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Markov model of the ship’s navigational safety on the open water area

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Abstract: In the paper the navigational safety model for ship on the open area Has been proposed. The Markov process has been used to describe the safety model. Futhermore, the characteristics of this model have been determined. 1. INTRODUCTION The navigational safety is based primarily on analysis of current situation and depends on the interaction between the man, technology and environment . The literature mentions that the errors at any of components have the greatest impact on the occurrence of hazardous situations. Therefore, the methods and criterions to settle the hazard situation and to evaluate of quality control and assessment in terms of traffic safety is very important. It could help to develop the best control or the best manoeuvres for given hazard situation . Thus, the ability to anticipate the navigation of a hazardous situation is possible.
For better analysis of the hazard situation at sea, two basic measures - the CPA and TCPA ([9]), for estimation of closer distance between ships were introduced. Another important approach to the risk of the ship is domain analysis ([1], [6]).
The article attempts to describe the stochastic model as a tool to analysis of the hazard situation. The Markov processes ([5], [10]) are used to describe the main characteristics of the considered model.
The main part of the analysis of particular navigational situation is an observation.
During this process the navigator’s focus on direction where the potential danger is the highest. Therefore the area of observation can take any symmetric or asymmetric shape and take different values of the collision probabilities. Hence, the concept of the random map of hazards was introduced in [11].
The model of the ship on the waterway is the operation process. In article, we used the following notations [11], [12]:
X ij - is two dimensional binary random variable representing random state of component e ij , which is equal to 1, when component e ij is free and is equal to 0, in the other case, i = 1,2,..., n, j = 1,2,..., li , p ij = P ( X ij = 1) - is the probability of event that component e ij is free, i = 1,2,..., n, j = 1,2,..., li , q ij = 1 − p ij = P ( X ij = 0 ) (...)

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