Probabilistic Damage Stability for Passenger Ships—The p-Factor Illusion and Reality

Abstract

The paper complements an earlier publication by the authors addressing the probability of survival in the IMO framework for damage stability assessment, the s-factor. The focus here is on the probability of occurrence of a certain damage scenario (breach), conditional on its dimensions and location (centre and port or starboard side), the p-factor. Pertinent assumptions and limitations are explained, following its evolution for specific application to passenger ships. Attempts to provide analytical descriptions of the damage breach distributions as tetrahedra shapes positioned along the ship length whilst accounting for changes in ship geometry, structural arrangements, and subdivision for consumption by the wider profession has led to misconceptions and misunderstandings of what exactly the p-factor is in the context of probabilistic damage stability calculations. This is evidenced by the fact that the same original damage breach distributions, derived in Project HARDER, based on largely cargo ships with the age spread over the last three decades of the previous century, are still being used today for all ship types, including modern passenger ships. Filling this gap, a new database for passenger ships developed in the EC-funded Project FLARE, is briefly presented, leading to new damage breach distributions specifically for passenger ships. It is believed that this paper will throw considerable light in enhancing understanding on the p-factor, which has been cluttered with unnecessary complexity from the outset.

The importance of first-principles tools for safety enhancement in the design of passenger ships in the case of flooding events

“…[4] The probabilities described by equation [3] result from the statistical analysis of damage databases, specifically for passenger ships. The probabilities of the damage case can be described by employing the common definition of the p and s-factors (Pawlowski, 2004, IMO,2009, Vassalos et al, 2022b. On the other hand, equation [4] describes the consequences of a hazard, which are given by the fatality rate FR and the number of people onboard POB.…”

“…The full details, justifications and also applied examples for the FLARE multi-level risk framework are provided by Vassalos et al (2022b) and are not rediscussed here for the sake of brevity. The individual definition of probabilities and values associated with occurrences, survivability and fatality changes not only with the selected level between the above-presented options but is also depend upon the phase of interest during the vessel life-cycle.…”

Critical damages identification in a multi-level damage stability assessment framework for passenger ships

“…The first level for damage stability assessment relates to static calculations. The process reflects the calculation techniques amended by SOLAS regulations [2] but applies the non-zonal approach with enhanced RQMC sampling [61]. The main target of the Level 1 assessment is the determination of ship survivability and the identification of possible vulnerable areas along the vessel.…”

Alternative Assessment of Passenger Ship Safety – Early Results from the EU Project FLARE

“…Over the last 30 years the development of a framework to facilitate life-cycle flooding risk management has been thoroughly pursued by many studies and EU research projects [2]. Activities are now progressing to target risk prevention, reduction, mitigation and control, especially in emergencies, and to provide tools and a guided process to the end users, i.e., shipyards and ship owners (see Table 1).…”