4. Application of the methodology

The method is applied on the analysis of the offloading operation, when the crude oil is transported to shore by shuttle tankers through an offloading arrangement with the use of a shuttle tanker with dynamic positioning systems (DP). From the point of view of the shuttle tanker, tandem offloading operation can in principle be summarized into the following five operational stages [15]: (1) approach, tanker approaches FPSO and stops at a predefined distance; (2) connection, messenger line, hawser, and loading hose are connected; (3) loading, oil is transferred from FPSO to tanker; (4) disconnection, manifold is flushed, and loading hose and hawser are disconnected; and (5) departure, tanker reverses away from FPSO while sending back hawser messenger line and finally sails away from oil field. In the first stage, the shuttle tanker approaches FPSO, at a maximum speed of 1.5 knots, and this stage finishes when shuttle tanker stood 50–100 m behind the FPSO; distance is considered appropriate to begin the connection stage. In the second stage, to physically connect shuttle tanker and FPSO, some activities are executed, for example, the messenger line crosses from one ship to the other allowing the mooring hawser and hose to be connected. The tanker may position itself by its own dynamic positioning system so that the hawser is not tensioned. As for safety reasons, a tug boat is also connected to the ship stern acting as a redundant component to control hawser tension. In the third stage, tests are realized, and the valves in vessels are open, and oil is transferred from FPSO to tanker. During this stage, transfer rates are slow initially as the integrity of both vessel systems are checked and gradually increased to a maximum transfer flow. When loading is completed and stopped, the hose is flushed, and the valves are closed. Finally, the hose is dropped and sends to FPSO the hose messenger line and the hawser. The shuttle tanker moves off away FPSO (MCGA [21]).

Pð Þ¼ λjE

one component of main engine.

Figure 3. Fault tree for fuel system failure.

ð Þ <sup>λ</sup>∙<sup>t</sup> <sup>r</sup> <sup>r</sup>! <sup>∙</sup>e�λ∙<sup>t</sup> h i<sup>∙</sup> βα∙λα�<sup>1</sup>

<sup>P</sup>ð Þ¼ <sup>λ</sup>j<sup>E</sup> <sup>β</sup> <sup>þ</sup> <sup>t</sup> � �<sup>α</sup>þ<sup>r</sup>

databases that recorded the rate failure to equipment used in offshore industry.

As an example, the posterior distribution is calculating for fuel system failure (see Figure 3)

Aiming to obtain the probability that K be true given the system is in the state ST represented by Eq. (2), it is necessary to estimate the posterior mean value of failure rate. To calculate the failure probability of hazard events, we use fault tree analysis. Then for all basic events of the fault trees, the failure probability was determined using Bayesian inference. The posterior distribution is calculated, using the conjugate distribution. By analyzing the type of information availability, the Gamma distribution is selected as appropriate prior distribution, and Poisson distribution is selected as likelihood function. We calculate substituting in Eq. (4) the failure rates for fuel system failure (see Table 3). The prior distribution was estimated using

The calculated probabilities for the basic events are used as input to a fault tree to determine the probability of the event hazard: "no fuel flow." Using probability theory and assuming that the fuel system is operated for t = 43,800 h (time between maintenance), the probability of "no

Ð ∞ 0 ð Þ <sup>λ</sup>∙<sup>t</sup> <sup>r</sup> <sup>r</sup>! ∙e�λ∙<sup>t</sup> h i<sup>∙</sup> βα∙λα�<sup>1</sup>

<sup>Γ</sup>ð Þ <sup>α</sup> <sup>∙</sup>e�β∙<sup>λ</sup> h i

Decision-Making Model for Offshore Offloading Operations Based on Probabilistic Risk Assessment

)

�ð Þ <sup>β</sup>þ<sup>t</sup> <sup>∙</sup><sup>λ</sup> (4)

http://dx.doi.org/10.5772/intechopen.75833

115

<sup>Γ</sup>ð Þ <sup>α</sup> <sup>∙</sup>e�β∙<sup>λ</sup> h i∙d<sup>λ</sup>

∙λαþr�<sup>1</sup>

∙e

Γð Þ α þ r " #

Patino Rodriguez et al. [15] found 56 hazardous events for shuttle tank. The connection stage is the phase with the highest number of hazardous event. In fact, this stage involves more activities associated with mooring hawser and hose connection, besides the smallest distance between shuttle tanker and FPSO. For all hazardous events, their causes were identified, as well as the activities executed aiming at minimizing the occurrence of these causes (mitigating scenarios). In a similar way, the consequences resulting from the hazardous event are identified. Some of these are characterized as catastrophic. Most of them are related to dynamic positioning system (DPS) failures. Considering that one of the most important aspects in the offloading operation is to keep the position between FPSO and shuttle tanker, the initiating event selected as for risk assessment is "DPS failure." The considered accident sequence is shown in Figure 2 modeled as an accident progression of four hazard events: (1) auxiliary engine failure, (2) main engine failure, (3) tug failure, and (4) towing cable failure.

