Peschansky A. Peschansky A.I. Semi-Markovian models of multi-component restorable systems maintenance

The thesis is dedicated to the building of multicomponent restorable systems maintenance mathematical models on the basis of semi-Markovian processes with a general phase field of states under the assumption of a general view of operating time to failure and system's elements restoration time distribution. Semi-Markovian models of maintenance in age, in useful life of elements, and in calendar maintenance have been built both for full and minimum restoration of elements after their failure. For the indicated maintenance strategies the explicit stationary distributions of embedded Markovian chains of semi-Markovian processes describing an evolution of systems have been found. Due to it the following stationary characteristics of systems have been defined in an explicit form: mean stationary operating time between failures; mean stationary restoration time; stationary steady state availability factor; mean specific income of a system per unit of calendar time; mean specific expenses per unit of system's good state. On account of criterion functions found in the work a complex of problems on defining an optimal frequency of maintenance with the purpose of gaining the best values of system's stationary characteristics has been solved. Sufficient conditions for existence of optimization problem's solution have been found. The adaptability and applicability of the results obtained for solving certain practical problems of complex technical systems' operation reliability and efficiency at the expense of choosing optimal frequency of maintenance execution have been shown.