—a Bayesian network for the Gulf of Finland; the Baltic Sea. J Hazard Mater 185:182–192

Hogström P, Ringsberg JW (2012) An extensive study of a ship's survivability after collision—a parameterstudy of material characteristics, non-linear FEA and damage stability analyses. Mar Struct 27(1):1–28

IMO (2002) Guidelines for Formal Safety Assessment (FSA) for use in the IMO rule-making process. MSC/Circ. 1023. London

IMO (2012) Formal Safety Assessment, Outcome of MSC 90. Draft revised FSA guidelines and darft HEAPguidelines.

IWRAP (2009) IALAWaterway Risk Assessment Programme. http://www.ialathree.org/iwrap/.Jebsen JJ, Papakonstantinou VC (1997) Evaluation of the Physical Risk of Ship Grounding. Massachusetts

Institute of Technology, CambridgeKaneko F (2010) A method for estimation of grounding frequency by using trajectories of ships and geometry

of seabed. In: International Conference on Collision and Grounding of Ships (ICCGS), EspooKaplan S (1997) The words of risk analysis. Risk Anal 17(4):407–417Kaplan S, Garrick BJ (1981) On the quantitative definition of risk. Risk Anal 1(1):11–27Karlsson M, Rasmussen FM, Frisk L (1998) Verification of ship collision frequency model. Paper presented at

the Ship Collision Analysis, BalkemaKite-Powell HL, Jin D, Jebsen J, Papakonstantinou V, Patrikalakis N (1999) Investigation of potential risk

factors for groundings of commercial vessels in U.S. Ports. Int J Offshore Polar Eng 9(1):16–21Kristiansen S (2005) Traffic-based models. Maritime transportation-safety management and risk analysis.

Elsevier Ltd., HungaryKristiansen S (2010) A BBN approach for analysis of maritime accident scenarios. In: Ale BJM, Papazpglou

IA, Zio E (eds) ESREL. Taylor & Francis, Rhodes

Modeling the risk of ship grounding - a risk management perspective

Lax R, Kujala P (2001) Statistics on ship groundings in Finnish waters and simulation of the grounding eventby model scale testing. Paper presented at the 2nd International Conference on Collision and Groundingof Ships (ICCGS), Copenhagen, Denmark, 1–3 July

Lecklin T, Ryömä R, Kuikka S (2011) A Bayesian network for analyzing biological acute and long-termimpacts of an oil spill in the Gulf of Finland. Mar Pollut Bull 62:2822–2835

Li S, Meng Q, Qu X (2012) An overview of maritime waterway quantitative risk assessment models. RiskAnal 32(3):496–512. doi:10.1111/j.1539-6924.2011.01697.x

Lin S, Kite-Powell HL, Patrikalakis NM (1998) Physical risk analysis of ship grounding. MassachusettsInstitute of Technology, Cambridge

Luxhøj JT, Coit DW (2006) Modeling low probability/high consequence events: an aviation safety risk model.Paper presented at the Annual reliability and Maintainability Symposium, Newport Beach

Macduff T (1974) The probability of vessel collisions. Ocean Industry 9(9):144–148Martins MR, Maturana MC (2010) Human error contribution in collision and grounding of oil tankers. Risk

Anal 30(4):674–698Mazaheri A (2009) Probabilistic modeling of ship grounding—a review of the literature. TKK-AM-10, vol 10.

Helsinki University of Technology, EspooMazaheri A, Kotilainen P, Sormunen O, Montewka J, Kujala P (2013a) Correlation between the ship

grounding accident and the ship traffic—a case study based on the statistics of the gulf of Finland. IntJ Mar Navig Saf Sea Transp 7(1):119–124, 10.12716/1001.07.01.16

Mazaheri A, Sormunen OVE, HyttinenN,Montewka J, Kujala P (2013b) Comparison of the learning algorithmsfor evidence-based BBN modeling - A case study on ship grounding accidents. Paper presented at theAnnual European Safety and Reliability Conference (ESREL 2013), Amsterdam, 29 September–2 October

Mazaheri A, Ylitalo J (2010) Comments on geometrical modeling of ship grounding. Paper presented at the5th International Conference on Collision and Grounding of Ships (ICCGS), Espoo

Merrick JRW, Dorp JR, Singh A (2005a) Analysis of correlated expert judgments from extended pairwisecomparisons. Decis Anal 2(1):17–29

Merrick JRW, van Dorp JR (2006) Speaking the truth in maritime risk assessment. Risk Anal 26(1):223–237.doi:10.1111/j.1539-6924.2006.00708.x

Merrick JRW, van Dorp JR, Dinesh V (2005b) Assessing uncertainty in simulation based maritime riskassessment. Risk Anal 25(3):731–743

Montewka J, Hinz T, Kujala P, Matusiak J (2010a) Probability modelling of vessel collisions. Reliab Eng SystSaf 95:573–589

Montewka J, Ståhlberg K, Seppala T, Kujala P (2010b) Elements of risk analysis for collision of oil tankers. Inproceedings of TransNav 2010: Reliability, risk and safety: back to the future, eds: Ale, Papazoglou andZio; pp. 1005–1013; Taylor & Francis Group, Gdynia, Poland

