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Probabilistic Ship/Platform Collision Model (PSPCM)

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1. General Description

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The Bercha Group Probabilistic Ship/Platform Collision Model (PSPCM) is a simulation model suitable for evaluating the probability of collision of different types of ship traffic in a shipping lane with a fixed platform on FPSO. PSPCMR, a variation of PSPCM, models collision with randomly or non-linearly moving vessels such as fishing vessels. Because of its versatile probabilistic capabilities, the model is suitable for the calculation of first order probabilities as well as second order adjustments to account for effects of vessel traffic management systems, changes in vessel distributions from year to year and environmental and operational parameters. PSPCM is implemented through a simulation program called @ Risk with a spreadsheet and graphic interface to Microsoft Excel.

2. Parameters
All input parameters can be either single value numbers or distributions of virtually any type. Both empirical numerical distributions and closed form distributions can be utilized. The following are the principal input variables:

L = Width of shipping lane in vicinity of targets (for non-normal distributions)
CPA = Closest Point of Approach
SD = Standard Deviation of vessel distribution in lane
F = Total vessel flux or the number of vessels per year crossing a line perpendicular to the edge of the shipping lane (as a CDF or triangular distribution)
Fi = Any number (i = 1, 2, 3…. n) of classes of ships constituting the total flux. Usually three classes are used (e.g., large, medium, small vessels).
Ki = Form of distribution of traffic intensity of Class i across the shipping lane
Bi = Beam of ship in Class i
Tj = Target located at xj, yj within shipping lane
Dj = Effective diameter of target Tj
pij = Conditional probability of collision of vessel of Class i on collision course with target Tj. This probability is calculated through a fault tree, which can take into effect numerous pre-disposing factors.

3. Modeling Process
For a given set of inputs (see attached example) the model is run for an optimal number of Monte Carlo trials. Outputs are distributions of probability of collisions per year for each class of ship with each platform, as well as the collision probability for all classes. The model lends itself to easily consider the second order effects of the presence of the targets by:

Change of distribution, Ki, of traffic across the lane to accommodate effects of VTM.
Reduction of probability of collision, Pij, given a collision course, as a result of location of targets on charts and communication through VTM.
The model is a generic model developed previously by the Bercha Group for use in risk analyses conducted for marine offshore operators and the Canadian Coast Guard. It has been adapted to make use of current software PC capabilities from it previous mainframe format.

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