The fault tree for the four hazard events that appears in the event tree was developed. For all basic events of the four fault trees, the parameter to be estimated is failure rate, and the Poisson distribution is selected as likelihood function. Poisson distribution is considered as appropriate function given information available in database is the number of failures, r, in each time interval, t, [22, 23]. Analyzing the type and source of information (expert judgment and literature data) as well as the nature of the time to failure that is the random variable of interest, gamma distribution is selected as appropriate "prior distribution." The conjugate family with respect to the risk model is shown in Table 1. Using Bayes' theorem (Eq. 2) the posteriori distribution is obtained:

Figure 2. Event sequence diagram of the accident progression for offloading operation.

Decision-Making Model for Offshore Offloading Operations Based on Probabilistic Risk Assessment http://dx.doi.org/10.5772/intechopen.75833 115

$$P(\lambda|E) = \frac{\left[\frac{(\lambda \cdot t)'}{r!} \cdot e^{-\lambda \cdot t}\right] \cdot \left[\frac{\beta^{a} \cdot \lambda^{a-1}}{\Gamma(\alpha)} \cdot e^{-\beta \cdot \lambda}\right]}{\int\_{0}^{\infty} \left[\frac{(\lambda \cdot t)'}{r!} \cdot e^{-\lambda \cdot t}\right] \cdot \left[\frac{\beta^{a} \cdot \lambda^{a-1}}{\Gamma(\alpha)} \cdot e^{-\beta \cdot \lambda}\right] \cdot d\lambda} \Rightarrow$$

$$P(\lambda|E) = \left[\frac{(\beta + t)^{a+r} \cdot \lambda^{a+r-1}}{\Gamma(\alpha+r)}\right] \cdot e^{-\left(\beta+t\right) \cdot \lambda} \tag{4}$$

As an example, the posterior distribution is calculating for fuel system failure (see Figure 3) one component of main engine.

Aiming to obtain the probability that K be true given the system is in the state ST represented by Eq. (2), it is necessary to estimate the posterior mean value of failure rate. To calculate the failure probability of hazard events, we use fault tree analysis. Then for all basic events of the fault trees, the failure probability was determined using Bayesian inference. The posterior distribution is calculated, using the conjugate distribution. By analyzing the type of information availability, the Gamma distribution is selected as appropriate prior distribution, and Poisson distribution is selected as likelihood function. We calculate substituting in Eq. (4) the failure rates for fuel system failure (see Table 3). The prior distribution was estimated using databases that recorded the rate failure to equipment used in offshore industry.

The calculated probabilities for the basic events are used as input to a fault tree to determine the probability of the event hazard: "no fuel flow." Using probability theory and assuming that the fuel system is operated for t = 43,800 h (time between maintenance), the probability of "no

Figure 3. Fault tree for fuel system failure.

knots, and this stage finishes when shuttle tanker stood 50–100 m behind the FPSO; distance is considered appropriate to begin the connection stage. In the second stage, to physically connect shuttle tanker and FPSO, some activities are executed, for example, the messenger line crosses from one ship to the other allowing the mooring hawser and hose to be connected. The tanker may position itself by its own dynamic positioning system so that the hawser is not tensioned. As for safety reasons, a tug boat is also connected to the ship stern acting as a redundant component to control hawser tension. In the third stage, tests are realized, and the valves in vessels are open, and oil is transferred from FPSO to tanker. During this stage, transfer rates are slow initially as the integrity of both vessel systems are checked and gradually increased to a maximum transfer flow. When loading is completed and stopped, the hose is flushed, and the valves are closed. Finally, the hose is dropped and sends to FPSO the hose messenger line and the hawser. The shuttle tanker

