A system subject to shocks that arrive following a Markovian arrival process is presented. The system is minimally repaired. It is replaced when a certain number of shocks arrive. A general model where the replacements are governed by a discrete phase-type distribution is studied. For this system, the Markov process governing the system is constructed, and the interarrival times between replacements and the number of replacements are calculated. A special case of this system is when it can stand a prefixed number of shocks. For this new system, the same performance measures are calculated. The systems are considered in transient and stationary regime.
- Markovian arrival process
- minimal repair
- phase-type distribution
Montoro-Cazorla, D., Pérez-Ocón, R., & Segovia, M. D. C. (2009). Replacement policy in a system under shocks following a Markovian arrival process. Reliability Engineering and System Safety, 94(2), 497-502. https://doi.org/10.1016/j.ress.2008.06.007