The paper is devoted to mathematical modeling of the analysis of the survival of an automated information system in enterprises, namely the survival of a file server for production management. Based on the studies, a methodology was developed for constructing a survival analysis model for an automated information system, which consisted of using beta distributions as a survival analysis model. This model can effectively predict the behavior of a system after an attack and the prospective life expectancy of both the whole system and its separate components, calculating risk parameters for a beta distribution of the probability density of damage and building the dependence of the values of the estimates of the survival function and instant risk function on specific factors.