Patino Rodriguez et al. [15] found 56 hazardous events for shuttle tank. The connection stage is the phase with the highest number of hazardous event. In fact, this stage involves more activities associated with mooring hawser and hose connection, besides the smallest distance between shuttle tanker and FPSO. For all hazardous events, their causes were identified, as well as the activities executed aiming at minimizing the occurrence of these causes (mitigating scenarios). In a similar way, the consequences resulting from the hazardous event are identified. Some of these are characterized as catastrophic. Most of them are related to dynamic positioning system (DPS) failures. Considering that one of the most important aspects in the offloading operation is to keep the position between FPSO and shuttle tanker, the initiating event selected as for risk assessment is "DPS failure." The considered accident sequence is shown in Figure 2 modeled as an accident progression of four hazard events: (1) auxiliary engine failure, (2) main engine failure, (3) tug failure, and

The fault tree for the four hazard events that appears in the event tree was developed. For all basic events of the four fault trees, the parameter to be estimated is failure rate, and the Poisson distribution is selected as likelihood function. Poisson distribution is considered as appropriate function given information available in database is the number of failures, r, in each time interval, t, [22, 23]. Analyzing the type and source of information (expert judgment and literature data) as well as the nature of the time to failure that is the random variable of interest, gamma distribution is selected as appropriate "prior distribution." The conjugate family with respect to the risk model is shown in Table 1. Using Bayes' theorem (Eq. 2) the

moves off away FPSO (MCGA [21]).

114 Probabilistic Modeling in System Engineering

(4) towing cable failure.

posteriori distribution is obtained:

Figure 2. Event sequence diagram of the accident progression for offloading operation.


Table 3. Failure rates and standard deviations of the basic events of fault tree for fuel system failure.

fuel flow" is 8.390E-04. The prior and posterior density of basic event that has more influence on system failure is shown in Figure 4, associated with the failure of the centrifugal pump. A 90% interval estimate for failure rate is found by computing the 5th and 95th percentiles of gamma distribution, and the interval is between 2,96E-04 and 5,08E-04.

The same procedure is used for other subsystems, and the probability of hazard event "main engine failure" is found by solving the fault tree associated with that failure. In the same way, that procedure is applied to find the probability of all hazard events as shown in Table 4.

Connected to the hazard event, the operation involves risks related to collisions during the offshore operation as presented in Figure 2. The event tree in Figure 5 is the failure scenario development associated with the failure in DPS, considering the probabilities presented in Table 4.

The failure scenario presented in Figure 5 can occur at any time during offloading operation. The position of the tanker in relation to FPSO during offloading is controlled. In case it reaches the alert zone, as shown in Figure 6, the tanker can be disconnected and the offloading is aborted. So the consequence of the failures considered in the study can be more severe depending of the

Table 4. Posterior probabilities for hazard events involved in the offloading operation and a 90% interval estimate for

Hazard event P(λ|E) [failure/h] 90% interval estimate for rate failure

Decision-Making Model for Offshore Offloading Operations Based on Probabilistic Risk Assessment

Dynamic positioning system (DPS) failure 1.58E-05 3.18E-07 5.29E-05 Auxiliary engine failure 1.97E-04 1.01E-04 3.18E-04 Main engine 4.95E-05 9.70E-06 1.14E-04 Tug failure 2.28E-05 1.17E-06 6.82E-05 Towing cable failure 2.18E-03 0.001837 0.002555

5% 95%

http://dx.doi.org/10.5772/intechopen.75833

117

Figure 4. The prior density and posterior density for centrifugal pump failure rate.

It is essential to consider the probability of the change of the shuttle tanker position from operational zone to alert zone, as shown in Figure 6, during offloading. The distribution parameters are estimated using a simulator that reproduces ship motions in a specific operation condition and environmental condition. We used these conditions of waves, wind, and

After finding the failure probability of all hazard events, the failure probability for scenarios is calculated by multiplying hazard events. The probability of each consequence

relative position of the tanker.

currents.

failure rate.

The proposed method for risk assessment seems to be suitable for complex systems analysis, since it not only allows for the identification of critical consequences, but it is also a tool to make decisions, because it enables a quantitative evaluation of accident progression in systems that change their operational condition throughout time.

The sequence of abnormal events is determined, and the consequences are estimated using the event tree. The initiating event selected is the shuttle tanker change from operational zone to alert zone. The accident sequence considered is modeled as an accident progression of five hazard events, and we have four consequence categories. The fault tree for the five hazard events was developed as shown in Figure 5. The shuttle tanker is loss of position in powered condition, and its subsequent collision with the FPSO is the most significant risk.

