The Operational Safety (OS) of Industrial Systems is today a true engineering discipline, applied in all the different phases of the life of an industrial system, from its conception to its decommissioning, going through the stages of development and operation. In a broad sense, the Operational Safety of Systems can be defined as "Science of Failures." It thus includes knowledge, assessment, prediction, measurement, and control of system failures. In a strict sense, the Operational Safety of Systems is the ability of a system to successfully accomplish the mission for which it was designed, without the occurrence of events with undesirable consequences not only for the components of the system but also the operators, the general public and environment with which the system is in interaction. The objective of the present work is to present the basic concepts and probabilistic methods applied in the different phases of the life of an industrial system to provide an adequate Operational Safety. For this, it begins by presenting some fundamental concepts, deepening in the main component concepts of OS: Reliability, Availability, Maintainability and Security. Next, the use of probabilities is discussed, as well as their most significant laws within the application fields of OS and formalizing the concept of risk. The allocation methods and the assessment methods of the safety of an industrial system are then presented and discussed. Finally, it is proposed a rational procedure for the safety analysis of systems, and ways of using this procedure to the design of systems.