Shock model in Markovian environment

A Markov modulated shock model is studied in this paper. In this model, both the interarrival time and the magnitude of the shock are determined by a Markov process. The system fails whenever a shock magnitude exceeds a pre-specified level η. Nonexponential bounds of the reliability are given when the interarrival time has heavy-tailed distribution. The exponential decay of the reliability function and the asymptotic failure rate are also considered for the light-tailed case.