Decision-Making Model for Offshore Offloading Operations Based on Probabilistic Risk Assessment http://dx.doi.org/10.5772/intechopen.75833 117

Figure 4. The prior density and posterior density for centrifugal pump failure rate.

fuel flow" is 8.390E-04. The prior and posterior density of basic event that has more influence on system failure is shown in Figure 4, associated with the failure of the centrifugal pump. A 90% interval estimate for failure rate is found by computing the 5th and 95th percentiles of

The same procedure is used for other subsystems, and the probability of hazard event "main engine failure" is found by solving the fault tree associated with that failure. In the same way, that procedure is applied to find the probability of all hazard events as shown in Table 4.

Connected to the hazard event, the operation involves risks related to collisions during the offshore operation as presented in Figure 2. The event tree in Figure 5 is the failure scenario development associated with the failure in DPS, considering the probabilities presented in

The proposed method for risk assessment seems to be suitable for complex systems analysis, since it not only allows for the identification of critical consequences, but it is also a tool to make decisions, because it enables a quantitative evaluation of accident progression in systems

The sequence of abnormal events is determined, and the consequences are estimated using the event tree. The initiating event selected is the shuttle tanker change from operational zone to alert zone. The accident sequence considered is modeled as an accident progression of five hazard events, and we have four consequence categories. The fault tree for the five hazard events was developed as shown in Figure 5. The shuttle tanker is loss of position in powered

condition, and its subsequent collision with the FPSO is the most significant risk.

gamma distribution, and the interval is between 2,96E-04 and 5,08E-04.

Table 3. Failure rates and standard deviations of the basic events of fault tree for fuel system failure.

that change their operational condition throughout time.

Table 4.

Equipment E[P0(λ)]

116 Probabilistic Modeling in System Engineering

[failure/h]

ST[P0(λ)] [failure/h]

Fuel pump control shaft 3.00E-05 3.00E-05 1.30E-05 Pressure regul.

P(λ|E) [failure/h]

Booster pump 1.10E-03 1.10E-03 2.24E-05 Fuel pumps 1.43E-03 1.13E-03 3.55E-05 Bypass valve 2.28E-05 1.50E-05 1.59E-05 Heater 4.54E-05 3.74E-05 1.93E-05 Centrifugal pump 7.36E-04 1.20E-04 3.95E-04 Main tank 2.13E-04 2.13E-04 2.06E-05 Centrifuge 1.69E-05 5.94E-06 1.55E-05 Mixing tank 9.50E-06 9.11E-06 6.87E-06 Check valve 3.60E-07 5.10E-07 3.49E-07 Piping: blockage 3.70E-07 6.18E-07 3.54E-07 Daily service tank 9.50E-06 9.11E-06 6.87E-06 Piping: breakage 4.40E-07 9.57E-07 4.03E-07

Engine centrif. Pump 1.13E-04 2.81E-05 8.62E-05 Settling 4.37E-04 6.26E-04 1.08E-05 Filter heated 2.00E-06 2.00E-06 1.84E-06 Settling tank 6.26E-05 1.12E-04 6.43E-06 Flow meter 1.32E-05 3.26E-06 1.27E-05 Three-way valve 2.28E-05 1.50E-05 1.59E-05 Fuel injector: blockage 7.24E-06 1.02E-05 4.43E-06 Transfer pump 7.36E-04 1.20E-04 3.95E-04 Fuel injector: breakage 2.00E-07 2.00E-07 1.98E-07 Viscosity regulator 6.39E-06 8.96E-06 4.12E-06 Fuel Pumps 1.43E-03 1.13E-03 3.55E-05 VIT system 2.06E-07 2.06E-07 2.04E-07

Valve

Equipment E[P0(λ)]

[failure/h]

ST[P0(λ)] [failure/h]

8.81E-06 1.25E-05 4.98E-06

P[λ|E] [failure/h]


Table 4. Posterior probabilities for hazard events involved in the offloading operation and a 90% interval estimate for failure rate.

The failure scenario presented in Figure 5 can occur at any time during offloading operation. The position of the tanker in relation to FPSO during offloading is controlled. In case it reaches the alert zone, as shown in Figure 6, the tanker can be disconnected and the offloading is aborted. So the consequence of the failures considered in the study can be more severe depending of the relative position of the tanker.

It is essential to consider the probability of the change of the shuttle tanker position from operational zone to alert zone, as shown in Figure 6, during offloading. The distribution parameters are estimated using a simulator that reproduces ship motions in a specific operation condition and environmental condition. We used these conditions of waves, wind, and currents.

