A warmstandby system under shocks and repair governed by MAPs

A system with n components, one online and the rest in standby subject to repair is considered. The source of failures of the online unit is different from the one of the standby units. They are governed by two independent Markovian arrival processes. The repair times also follow another Markovian arrival process, independent of the previous ones. As a consequence of these assumptions, the interarrival times between failures are dependent, and the same for the consecutive repair times. The multidimensional Markov process governing the system is constructed and the availability, reliability, and the rate of occurrence of failures are calculated. The renewal process associated to the replacements when the system is down is determined and the number of replacements with time are calculated. This system is general in several ways and it extends others previously published in the literature. A numerical application considering three simulated MAPs is performed; the descriptors of the MAPs and the performance measures of the system are calculated.