Montewka J, Krata P, Goerlandt F, Mazaheri A, Kujala P (2011) Marine traffic risk modelling—an innovativeapproach and a case study. Proc IME O J Risk Reliab 225(3):307–322. doi:10.1177/1748006X11399988

Mullai A, Paulsson U (2011) A grounded theory model for analysis of marine accidents. Accid Anal Prev43(4):1590–1603

Nyman T (2009) Review of collision and grounding risk analysis methods which can utilize the historical AISdata and traffic patterns in seawaters. SKEMA Study, vol SE3.2.1. VTT,

Otto S, Pedersen PT, Samuelides M, Sames PC (2002) Elements of risk analysis for collision and grounding ofa RoRo passenger ferry. Mar Struct 15:461–474

Paté-Cornell ME (1996) Uncertainties in risk analysis: six levels of treatments. Reliab Eng Syst Saf 54:95–111Paté-Cornell ME (2007) The engineering risk analysis method and some applications. In: EdwardsW, Jr., Miles

RF, vonWinterfeldt D (eds) Advances in decision analysis, from foundations to applications. pp 303–324.Cambridge University Press, New York

Pedersen PT Collision and Grounding Mechanics. In: Proceedings of WEMT ‘95, Copenhagen, Denmark,1995. The Danish Society of Naval Architecture and Marine Engineering

Pedersen PT (2010) Review and application of ship collision and grounding analysis procedures. Mar Struct13(3):241–262

Pedronia N, Zio E, Ferrario E, Pasanisi A, Couplet M (2012) Propagation of aleatory and epistemicuncertainties in the model for the design of a flood protection dike. Paper presented at the PSAM 11 &ESREL 2012, Helsinki

Przywarty M (2008) Models of ships groundings on coastals areas. J KONBiN 2(5):140–147. doi:10.2478/v10040-008-0045-3

Pyy P (2000) Human reliability analysis methods for probabilistic safety assessment. VTT Publications no.422, Technical Research Center of Finland, Espoo

A. Mazaheri et al.

Quy NM, Vrijling JK, Gelder PHAJMv, Groenveld R (2006) On the assessment of ship grounding risk inrestricted channels. Paper presented at the The 8th International Conference on Marine Sciences andTechnologies—Black Sea Conference, Varna, Bulgaria, 25–27 September

Rae A, McDermid J, Rob A (2012) The science and superstition of quantitative risk assessment. Paperpresented at the PSAM 11&ESREL 2012, Helsinki

Rambøll (2006) Navigational safety in the sound between Denmark and Sweden (øresund). Rambøll DanmarkA/S, Denmark (trans: hydrography TRDAoNa, authority TDM, administration TSM)

Roelen ALC (2008) Causal risk models of air transport: comparison of user needs and model capabilities. IOSPress, The Netherlands

Roelen ALC, Lin PH, Hale AR (2011) Accident models and organizational factorsin air transport: the need formulti-method models. Saf Sci 49(1):5–10

Rosqvist T (2003) On the use of expert judgment in the quantification of risk assessment. Helsinki Universityof Technology, Espoo

Rosqvist T (2010) On the validation of risk analysis—a commentary. Reliab Eng Syst Saf 95(11):1261–1265Rosqvist T, Tuominen R (2004) Qualification of formal safety assessment: an exploratory study. Safety

Science 42(2):99–120Rowe WD (1994) Understanding uncertainty. Risk Anal 14(5):743–750Samuelides MS, Ventikos NP, Gemelos IC (2009) Survey on grounding incidents: statistical analysis and risk

assessment. Ships Offshore Struct 4(1):55–68Sergejeva M, Laanearu J, Tabri K (2013) Hydraulic modelling of submerged oil spill including tanker

hydrostatic overpressure. In: Proceedings of 4th International Conference on Marine Structures,MARSTRUCT 2013: 4th International Conference on Marine Structures, 25–27.03.2013, Espoo,Finland. Taylor & Francis, p 209–217

Simonsen BC (1997) Mechanics of ship grounding. Technical University of Denmark, Kongens LyngbySinger D (1990) A fuzzy set approach to fault tree and reliability analysis. Fuzzy Set Syst 34:145–155Stirling A, Gee D (2002) Science, precaution, and practice. Public Health Rep 117(6):521–533TalaveraA,AguascaR,GalvanB, CacerenoA (2013)Application of Dempster–Shafertheoryforthequantificationand

propagation of the uncertainty caused by the use of AIS data. Reliab Eng Syst Saf 111:95–105Tavakoli MT, Amdahl J, Leira BJ (2010) Analytical and numerical modelling of oil spill from a side damaged

tank. Paper presented at the 5th International Conference on Collision and Grounding of Ships (ICCGS),Espoo, 14–16 June

Uluscu ÖS, Özbas B, Alitok T, Or I (2009) Risk analysis of the vessel traffic in the strait of Istanbul. Risk Anal29(10):1454–1472

van de Wiel G, van Dorp J (2009) An oil outflow model for tanker collisions and groundings. Ann Oper Res26(1):1–26

vanDorp JR,Merrick JRW (2009) On a risk management analysis of oil spill risk usingmaritime transportationsystem simulation. Ann Oper Res 187:249–277. doi:10.1007/s10479-009-0678-1

Winkler RL (1996) Uncertainty in probabilistic risk assessment. Reliab Eng Syst Saf 54:127–132

Modeling the risk of ship grounding - a risk management perspective