Application of theory of semi-Markov processes to determining distribution of probabilistic process of marine accidents resulting from collision of ships

Abstract

In this paper is presented possible application of the theory of semi-Markov processes to elaborating an eight-state model of the process of occurrence of serviceability state and unserviceability states of sea-going ships making critical manoeuvres during their entering and leaving the ports. In the analysis it was taken into account that sea-going ships are in service for a very long time t (t →∞). The model was elaborated to determine the probability (P₀) of correct execution of critical manoeuvres during ship’s entering and leaving the port as well as the probabilities P_j(j = 1, 2, 3, …, 7) of incorrect execution of critical manoeuvres by a ship, that leads to marine accidents. It was assumed that such accidents result from: ship’s grounding on port approaching fairway, collision with a ship on port approching fairway, collision with a pierhead during passing through port entrance, collision with a hydrotechnical structure during ship’s passing through port channels, collision with a port quay during coming alongside it and collision with a ship already moored to the quay. The probability (P₀) was assumed a measure of safe execution of a critical manoeuvre. The probability characterizes possibility of avoiding any collision during ship’s entering and leaving the port. The probability P_a = 1 – P₀ was assumed a measure of occurrence of a collsion and - consequently - marine accident. The probability Pa was interpreted as a sum of the probabilities P_j(j = 1, 2, 3, …, 7) of occurrence of all the selected events. In summing up the paper, attention was drawn to its merits which - in opinion of this author - are crucial for research on real process of accidents during entering the port and leaving it by sea-going ship in difficult navigation conditions.