A measure of the safety of a system’s object can be the value of an associated risk which is based on the risks of its constituent factors (elements). The main task of the paper is the definition of the integral risk of an object and a system as a whole. This is as follows. Summing up of risks of all elements is not acceptable, since they may have, for example, different measures (the number of fatalities during a certain period of time is a social risk, and the cost of losses is an economic one). We need some other methodological tool that can transform different measures of safety of objects (elements) into a certain single integral measure of a system’s risk. Such tasks occur in medicine, food industry, in transport sector, etc. The paper offers a method to define the integral risk of a system based on the processing of a common field of the results of decisions taken on the level of risks of a system’s elements. The results of decisions are based on ALARP principle. Each of these results is one of several further probable decisions, for example, one of four decisions: intolerable risk level, undesirable level, tolerable and negligible risk level. Digitalization of these decisions of constituent elements with consideration of nonlinear growth of danger of the risk approaching to the intolerable level is made using a power function. It helps to define a numerical value equivalent to a component risk level, and then to find a weighted mean resulting numerical value equivalent to a risk level for all system components and solve an inverse task of definition of the integral risk of a system. This article describes an example of how this method could be used to solve the task of the investment priority for the works on technical maintenance of railway track. This task is limited to the ranking of track sections by priority of overhaul performance depending on the level of risks of the following factors: number of defective and flawed rails per 1 track km.; number of defective clamps per 1 track km.; number of pumping sleepers per 1 track km; number of faulty wooden sleepers per 1 track km.; number of places of temporary repair; defects of roadbed; failure rate. Based on the risk matrices constructed by the method described above in relation to each of the listed factors, an integral risk matrix is formed for the list of sections, and based on the integral estimation each section gets a priority of an overhaul performance. The given example is indicative of the efficiency and practicability of the method offered.