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Probabilities could be attached to different hazards when second and further down levels in fault trees are identified. Therefore the next step in the identification of hazards and estimation of their probabilities is construction of fault trees and event trees.
Table 1. Hazards classification
R Description Frequency per ship Frequency per fleet Probability (hourly)
1 Frequent Likely to occur frequently -one or more times per year Continuously Greater than 10"3 do 10"4
2 Probable Several times per ship's lifetime - once every few years Once or more times in a year 10"4 do 10"5
3 Occasional Likely to occur once during the lifetime of the ship Several times during fleet's lifetime -once every few tears 10"5 do 10"'
4 Remote Unlikely, but possible during lifetime of the ship Probable once during lifetime of the fleet <10"7
5 Extremely improbable So extremely remote that it does not to be considered as possible to occur Substantially less than 10"7
Table 2. Averaged ranking of hazards as assessed by the group of experts
Hazard Ranking
Ferry Passenger ship Container Bulk carrier
Insufficient 1 4 2 2
stability
Forces of 4 4 3 4
the sea
Cargo shifting 4 1 3 3
Icing 4 4
HOE 3 5 2 4
External 2 3 3 2
heeling
moments
Cargo and ballast 3 4 3
operations
Fire and 4 4 3 4
explosion
5. Risk evaluation
Risk is defined as a product of hazard probability and hazard severity (consequences):
R = P S
To facilitate the ranking and validation of ranking IMO [11] recommended to define consequence and probability indices on a logarithmic scale. A risk index may therefore be established by adding the probability (frequency) and consequence indices. We have then:
Log (risk) = Log (frequency) + Log (consequence)
In order to assess risk, both quantities in the above equation should be evaluated. IMO recommended for the maritime safety uses-for the frequency of accidents ranking from FI=7 (frequent) to FI=1 (extremely improbable) and for consequences scale SI=1 (negligible), SI=2 (marginal), SI=3 (critical) and SI=4 (catastrophic). This classification is useful for the safety assessment in particular for the evaluation of risk control options.
With regard to safety against capsizing obviously we may consider only levels of frequency 1 to 4 and hazard severity of the category SI=3 (critical) and SI = 4 (catastrophic) because capsizing or loss of stability accident has always catastrophic or critical consequences and, on the other hand, probability of capsizing must be kept low. Catastrophic effect (Category SI = 4) would mean capsizing and loss of the ship, whether critical hazardous effect (Category SI =3) would mean dangerous list and loss of ability to sailing further, which, according to definition would mean loss of stability accident (LOSA).
Based on the above risk index matrix could be constructed (Table 3). The risk indexes applicable to stability (safety against capsizing or against LOSA accident) are grouped in the lower right corner of the matrix.
Figure 2. Basic events tree for stability
For assessment of risk index and in order to construct risk matrix, IMO resolution recommended using hazards and operability study (HAZOP). Frequencies of hazards could be assessed on the basis of risk contribution trees (RCT) being a set and combination of all fault trees and event trees as defined below [11].
A fault tree is a logic diagram showing the casual relationship between events, which singly or in combination occur to cause the occurrence of higher level event. It is used to determine the probability of the
top event. Fault tree is to"down procedure systematically considering the causes and events at levels below the top event. The top events are events shown in the Figure 2.
Table 3. Risk matrix
Risk Index (RI)
FI FREQUENCY SEVERITY
1 2 3 4
Minor Signifie ant Severe Catastr ophic
7 Frequent 8 9 10 11
6 7 8 9 10
5 Reasonably probable 6 7 8 9
4 5 6 7 8
3 Remote 4 5 6 7
2 3 4 5 6
1 Extremely remote 2 3 4 5
An event tree is logic diagram used to analyse the effect of an accident, a failure or an unintended event. The diagram shows the probability or frequency of the accident linked to those safeguard actions required to be taken after occurrence of the event to mitigate or prevent escalation. An event tree is down-top procedure starting from the undesired event and leading to possible consequences.
In the risk analysis of stability safety a number of risk contribution trees (RCT) have to be constructed, for each of the undesired event (hazard) in the first level hazard identification tree (Figure 2). Moreover, for some hazards require more than one fault and event tree to be constructed, because of possibility of different capsizing scenarios. Therefore, before RCT are constructed, different modes or scenarios of capsizing must be identified. This is particularly important with regard to forces of the sea, where more than twenty different capsizing scenarios could be identified.
Generally it appears that within risk analysis the system of RCT's may be quite complex, but in cases of risk analysis for concrete design it may by considerably simplified, because some of the hazards identified may be not applicable. As an example of this method risk contribution trees in the case of icing is shown.
6. A case study - icing
Icing was considered by the group of experts as one of the most serious hazards that may cause LOSA. Generally icing is considered dangerous for small ships and in particular for ships operating in high latitudes. However experts were of the opinion that icing is also dangerous for larger ships and not necessary operating in arctic water. As an example it was shown the photograph of icing that happened onboard M/S STEFAN BATORY in North Atlantic (Figure 3).
Figure 3. Example of icing in North Atlantic.(Photo: Kpt. Z.W. Hieronim Majek)
Requirements concerning icing are currently included in the recommendatory part of the IS Code [12]. They are limited to the specification of amount of ice that has to be taken when calculating stability of ships sailing in certain areas. Those are general recommendations, the Administrations are encouraged to use different values of accrued ice if they have their own experience.
Te ice accretion is, however, o complex process. Not entering into details, it can be stated that ice accretion depends on several factors, of which the sea state, air and sea temperatures, wind velocity, ship speed and heading with regard to wind direction are of importance. In many cases ice accrued may exceed several times values recommended by IMO IS Code. Analysis of LOSA accidents reveals several casualties caused by ice accretion, some of them even in Black Sea [21].
The structural model for calculating effect of ice accretion is simple and it is identical to putting additional load onboard, but as the ice is accrued mostly on exposed decks, superstructures and rigging, the centre of gravity of ice accrued is positioned high. Therefore stability of the ship is impaired and the ship might be in dangerous situation.
The branch of fault tree for the case of dangerous icing must take into account
Figure 4. Branch fault tree for dangerous ice accretion
