The problem of emergency combinations of events during the inspection of industrial facilities by unmanned aerial vehicles is investigated. Emergency combinations are made up of relatively harmless individually events. A formal and meaningful formulation of this problem is proposed. The first stage of solving the problem is considered: representation of the processes of development of accidents from a combination of individually non-hazardous events. For such a representation, fault trees and their minimum sections are used. At the same time, failures are understood not only as manifestations of hardware and software malfunctions, but also operator errors, as well as environmental influences. Each minimum section of such a fault tree underlies one or more scenarios for the development of accidents. An example of a fault tree with a set of minimum sections and examples of scenarios for the development of an accident during the inspection of industrial facilities by unmanned aerial vehicles is given.