3.2.2 Results of the Analysis of Intact Stability Casualty Records and Stability Parameters
3.2.2.1 Analysis of details relevant to the casualties
3.2.2.1.1 The evaluation of details relevant to the casualties is shown in Figures 2 to 7.
3.2.2.1.2 In all 166 casualties reported, the ships concerned were: 80 cargo ships, 1 cargo and passenger ship, 1 bulk carrier, 4 off-shore supply ships, 7 special service vessels, and 73 fishing vessels. Distribution of ship’s length is shown in figure 2. It is seen that the majority of casualties occurred in ships of less than 60 m in length.
3.2.2.1.3 A great variety of cargoes were carried so that no definite conclusions could be drawn. It may be noted, however, that in 35 cases of the 80 cargo ships reported, deck cargo was present.
3.2.2.1.4 The result of the analysis of the location of the casualty is shown in Figure 3. It may be seen that the majority of casualties (72% of all casualties) occurred in restricted water areas, in estuaries and along the coastline. This is understandable because the majority of ships lost were small ships of under 60 m in length. From the analysis of the season when the casualty occurred (Figure 4) it may be seen that the most dangerous season is autumn (41% of all casualties).
3.2.2.1.5 The result of the analysis of the weather conditions is shown in Figure 5. About 75% of all casualties occurred in rough seas at a wind force of between Beaufort 4 to 10. Ships were sailing most often in beam seas, less often in quartering and following seas.
3.2.2.1.6 The manner of the casualty was also analysed (Figure 6). It showed that the most common casualty was through gradual or sudden capsizing. In about 30% of casualties, ships survived the casualty and were heeled only.
3.2.2.1.7 In Figure 7 the results of the analysis of the age of ships are shown. No definite conclusions could be drawn from this analysis.
3.2.2.1.8 The distributions of stability parameters for ships’ condition at time of loss are shown in Figures 8 to 14.
3.2.2.2 Analysis of stability parameters using Rahola method
3.2.2.2.1 The stability parameters for casualty condition were analysed by plotting in a similar manner, as was done by Rahola, together with parameters for ships operated safely for comparison.
3.2.2.2.2 The parameters chosen for analysis were GM0, GZ20, GZ30, GZ40, GZm, e40, and 
m.
From the available data, histograms were prepared, where respective values of stability parameters for casualty condition were entered by starting with the highest value at the left of the vertical line (ordinate) down to the lowest value, and the values of the same parameter for safe ships were entered on the right side by starting from the lowest and ending with the highest value. Thus, at the ordinate, the highest value of the parameter for casualty condition is next to the lowest value of the parameter for the safe case. In Figure 15 an example diagram for righting levers comprising all ships analysed is shown. In the original analysis [IMO 1966, 1966a, 1985] diagrams were prepared separately for cargo and fishing vessels, but they are not reproduced here.
3.2.2.2.3 In the diagram (Figure 15), the values for casualty condition are shaded, only those that have to be specially considered due to exceptional circumstances were left blank. On the right side of the ordinate the areas above the steps were shaded in order to make a distinction between the safe and unsafe cases easier. The limiting lines or the imaginary static stability lever curves were drawn in an identical way as in the Rahola diagram. Percentages of ships in arrival condition, the respective stability parameters which are below the limiting lines are shown in table 1. The lower percentages mean in general that there is better discrimination between safe and unsafe conditions.
Table 1 – Percentages of ships below limiting line
3.2.2.2.4 The type of analysis described above is not entirely rigorous; it was partly based on intuition and allows arbitrary judgement. Nevertheless, from the point of view of practical application, it provided acceptable results and finally was adopted as a basis for IMO stability criteria.
3.2.2.3 Discrimination Analysis
3.2.2.3.1 When two populations of data, as in this case, data for capsized ships and for ships considered safe, are available and the critical values of parameters from these two sets have to be obtained, the method of discrimination analysis may be applied.
3.2.2.3.2 The application of the discrimination analysis in order to estimate critical values of stability parameters were contained in a joint report by [IMO 1966, 1966a], and constituted the basis for development of IMO stability criteria along the previously described Rahola method.
3.2.2.3.3 In this investigation, discrimination analysis was applied independently to nine stability parameters. Using data from intact stability casualty records (group 1) and from intact stability calculations for ships considered safe in operation (group 2) the distribution functions were plotted, where for group 1 the distribution function F1 and for group 2 function (1 - F2) were drawn. Practically, on the abscissa axis of the diagram, values for the respective stability parameter were plotted and the ordinates represent the number of ships in per cent of the total number of ships considered having the respective parameter smaller than the actual value for ships of group 1 and greater than the actual value for ships of group 2 considered safe.
