Aggregated semi-Markov repairable systems with history-dependent up and down states

This paper introduces a Markov model for a multi-state repairable system in which some states are changeable in the sense that whether those states are up or down depends on the recent system evolution history. Several reliability indexes, such as availability, mean up time, steady-state reliability, are calculated using the matrix method. A sufficient condition under which the availabilities of the monotone repairable systems with history-dependent states can be compared is also obtained. Some examples are presented to illustrate the results in the paper. Mathematics Subject Classification: 60K10.