On Polynomial Convergence Rate for Extended Reliability Standby System

Obviously, in a reliability system consisting of two restorable elements, the distributions of work and repair times are exponential. And obviously, the switching between operating mode and repair mode and vice versa is instantaneous. In this paper, we consider the case when the behaviour (intensity of wear-out or repair) of both elements depends on each other, and the switching can be delayed. The time of such switching can be random, yet we suppose that it is limited. The random time of work and repair of elements is determined using intensities. The work and repair intensities depend on the full state of the system, i.e. on the status (element work or no) of each element and on its elapsed times in their statuses. If the distribution of work or repair time of at least one element is non-exponential, the random process describing the behaviour of such a system is not regenerative. Sufficient conditions for the ergodicity of such a process are formulated. Also, sufficient conditions for the possibility of calculating the upper polynomial bound for the rate of convergence of the numerical characteristics of the system under consideration are proposed.