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This article deals first in a theoretical fashion – a kind of a literature review – with the concept of randomness, as this appears in various disciplines. Second, an empirical approach is performed with actual data concerning marine accidents in the form of ships totally lost in two counts: ships lost per area and ships lost per month. The first appears non random and the latter is random! This finding is very crucial for the countries with the most dangerous areas, as well as for IMO. The test used for non‐randomness is the BDS statistic. The BDS statistic tests for the nonlinear dependence. The test proved randomness for monthly time series at both 95 per cent and 99 per cent confidence and non‐randomness for area data at the same confidence levels as above.

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