3 The probability density functions (pdf's)

  3.1 The Revised Interim Guidelines contain probability density functions (pdf's) describing the location, extent and penetration of side and bottom damage. These functions were derived from historical damage statistics for 52 collisions and 63 groundings, compiled by the classification societies at IMO's request ^{(2) footnote}. These statistics were derived from casualties to oil tankers, chemical tankers, and combination carriers of 30,000 tonnes deadweight and above, for the period 1980 to 1990.

  3.2 Figure 1 shows the statistic data and piecewise linear probability density function, representing the longitudinal extent of damage when subject to bottom damage. Other forms of curve fitting such as beta distributions were also considered. However, they were found to have little impact on the overall analysis, and therefore the easier to apply piecewise linear fit was adopted for the Revised Interim Guidelines.

  3.3 Side damage pdf's as shown in figures 2 through 6 provide the probability of damage as a function of:

• Longitudinal location
• Longitudinal extent
• Vertical location
• Vertical extent
• Transverse penetration

  3.4 Bottom damage pdf's as shown in figures 7 through 11 provide the probability of damage as a function of:

• Longitudinal location
• Longitudinal extent
• Transverse location
• Transverse extent
• Vertical penetration

  3.5 The density scales are normalized by the ship length for longitudinal location and extent, by ship breadth for transverse location and extent, and by ship depth for vertical location and extent. The pdf variables are treated independently for the lack of adequate data to define their dependency.

  3.6 These functions are based on limited statistics consisting of damages to largely single-hulled tankers. These statistics should be periodically reviewed as new data becomes available.