The international crude oil maritime transportation system has always been disturbed by the external environment and its own mechanism of supply and demand, which can sometimes last for a long time. BDTI (Baltic Exchange Dirty Tanker Index) is one of the most typical indexes in the crude oil maritime transportation market, which is affected by many uncertain events and often lasts for a long time. So it is very significant to study fluctuation characteristics of the crude oil maritime transportation system and assess the impact of critical events, which have been referred to in this paper by improving the R/S model and selecting three international transportation lines in marine shipping ranging from 2008 to 2019. Through model applications, numerical results validate the effectiveness of this method, showing all of the three transportation lines possess long-term memory. The impact of the four critical events has also been evaluated. The study will help crude oil enterprises make investment decision on potential transportation lines and give policymakers advice to maintain stability of the crude oil industry.