According to statistics, the number of accidents related to the failures of ship engine and propulsion systems remains in second place among the total number of accidents. One of the reasons for the destruction of diesel crankshafts, intermediate and propeller shafts, elastic couplings and other elements of shaft lines are torsional vibrations in combination with other types of fluctuations and vibrations. The main method for monitoring the level of torsional vibrations in ship’s shaft lines remains periodic torsiography or strain measurement. The widespread introduction of diagnostic and control systems on ships leads to the technical possibility of constant monitoring of the level of torsional vibrations, which will allow you to reduce the risks of accidents in the periods between torsiography. Like any new technical solution, the introduction of torsional vibration monitoring systems requires a scientific justification of the need for their application, which can be carried out with using risk theory. The results of applying the risk matrix to justify the installation of torsional vibration monitoring systems in marine propulsion systems are presented in the paper. As a result, a risk matrix with quantitative parameters is obtained to justify the installation of torsional vibration monitoring systems and reduce the risks of ship’s shaft line breakdowns. As an example, the application of the risk matrix for “OT” type tugs, which are widely used for various operations on the Russian waterways, is considered. It is established that for these types of vessels, the use of a monitoring system will be justified to reduce the risks of accidents, serious accidents and catastrophes that may arise from the development of dangerous torsional vibrations. A method for applying the assessment of the damage degree from an accident occurrence to determine the reduction of economic costs when using torsional vibration monitoring systems is proposed in the paper. It is found that for the “OT” type tugs, the installation of torsional vibration monitoring systems will be justified, both from the point of view of economics and reducing the accidents risks of ship engine and propulsion systems.