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Threshold Values for the Insufficient Stability Event Index
A general problem occurring when assessing safety by probabilistic methods is the definition
of threshold probabilities. As it is not possible to achieve a residual failure probability of 0,
certain levels have to be accepted. The acceptance criteria usually consist of economic
components, which contain the overall costs caused by a certain accident, components
related to the probability of crew, passengers and third parties being injured or killed and also
components related to environmental pollution. The accepted probability related to injuries
and fatalities is split into an individual point of view, which is the probability for an individual
person and thus is always related to one injury or fatality and a societal one, which describes
the accepted residual probability in dependency of the number of expected injuries or
fatalities. That the accepted safety level differs significantly with the point of view can be
illustrated by the following example. Given a capsizing probability of 10 -3 /year a crew
member faces a probability to be killed during the total loss of his ship once in 1000 years.
Most likely he is willing to accept this probability as from his individual point of view this
seems to be very remote. From a societies point of view this failure probability might be
unacceptably high if the total merchant fleet consists of 1000 ships and in each year one of
them is lost. All this illustrates the difficulties in assigning a threshold value to a certain
criterion.
To address the problem of quantifying failure probabilities and to define acceptable safety
levels the International Maritime Organization has introduced the so called „Formal Safety
Assessment“ (FSA) which is published in IMO(2002) and IMO(2007). Here the safety level
is connected to the term risk which is the product of the probability of occurrence times the
consequence to be expected from a certain hazard. According to the published matrices an
extremely remote accident would be associated with an annual frequency of 10 -5 whilst the
severity index, which is a dimensionless measure for consequence, associates a value of 10
for catastrophic consequences, like total loss. This would then result in an annual risk R=10 -4
for such type of accident. The maximum tolerable risk according to IMO(2007) lies between
10 -5 and 10 -3 depending on which type of person (crew, passenger, third party) is addressed.
The question now being addressed is, at which ISEI values an acceptably high safety level is
reached. While the boundary of the safe domain remains unknown, the ISEI values which
are associated to clearly un-safe situations can be clearly identified by the application of the
criterion to ships which were lost by capsizing. A selection of the accidents re-investigated for
this purpose is shown in the previous chapter. The ISEI values calculated for the accident
loading condition all have the order of magnitude of 10 -1 . It can be concluded that such ISEI
values clearly represent situations in which ships are considered to be un-safe on a not
acceptable level. In a second step the stability of the capsized ships is increased to a level
where a selection of other stability criteria is fulfilled. For this second loading condition the
ISEI values typically lie below 10 -2 . Fig. 7 shows the ISEI values calculated for a selection of
ships in different loading conditions, including the ships from the investigated accidents.
The ISEI criterion was further evaluated for a large number of modern ships. Each ship is
tested in three loading conditions, whereas the first equals the intact stability limit according
to the IMO Res. A.749. The second an the third loadcase have GMs increased by 0.5 meters
and 1.0 meters, respectively. The second loadcase roughly lies in the region where modern
ship types have their stability limit according to the damage stability regulations.
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