After finding the failure probability of all hazard events, the failure probability for scenarios is calculated by multiplying hazard events. The probability of each consequence

Mk <sup>¼</sup> <sup>1</sup> � <sup>p</sup>12k∙Δ<sup>θ</sup> <sup>p</sup>21k∙Δ<sup>θ</sup>

where pij(θ)Δθ is the probability of the system, which is operational zone at position θ, will

The state transition rates correspond to the following event rates: the shuttle tanker gets out of the operational zone, and the shuttle tank gets into the operational zone. In each state (ST) there are a number of possible events that can cause a transition. A ship dynamics simulator that determines ship maneuvering characteristics was used to calculate the transition. The simulator can accurately reproduce ship motion in the presence of waves, wind, and currents. Table 5 shows typical environmental conditions in the fall and in the spring for Campos Basin (Brazil). Hence, with the program outputs, it was possible to calculate the angle between FPSO

According to the standards of the offloading operation in Brazil, this angle within the operational zone should not be greater than 45 degrees. Weibull probability functions were found as proper distributions to represent the angle between FPSO and shuttle tanker during the offloading operation both inside and outside the operational zone. The parameters and transi-

Then, using the recurrent algorithm shown in the section of Markovian process, the probability (P(ST)) that the shuttle tanker is inside the operational zone, without any failure, is 0.7918. In the same way, inducing the hazard events in ship dynamics simulator is possible to simulate the consequence categories and to determine the probability that the system was in the ST state

Applying Eq. (2) the probability that a scenario K is true given the system is in the state ST is obtained. For instance, the probability that shuttle tanker is without main propulsion, making

Current [m/s] Wind [m/s] Wave [m] 0.71 S 11.16 SE 2.9 SE

State Parameter Weibull distribution Transition

β = 1.596; η = 13.05

β = 8.604; η = 60.51

0 CBA

rate equation Consequence category

β = 1.473; η = 12.01

β = 8.499; η = 60.40

β = 1.691; η = 14.34

β = 7.259; η = 63.21

β <sup>η</sup> <sup>∙</sup> <sup>θ</sup><sup>k</sup> η <sup>β</sup>�<sup>1</sup>

and shuttle tanker at any moment during the offloading operation.

come alert zone in the interval (θ, θ+Δθ).

tion rate equation are shown in Table 6.

given a scenario K as shown in Table 7.

Table 5. Environmental conditions.

Inside the operational zone β = 1.641;

Outside the operational zone β = 10.99;

η = 12.97

η = 30.07

Table 6. Parameters and transition rate for offloading operation.

p12k∙Δθ 1 � p21k∙Δθ

Decision-Making Model for Offshore Offloading Operations Based on Probabilistic Risk Assessment

(5)

http://dx.doi.org/10.5772/intechopen.75833

119

Figure 5. Event tree for the offloading operation.

Figure 6. Markov state transition diagram.

category is calculated by adding the probabilities of the scenarios with the same consequence category. The random variable that corresponds to the angle between the FPSO and shuttle tanker during offloading operation is modeled as Weibull distribution. According to the standards of the offloading operation in Brazil, the angle in the operational zone should not be greater than 45 degrees; as a result of these conditions, the parameter of four consequence categories was estimated, and the equation for transition rate is determined. Let us consider the two states established before: operational zone and alarm zone.

The transition rates between states are not constant; then the stochastic process can be modeled as semi-Markov process which shows the probability of the position of the shuttle tanker changing from operational zone to alert zone in a given environmental condition.

By applying the results obtained from the simulation, Markovian analysis, and event tree, the probability that a K scenario is true is obtained, given the system is in the ST state.

In Eq. (5) we define a K K state transition probability matrix Mk.

$$M\_k = \begin{bmatrix} 1 - p\_{12k} \cdot \Delta \theta & p\_{21k} \cdot \Delta \theta \\ p\_{12k} \cdot \Delta \theta & 1 - p\_{21k} \cdot \Delta \theta \end{bmatrix} \tag{5}$$

where pij(θ)Δθ is the probability of the system, which is operational zone at position θ, will come alert zone in the interval (θ, θ+Δθ).

The state transition rates correspond to the following event rates: the shuttle tanker gets out of the operational zone, and the shuttle tank gets into the operational zone. In each state (ST) there are a number of possible events that can cause a transition. A ship dynamics simulator that determines ship maneuvering characteristics was used to calculate the transition. The simulator can accurately reproduce ship motion in the presence of waves, wind, and currents. Table 5 shows typical environmental conditions in the fall and in the spring for Campos Basin (Brazil). Hence, with the program outputs, it was possible to calculate the angle between FPSO and shuttle tanker at any moment during the offloading operation.