3.2.2.3.4 The point of intersection of both curves in the diagram provides the critical value of the parameter in question. This value is dividing the parameters of group 1 and of group 2. In an ideal case, both distribution functions should not intersect and the critical value of the respective parameter is then at the point between two curves (see Figure 16).
3.2.2.3.5 In reality, both curves always intersect and the critical value of the parameter is taken at the point of intersection. At this point, the percentage of ships capsized having the value of the respective parameter higher than the critical value is equal to the percentage of safe ships having the value of this parameter lower than the critical value.
3.2.2.3.6 The set of diagrams was prepared in this way for various stability parameters based on IMO statistics for cargo and passenger ships and for fishing vessels. One of the diagrams is reproduced in Figure 17. It means that the probability of capsizing of a ship with the considered parameter higher than the critical value is the same as the probability of survival of a ship with this parameter lower than the critical value.
Figure 16 – Estimation of critical parameter
3.2.2.3.7 In order to increase the probability of survival, the value of the parameter should be increased, say up to x* (Figure 16), at which the probability of survival (based on the population investigated) would be 100%. However, this would mean excessive severity of the criterion, which usually is not possible to adopt in practice because of unrealistic values of parameters obtained in this way curves do intersect could be explained in two ways. It is possible that ships of group 2 having values of the parameter in question x < xcrit are unsafe, but they were lucky not to meet excessive environmental conditions which might cause capsizing. On the other hand, the conclusion could also be drawn that consideration of only one stability parameter is not sufficient to judge the stability of a ship.
3.2.2.3.8 The last consideration led to an attempt to utilize the IMO data bank for a discrimination analysis where a set of stability parameters was investigated [Krappinger and Sharma 1974]. The results of this analysis were, however, available after the SLF Sub-Committee had adopted criteria included in resolutions A.167(ES.IV) and A.168(ES.IV) and were not taken into consideration.
3.2.2.3.9 As can be seen from Figure 17, the accurate estimation of the critical values of the respective parameters is difficult because those values are very sensitive to the running of the curves in the vicinity of the intersection point, especially if the population of ships is small.
3.2.2.4 Adoption of the final criteria and checking the criteria against a certain number of ships
3.2.2.4.1 The final criteria, as they were evaluated on the basis of the diagrams, are prepared in the form as shown in Figures 15 and 17. The main set of diagrams did show righting lever curves (Figure 15), but diagrams showing distribution of dynamic stability levers were also included. Diagrams were prepared jointly for cargo and passenger vessels and for fishing vessels, except vessels carrying timber deck cargo. Sets of diagrams were also separately prepared for cargo ships and fishing vessels. Diagrams in the form as shown in Figure 17 were prepared separately for each stability parameter and separately for cargo and passenger ships and for fishing vessels.
3.2.2.4.2 After discussion by the Working Group on Intact Stability and the SLF Sub-Committee, the stability criteria were rounded off and finally adopted in the form as they appear in the resolutions A.167(ES.IV) and A.168(ES.IV).
3.2.2.4.3 In the original analysis the angle of vanishing stability was also included. However, due to the wide scatter of values of this parameter, it was not included in the final proposal.
3.2.2.4.4 As each criterion or system of criteria has to be checked against a sample of the population of existing ships, it was necessary to find the common basis for comparison results achieved with the application of different criteria. The most convenient basis for the comparison was the value of KGcrit that is the highest admissible value of KG satisfying the criterion or system of criteria, and the higher the value of KGcrit, the less severe the criterion.
3.2.2.4.5 As an example, criteria related to the righting lever curves could be written as:
3.2.2.4.6 If for GZ and 
, values of respective criterion are inserted, values of KGcrit for
respective displacement are obtained. Then the curve KG = f (
) crit could be drawn. KGcrit
could also be obtained graphically as shown in Figure 18. It is possible to calculate values KGcrit
also for dynamic criteria, although the method is more complicated.
3.2.2.4.7 Figure 19 shows the results of calculations of KGcrit for a fishing vessel ([IMO 1966]). Curves KGcrit = f (
) for 11 different criteria are plotted in the Figure. By having such curves for each individual criterion, it is easy to determine critical KG curve for a system of criteria by drawing envelope.
3.2.2.4.8 Curves for KGcrit, as shown in Figure 19, also allow conclusions to be drawn regarding the relative severity of various criteria or systems of criteria and to single out the governing one. If, in addition, actual values of KG for the particular ship are available, then it is possible to estimate whether the ship satisfies the criteria and which criterion leads to the condition most close to the actual condition. If it is assumed that ships in service are safe from the point of view of stability, it could be concluded which criterion or system of criteria fits in the best way without excessive reserve of stability.
3.2.2.4.9 With
a histogram of distribution of k is shown for the group of ships analysed (Figure 20).
