1 The harmonized SOLAS regulations on subdivision
and damage stability, as contained in revised SOLAS chapter II-1, adopted by resolution MSC.194(80)
footnote, 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. This can be
considered an objective measure of ship 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 these regulations
are the forward and bottom regions which are dealt with by special
subdivision rules provided for the 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
the 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 Due to this, the effect of a three-dimensional
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
due 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 of 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 a 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 surviving such damages
as lead 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, calculation
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:
A ≥ R
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:
A
= ∑pisi
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.
The value of "pi" 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 their own probability of occurrence.
The value of "si" 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 was
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 five-dimensional 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 the ship.