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"Probabilistic damage" refers to a method for computing a measure of probable damage survivability which takes into account not only the vessel's stability when certain subdivisions of the ship are damaged but assigns probabilities to various extents of damage as well as to the survivability when so damaged. The products of these probabilities are summed over the various possible combinations of flooding which could occur from a single breach of the hull, and the result is called the "Attained Subdivision Index".

In GHS terminology, a subdivision of the ship is called a "division". A division is a collection of one or more adjacent tanks/compartments.

In essence, the procedure is as follows:

1) A certain load condition is set for the ship (weight and CG, possibly including loaded tanks).

2) An accumulator variable A (the Attained Index) is initialized to zero.

3) For a given subdivision of the ship, a probability of damage (P) is determined by the size and location of the division. (The longer the division, relative to the length of the ship, the higher its probability of damage).

4) A probability of survival (S) relative to the division is determined by examining the damaged stability characteristics with the division flooded.

5) The product, P*S is added to the attained index: A <-- A + P*S

6) Steps 3 through 5 are repeated for each division.

7) Steps 1 through 6 are repeated for additional load condition(s) and the attained indices for each are averaged.

A certain minimum average Attained Index is required by the rules, based on the size of the ship.

The actual procedure is somewhat more complicated since it can look at fractions of a division being flooded independently as well as multiple divisions being flooded together.

Note that it is inherent in this procedure that all subdivisions of the vessel need not be included in the analysis as long as the Attained Index reaches the minimum required value.

The first step is to define the division geometry, since GHS needs to know what are considered divisions. It does not assume that each tank and compartment is an independent division. Normally, each double bottom tank should be included with at least one other compartment, rather than being a division by itself.

For defining divisions, use the command

DIVISION (which assigns a unique numbern) =TankList[/WING:b] [/HBHD:v]

When performing the probabilistic damage procedure, GHS sorts the divisions into order according to their forward longitudinal locations. It then proceeds to use the divisions from bow to stern. After completing the survivability analysis using the first (forwardmost) division, it takes the next division which starts at or after the aft end of the present division. Hence any overlapping division will be ignored.

For this purpose, the nominal forward and aft ends of the division are used. The nominal ends are the same as the actual ends taken from the geometry unless the /FWD and /AFT parameters are used with the DIVISIONS command to set nominal ends at other locations. By this means, divisions which do overlap can be made acceptable. See the DIVISIONS command in the GHS User's Manual for more details.

After all of the divisions have been defined, the Attained Subdivision Index in the current loading condition may be obtained by the command

DAMSTAB [(which computes and displays the probability of damage and probability of survival for each damage case as well as the attained index. IfDivList)] [/L:L1,L2] [/B:B] [/H:Hmax] /SDIC

Following is an example of a subdivision index Run File.

PROJECT CARGO1 READ REPORT

DIV(1) workspc.c, fwctk.c, apt.c /AFT:107.3

DIV(2) no2dot.s, btmineng.c, enginrm.c /FWD:82.9

DIV(3) hold5.c, no4wbt.s, void5.s /AFT:82.2 /FWD:69.6

DIV(4) fwt.s, void4.s, no4wbt.s, hold4.c /AFT:69.6 /FWD:56.3 /WING:3.0

DIV(5) no3wbt.s, no2wing.s, void3.s, hold3.c /AFT:56.3 /FWD:43. /WING:3.0

DIV(6) no3wbt.s, no1wing.s, void2.s, hold2.c /AFT:43. /FWD:29.7 /WING:3.0

DIV(7) no2wbt.s, void1.s /AFT: 29.7 /FWD:20.6

DIV(8) hold1.c, no1wbt.c, no2wbt.s, void1.s /AFT:20.6 /FWD:9.4

DIV(9) thrstrm.c DIV(10) fpt.c /FWD:-4.80 DIV

MACRO case TRIM = 0 HEEL = 0 DRAFT = %1 VCG = %2 SOLVE WEIGHT, LCG DAMSTAB /SDIC /

.case 6.5, 7.13 .case 4.684, 6.564

QUIT

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