A mathematical model of the information system (IS) for monitoring the state of objects that may be exposed to extreme influences has been built. The system consists of n devices that work independently of each other. To construct the specified information system, which has the minimum permissible reliability of event recognition, a class of structures of the type «k with n» is considered. Formulas for determining the probabilistic characteristics of n parallel reserved sensors for structures of the «k with n» type were derived; the probability of these events was calculated; and plots of their distribution were constructed. The peculiarity of the derived formulas is that they can be implemented on logical elements with which one can build a physical decision support device. The number of sensors and their corresponding probabilities of correct detection of fire at the given majority values of fire probability were also determined; the cost indicators of the information system were defined. A method for improving the reliability of IS has been developed, based on the use of the optimal number of information sensor. The ratio of finding probabilistic states of IS for structures of the «k with n» type was obtained. Algorithms for calculating the probabilities of IS states, as well as an algorithm for determining the number of information sensors and the corresponding probabilities of fire detection, have been developed. The feature of these algorithms is that they make it possible to determine the optimal number of information sensors. An estimate of the effectiveness of IS indicators of the considered types of structures was found: the probability of correct detection, the probability of non-detection, and false alarm. The reported results can be used to select the optimal structure for recognizing dangerous flight situations: choosing the number of sensors corresponding to the high probability of correct detection and the minimum probabilities of non-detection and false alarms, taking into consideration the cost of sensors.

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