# Figure 10 . Illustration of Latin hypercube sampling technique for case with two variables and eight samples.

## Context

When sampling a function of N variables (i.e., collision parameters) using LHS technique, the range of each variable is divided into M equally probable strata (intervals) as shown in Fig. 10. One sample is chosen from each stratum (e.g., assuming uniform probability over the stratum). M -th column in the N -th dimension of the hypercube corresponds to the value from M -th stratum of the N -th random variable. Sample points are then placed to satisfy the Latin hypercube requirements – see Fig. 10. This forces the number of divisions M to be equal for each variable. Also note that this sampling scheme does not require more samples for more dimensions (variables), which is one of the main advantages. In this study, fifty scenarios are randomly selected using the LHS technique. The selected PDF for each of the studied collision parameters is divided into fifty ranges, with the interval of each range determined to ensure that the area below the curve between the probability density versus collision parameter is equal. For double hull oil tankers, fifty scenarios were randomly selected using the LHS technique which as indicated in Table 2. Figure 11 shows PDFs of the selected fifty scenarios for each collision parameter. In table 2, each of the collision parameters is randomly selected within a specified range based on the gathered historical data to cover all possible collision scenarios. If the struck tanker particulars are known, the striking ship displacement, speed and draughts at time of accident will be known for fifty collision cases using table 2. For the striking ship type parameter, LHS technique produced randomly fifty different values, each one represent a certain type of ship as discussed in section 4.2.1. This paper presents an innovative method using probabilistic approaches to select relevant sets of ship-ship collision accident scenarios which represent all possible ones.
When sampling a function of N variables (i.e., collision parameters) using LHS technique, the range of each variable is divided into M equally probable strata (intervals) as shown in Fig. 10. One sample is chosen from each stratum (e.g., assuming uniform probability over the stratum). M -th column in the N -th dimension of the hypercube corresponds to the value from M -th stratum of the N -th random variable. Sample points are then placed to satisfy the Latin hypercube requirements – see Fig. 10. This forces the number of divisions M to be equal for each variable. Also note that this sampling scheme does not require more samples for more dimensions (variables), which is one of the main advantages. In this study, fifty scenarios are randomly selected using the LHS technique. The selected PDF for each of the studied collision parameters is divided into fifty ranges, with the interval of each range determined to ensure that the area below the curve between the probability density versus collision parameter is equal. For double hull oil tankers, fifty scenarios were randomly selected using the LHS technique which as indicated in Table 2. Figure 11 shows PDFs of the selected fifty scenarios for each collision parameter. In table 2, each of the collision parameters is randomly selected within a specified range based on the gathered historical data to cover all possible collision scenarios. If the struck tanker particulars are known, the striking ship displacement, speed and draughts at time of accident will be known for fifty collision cases using table 2. For the striking ship type parameter, LHS technique produced randomly fifty different values, each one represent a certain type of ship as discussed in section 4.2.1. This paper presents an innovative method using probabilistic approaches to select relevant sets of ship-ship collision accident scenarios which represent all possible ones.