Replacement policy in a system under shocks following a Markovian arrival process

• Published in: Reliability engineering & system safety Vol. 94; no. 2; pp. 497 - 502
• Main Authors: Montoro-Cazorla, Delia, Pérez-Ocón, Rafael, del Carmen Segovia, Maria
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.02.2009; Elsevier
• Subjects: Applied sciences; Exact sciences and technology; Markovian arrival process; Minimal repair; Operational research and scientific management; Operational research. Management science; Phase-type distribution; Reliability theory. Replacement problems; Replacement; Markovian arrival process; Replacement; Phase-type distribution; Minimal repair; Performance evaluation; Markov process; Replacement problem; Modeling; Stationary condition; Transients; Discrete distribution; Arrival process; Repair
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2008.06.007

We present a system subject to shocks that arrive following a Markovian arrival process. 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.