Simulation of a single-component system using the trajectories method taking into account the scheduling preventive maintenance

Abstract

This article describes the functioning of a single-component system based on scheduling preventive maintenance. Its semi-Markov model using the trajectories method is constructed considering the following assumption: the time of preventive maintenance is much less than the time between failures and the time of system recovery. In addition, as a rule, the preventive maintenance is conducted out of working time fund, which justifies the assumption of its momentary execution. The employed method of trajectories is applicable only for the discrete systems. Thus, while modeling the current system, which is the system with a continuous phase space of states, the algorithm of phase consolidation for the transition to a system with a discrete phase space of states was applied. This method allows to obtain the exact solution of the task of finding the distribution function in the Laplace images, as opposed to the known methods. In order to validate the obtained results there has been a comparison of mathematical expectations of time staying in subset of operational conditions obtained due to the distribution function detected and based on the theorem of the average stationary stay time of the semi-Markov process in the subset of states.