Maritime transportation is the essence of the international economy. Today, about ninety percent of world trade is carried out by sea through 50,000 merchant ships. Most of these vessels are powered by mainline diesel engines due to their reliability and fuel efficiency. Reliability of system elements in general depends on random failures, significant wear during operation, additional wear during start-up. Accidental damage to diesel engine components is a major hazard during operation, as some parts (such as cylinder liners and pistons) are usually replaced during repairs. On the other hand, preventive service does not eliminate random malfunctions. Therefore, in the general problem of assessing the reliability of a diesel engine, there is a mathematical problem of assessing the reliability and durability, taking into account only the random failures of its elements, which are of the greatest practical importance. The purpose of the work is a mathematical study of the reliability of parts of the cylinder-piston group of the main engines of dry cargo ships. Using a systematic approach and a probabilistic statistical method, it was established that the most common and difficult case is the simultaneous action on a system element (for example, a cylinder sleeve) of factors that cause wear during the period of operation (including during the start-up period) and accidental failures. It was determined that the quality of the cylinder-piston system in ships of the "Ostriv Rosiyskiy" type is higher than in the ships of the "Simferopol" and "Murom" types. Empirical formulas for estimating the probability of emergency failure of main engine system elements during the period of operation between factory repairs were obtained, where the main danger during the period of operation was carried by accidental failures. Based on the results of the study, it is possible to establish a schedule for the periodicity of maintenance of the ship's main engine and the cost of losses due to ship downtime due to failures, and can also be used in the reliability study of other types of ship's main engines. The results make it possible to determine the reliability of the parts of the cylinder-piston group of the main engines of dry cargo ships. and, in particular, to establish the maintenance schedule of the ship's main engine and the cost of damages due to ship downtime due to failures, and can also be used in the study of the reliability of other types of main engines of other series of ships