Stationary characteristics of unreliable system with branching structure and elements’ maintenance

The research object is a tree-system of the branching structure. Each element of any level controls several elements of a lower level and is controlled by one element of a higher level. The elements of the same rank are assumed to be of the same type. Any element failure of the system is detected instantly and its restoration begins immediately. During the element failure, all the following associated elements stop operating and being restored. It also disables all elements that precede the failed element and do not belong to any other operable path. When the element is restored, all the previously disabled functional elements, which form a workable path with the restored element, also begin operating. The system is considered to fail if there is not a single operable path connecting the main element and output. All the random variables describing the system are assumed to have distributions of general kind. To improve stationary reliability and economical indexes preventive maintenance is carried out according to the age strategy. By means of an apparatus of the theory of semi-Markov processes with a discrete-continuous set of states, iteration formulas for calculating operating efficiency, average specific income and average specific expenses are obtained. The expressions obtained for these stationary characteristics in explicit form allow to get optimal intervals of elements’ maintenance. A numerical example of applying the obtained calculation formulas is given.