The article discusses mathematical models and algorithms used in automated control systems to increase the safety of oil refineries in the Republic of Kazakhstan and reduce the likelihood of accidents due to a critical combination of events. The main attention is paid to the mathematical apparatus, which allows identifying and preventing the occurrence of critical combinations of events, each of which individually does not significantly affect the safety of the operation of the oil refinery. For this purpose, along with the traditionally used fault trees, it is proposed to use the tree in the form of a dynamic graph, which will allow us to take into account when preparing and making decisions to improve the safety of functioning also the rapidly changing cause-effect relationships between the modeled variables. An example of such a fault tree describing the development of a fire in the tank farm of an oil refinery is considered in detail in the article. For this fault tree, for the five-element minimum section of the state graph of the functioning process, a list of minimum sections is defined that formalize the critical combinations of events consisting of 5 independent events. A general algorithm has been developed for solving the problem of identifying and preventing critical combinations of events. It is based on the apparatus of Markov chains, which allows, under certain limitations imposed on the process of occurrence of critical combinations of events during the operation of an oil refinery, to consider it as a random process satisfying the Markov property with natural filtration. This assumption allows us to use when determining the probability of occurrence of critical combinations of events of the Kolmogorov-Chapman system of equations, the solution of which is carried out in the article using the fourth-order accuracy numerical Runge-Kutta method. The developed software will be used during the modernization of company group “Condensate” of the Republic of Kazakhstan.