1 The harmonized SOLAS regulations on subdivision and damage stability, as
contained in SOLAS chapter II1, are based on a probabilistic concept which
uses the probability of survival after collision as a measure of ships' safety in a
damaged condition. This probability is referred to as the "attained subdivision index
A" in the regulations. It can be considered an objective measure of ships'
safety and, ideally, there would be no need to supplement this index by any
deterministic requirements.
2 The philosophy behind the probabilistic concept is that two different ships with the
same attained index are of equal safety and, therefore, there is no need for special
treatment of specific parts of the ship, even if they are able to survive different
damages. The only areas which are given special attention in the regulations are the
forward and bottom regions, which are dealt with by special subdivision rules provided
for cases of ramming and grounding.
3 Only a few deterministic elements, which were necessary to make the concept
practicable, have been included. It was also necessary to include a deterministic "minor
damage" on top of the probabilistic regulations for passenger ships to avoid ships being
designed with what might be perceived as unacceptably vulnerable spots in some part of
their length.
4 It is easily recognized that there are many factors that will affect the final
consequences of hull damage to a ship. These factors are random and their influence is
different for ships with different characteristics. For example, it would seem obvious
that in ships of similar size carrying different amounts of cargo, damages of similar
extents may lead to different results because of differences in the range of
permeability and draught during service. The mass and velocity of the ramming ship is
obviously another random variable.
5 Owing to this, the effect of a threedimensional damage to a ship with given watertight
subdivision depends on the following circumstances:

.1 which particular space or group of adjacent spaces is flooded;

.2 the draught, trim and intact metacentric height at the time of damage;

.3 the permeability of affected spaces at the time of damage;

.4 the sea state at the time of damage; and

.5 other factors such as possible heeling moments owing to unsymmetrical
weights.
6 Some of these circumstances are interdependent and the relationship between
them and their effects may vary in different cases. Additionally, the effect of hull
strength on penetration will obviously have some effect on the results for a given ship.
Since the location and size of the damage is random, it is not possible to state which
part of the ship becomes flooded. However, the probability of flooding a given space can
be determined if the probability of occurrence of certain damages is known from
experience, that is, damage statistics. The probability of flooding a space is then
equal to the probability of occurrence of all such damages which just open the
considered space to the sea.
7 For these reasons and because of mathematical complexity as well as insufficient data,
it would not be practicable to make an exact or direct assessment of their effect on the
probability that a particular ship will survive a random damage if it occurs. However,
accepting some approximations or qualitative judgments, a logical treatment may be
achieved by using the probability approach as the basis for a comparative method for the
assessment and regulation of ship safety.
8 It may be demonstrated by means of probability theory that the probability of ship
survival should be calculated as the sum of probabilities of its survival after flooding
each single compartment, each group of two, three, etc., adjacent compartments
multiplied, respectively, by the probabilities of occurrence of such damages leading to
the flooding of the corresponding compartment or group of compartments.
9 If the probability of occurrence for each of the damage scenarios the ship
could be subjected to is calculated and then combined with the probability of surviving
each of these damages with the ship loaded in the most probable loading conditions, we
can determine the attained index A as a measure for the ship's ability to sustain
a collision damage.
10 It follows that the probability that a ship will remain afloat without
sinking or capsizing as a result of an arbitrary collision in a given longitudinal
position can be broken down to:

.1 the probability that the longitudinal centre of damage occurs in just the
region of the ship under consideration;

.2 the probability that this damage has a longitudinal extent that only includes
spaces between the transverse watertight bulkheads found in this region;

.3 the probability that the damage has a vertical extent that will flood only the
spaces below a given horizontal boundary, such as a watertight deck;

.4 the probability that the damage has a transverse penetration not greater than
the distance to a given longitudinal boundary; and

.5 the probability that the watertight integrity and the stability throughout the
flooding sequence is sufficient to avoid capsizing or sinking.
11 The first three of these factors are solely dependent on the watertight
arrangement of the ship, while the last two depend on the ship's shape. The last factor
also depends on the actual loading condition. By grouping these probabilities,
calculations of the probability of survival, or attained index A, have been
formulated to include the following probabilities:

.1 the probability of flooding each single compartment and each possible group of
two or more adjacent compartments; and

.2 the probability that the stability after flooding a compartment or a group of
two or more adjacent compartments will be sufficient to prevent capsizing or
dangerous heeling due to loss of stability or to heeling moments in intermediate
or final stages of flooding.
12 This concept allows a rule requirement to be applied by requiring a
minimum value of A for a particular ship. This minimum value is referred to as
the "required subdivision index R" in the present regulations and can be made
dependent on ship size, number of passengers or other factors legislators might consider
important.
13 Evidence of compliance with the rules then simply becomes:
13.1 As explained above, the attained subdivision index A is determined by a
formula for the entire probability as the sum of the products for each compartment or
group of compartments of the probability that a space is flooded, multiplied by the
probability that the ship will not capsize or sink due to flooding of the considered
space. In other words, the general formula for the attained index can be given in the
form:
13.2 Subscript "i" represents the damage zone (group of compartments) under
consideration within the watertight subdivision of the ship. The subdivision is viewed
in the longitudinal direction, starting with the aftmost zone/compartment.
13.3 The value of "p_{i}" represents the probability that only the
zone "i" under consideration will be flooded, disregarding any horizontal
subdivision, but taking transverse subdivision into account. Longitudinal subdivision
within the zone will result in additional flooding scenarios, each with its own
probability of occurrence.
13.4 The value of "s_{i}" represents the probability of survival
after flooding the zone "i" under consideration.
14 Although the ideas outlined above are very simple, their practical
application in an exact manner would give rise to several difficulties if a
mathematically perfect method were to be developed. As pointed out above, an extensive
but still incomplete description of the damage will include its longitudinal and
vertical location as well as its longitudinal, vertical and transverse extent. Apart
from the difficulties in handling such a fivedimensional random variable, it is
impossible to determine its probability distribution very accurately with the presently
available damage statistics. Similar limitations are true for the variables and physical
relationships involved in the calculation of the probability that a ship will not
capsize or sink during intermediate stages or in the final stage of flooding.
15 A close approximation of the available statistics would result in extremely numerous
and complicated computations. In order to make the concept practicable, extensive
simplifications are necessary. Although it is not possible to calculate the exact
probability of survival on such a simplified basis, it has still been possible to
develop a useful comparative measure of the merits of the longitudinal, transverse and
horizontal subdivision of a ship.