According to the standards of the offloading operation in Brazil, this angle within the operational zone should not be greater than 45 degrees. Weibull probability functions were found as proper distributions to represent the angle between FPSO and shuttle tanker during the offloading operation both inside and outside the operational zone. The parameters and transition rate equation are shown in Table 6.

Then, using the recurrent algorithm shown in the section of Markovian process, the probability (P(ST)) that the shuttle tanker is inside the operational zone, without any failure, is 0.7918. In the same way, inducing the hazard events in ship dynamics simulator is possible to simulate the consequence categories and to determine the probability that the system was in the ST state given a scenario K as shown in Table 7.

Applying Eq. (2) the probability that a scenario K is true given the system is in the state ST is obtained. For instance, the probability that shuttle tanker is without main propulsion, making


Table 5. Environmental conditions.

category is calculated by adding the probabilities of the scenarios with the same consequence category. The random variable that corresponds to the angle between the FPSO and shuttle tanker during offloading operation is modeled as Weibull distribution. According to the standards of the offloading operation in Brazil, the angle in the operational zone should not be greater than 45 degrees; as a result of these conditions, the parameter of four consequence categories was estimated, and the equation for transition rate is determined. Let us consider the two states established before: operational zone and alarm

The transition rates between states are not constant; then the stochastic process can be modeled as semi-Markov process which shows the probability of the position of the shuttle tanker

By applying the results obtained from the simulation, Markovian analysis, and event tree, the

changing from operational zone to alert zone in a given environmental condition.

probability that a K scenario is true is obtained, given the system is in the ST state.

In Eq. (5) we define a K K state transition probability matrix Mk.

zone.

Figure 5. Event tree for the offloading operation.

118 Probabilistic Modeling in System Engineering

Figure 6. Markov state transition diagram.


Table 6. Parameters and transition rate for offloading operation.


The method is a proactive methodology to prevent accidents through risk assessment aiming at identifying and depicting a system, to reduce failures and to minimize consequences of the hazardous events. The results of the analysis support the development of mitigating scenarios for the causes of hazardous events and contingency scenarios for the consequences of hazard-

Decision-Making Model for Offshore Offloading Operations Based on Probabilistic Risk Assessment

http://dx.doi.org/10.5772/intechopen.75833

121

Department of Industrial Engineering, Engineering College, University of Antioquia,

[2] Tanker Operator. Shuttles forged in the crucible. Tanker Operator, April 2003

[1] Hujer K. Trends in Oil Spills from Tanker Ships 1995–2004. London: International Tanker

[3] ONIP. Programa Nacional de Mobilização da Indústria Nacional do Petróleo e Gás Natural, 01 11 2002. [En línea]. Available from: www.onip.org.br. [Último acceso: 25 05 2008]

[4] Reis SP. Transporte marítimo de petróleo e derivados na costa brasileira: Estrutura e implicações ambientais. Rio de Janeiro: Universidade Federal do Rio de Janeiro; 2004

[5] Patino-Rodriguez C. Análise de risco em operações de "offloading" – um modelo de avaliação probabilística dinâmica para a tomada de decisão. Sao Paulo: Universidade de

[6] Nilson F. Risk-based approach to plant life management. Nuclear Engineering and Design.

[7] Aven y T, Kvaloy JT. Implementing the Bayesian paradigm in risk analysis. Reliability Engin-

[8] Siu NO, Kelly DL. Bayesian parameter estimation in probabilistic risk assessment. Reli-

[9] Jun C-H, Chang SY, Hong Y, Yang H. A Bayesian approach to prediction of system failure rates by criticalities under event trees. International Journal Production Economics. 1999;

ous events.

Author details

C. E. Patiño Rodriguez

Medellín, Colombia

Sao Paulo; 2012

2003:293-300

60:623-628

References

Address all correspondence to: elena.patino@udea.edu.co

Owners Pollution Federation; 2005

eering and System Safety. 2002;78:195-201

ability Engineering and System Safety. 1998;62:89-115

Table 7. Probabilities that the tanker is inside a given location each for each consequence category.

possible the collision between the shuttle tanker and the FPSO, given that shuttle tanker is in the inside the operational zone is

$$P(\text{K} = \text{C} | \text{ST} = 1) = \frac{(0.1954) \cdot (0.43)}{0.7918} = 0.1059$$
