Igor B. Shubinskiy
R & D Complex for Train Safety Ensuring and Station Processes Automation Systems, Research and Design Institute for Information, Automation and Communication in Railway Transport, Moscow, Russia.

Leonid A. Baranov
Department of Information Management and Protection, Russian University of Transport (MIIT), Moscow, Russia.

Aleksey M. Zamyshliaev
R&D Complex for Train Safety Ensuring and Station Processes Automation Systems, Research and Design Institute for Information, Automation and Communication in Railway Transport, Moscow, Russia.

DOI https://doi.org/10.33889/IJMEMS.2020.5.3.042

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Abstract

Now the scientific methodology is created, the theory and practice of the analysis and synthesis of functional safety of responsible electronic programmable devices and systems at all stages of their life cycle are developed. The basics of the methodology are fixed by standards. Methods of analysis and synthesis of functional safety are strictly formalized. They are based on the calculations of functional safety indicators with respect to failures of constituent elements and, especially, dangerous and protective failures of the system. Known methods of calculation are focused on determining the intensity and probability of dangerous failures. The objective of the proposed method lies in the fact that, in graph form, without resorting to the solution of the system of equations in the operator transformations to establish the distribution function of time until the threat or security failure, or any unhealthy condition of the system. These distribution functions determine all the necessary indicators of mean time (and, if necessary, the variance of this time) to a dangerous or protective failure. The proposed semi-Markov (Markov) operator method allows to solve a number of problems of calculation and prediction of functional safety of critical (responsible) systems. The method is formalized and suitable for subsequent computer implementation. This fact testifies to the expediency of further development of graph methods, convenient for the study of the safety of complex critical systems, devoid of the shortcomings of the proposed method in terms of the complexity of the preparatory work to determine the analytical expressions of transition probabilities in the Laplace - Stieltjes transformations. The given example of using the method has an independent value – it allows you to assess the advantages and disadvantages of ensuring functional safety by building a two-channel system without restarting the channels

Keywords- Of functional safety parameters, Hazardous and protection failures, Markov and semi-Markov stochastic processes, The weight of a path in a graph, The weight of decomposition on the graph.

Citation

Shubinskiy, I. B., Baranov, L. A., & Zamyshliaev, A. M. (2020). On the Calculation of Functional Safety Parameters of Technical Systems. International Journal of Mathematical, Engineering and Management Sciences, 5(3), 507-517. https://doi.org/10.33889/IJMEMS.2020.5.3.042.