Markov repairable systems with stochastic regimes switching

Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system can be used to model the dynamics of a repairable system whose performance regimes switch accord- ing to the external conditions. For example, to satisfy the demand variation that is typical for the power and communication systems and reduce the cost, these systems usually adjust their operat- ing regimes. The transition rate matrices under distinct operating regimes are assumed to be different and the sojourn times in dis- tinct regimes are governed by a finite state Markov chain. By using the theory of Markov process, Ion channel theory, and Laplace transforms, the up time of the system are studied. A numerical example is given to illustrate the obtained results. The effect of sojourn times in distinct regimes on the availability and the up time are also discussed in the numerical example.