A Functioning Mathematical Model of an Element Affecting the Operational Safety of a Complex Technical System

A mathematical model is developed that allows establishing an analytical relationship between the probability of detecting an element that affects the safety of a complex technical system in a state that creates prerequisites for an incident. Graphs of possible operating states are considered in cases where the analyzed system element is constantly involved in a potentially hazardous operation or is waiting to participate in a potentially hazardous operation or safety operation. The use of numerical methods gives the developed mathematical model flexibility, since there are no restrictions on the type of distribution functions under consideration. The obtained results can be used to assess the integrated index of the complex technical system safety and to determine rational parameters for their safe maintenance.