Using the method of trajectories for constructing a semi-Markov model of a ‘technological cell – storage device’ structure

The article presents and proves a theorem about the distribution functions for the times that the system spends in specific states taking into account the repeated enterings. The proof is based on the theorem of the mathematical expectation of the time the system spends in a given subset of states. The theorem can be used only for discrete systems. In the case of a system with a continuous phase space of states it is necessary to use the algorithm phase consolidation in order to bring the system to a discrete form. The trajectories method that allows to determine the distribution function for the time the system spends in a subset of states is presented. The current method gives the opportunity to not approximately but exactly determine the form of the distribution function for the time the system spends in a subset of states in the area of Laplace images. The trajectories method is compared to the classical method using integral Markov renewal equations on a specific example of the ‘technological cell – storage device’ structure with regard to the reliability of both the cell and the storage drive.