Reliability of a system under two types of failures using a Markovian arrival process. (English) Zbl 1152.90408

Summary: We consider a system subject to external and internal failures. The operational time has a phase-type distribution (PH-distribution). Failures arrive following a Markovian arrival process (MAP). Some failures require the replacement of the system, and others a minimal repair. This model extends previous papers with arrivals governed by PH-renewal processes.


90B25 Reliability, availability, maintenance, inspection in operations research
62N05 Reliability and life testing
60K05 Renewal theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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