A redundant n-system under shocks and repairs following Markovian arrival processes

• An n-system under shocks and repair is studied under matrix-analytic methods.
• The shocks and repairs arrive following independent Markovian arrival processes.
• The interarrival times between shocks and between completed repairs are dependent.
• The system is studied in transient and stationary regime.

A system with n components, one online and the rest in standby subject to repair is considered. The shocks causing the failure of the system follow a Markovian arrival process and the successive repair times are governed by another Markovian arrival process independent of the first one. In this way, the interarrival times between successive shocks are dependent and the same for the successive repair times. The Markov process governing the system is constructed and it is studied in a transient and stationary regime, calculating the availability, the reliability and the rate of occurrence of failures. We show how this system extends others previously published in the literature. A numerical application is performed.