The article presents the results of developing of mathematical models of reliability for systems of railway automatics and telemechanics, at the stage of use by the end of the period after commissioning of the system to the cancellation, taking into account the protection failures and four system states: the new, aging, pre-failure state, failure. Created graph models of protection failures and recoveries had supplied an opportunity to develop a system of differential equations of A. N. Kolmogorov for the general case of technical operation of the system and the functioning of the system in the most likely mode of its operation. When synthesiz-ing the second model author takes into account that the state transitions of aging to new and state of failure to pre-failure state, and the emergence of failures during the performance of modernization of the systems, equipment replacements and on-site repair are unlikely. Under certain numerical values of transitions intensity developed models allow to calculate the probability of fi nding the system in any of the states by substituting these values in the points of a system of differential equations.Also author has developed a model based on stochastic matrices, using the probabilities of transitions from one state to another. The sequence of changes of the state in time is described by a Markov chain with stationary transition probabilities. The mathematical model of the process includes a column vector that specifi es the probabilistic distribution of the states at time zero, and the stochastic matrix of transition probability from one state to another. Such models are evident and are the most complete, when the transition between all possible states of an object or pending is taken into account. There is an example of the use of models based on stochastic matrices.
systems of automation and telemechanics on railways, reliability, graph model, system state, state transitions, Kolmogorovs differential equations, stochastic matrix of transition probabilities, the probability of stay of system in a certain state
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