Summary
We consider a parallel system consisting ofn identical components subject to failures. Failed components are repaired by a single repairman. Under the assumptions that the failure times are exponential and the repair times are of phase type, it is shown that the busy period of the repairman, the density of the number of components repaired during a busy period and the stationary down time of the system are also of phase type. Some numerical examples and an algorithmically tractable steady state analysis of the model are presented.
Zusammenfassung
Wir betrachten ein Parallelsystem ausn identischen fehleranfälligen Komponenten. Ausgefallene Komponenten werden in einem Reparaturkanal repariert. Unter der Annahme, daß die Lebensdauern exponentialverteilt sind und die Reparaturdauern eine Verteilung vom Phasentyp besitzen, zeigen wir: Die Verteilung der Beschäftigungsperiode im Reparaturkanal, der Anzahl der während der Beschäftigungsperiode reparierten Komponenten und der stationären Ausfallzeit des Systems sind ebenfalls vom Phasentyp. Wir geben eine auch algorithmisch brauchbare Analyse des stationären Verhaltens Modells und berichten über einige numerische Ergebnisse.
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This research was supported by the National Science Foundation under Grant No. ENG-7908351 and by the Air Force Office of Scientific Research under Grant No. AFOSR-77-3236
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Chakravarthy, S. Reliability analysis of a parallel system with exponential life times and phase type repairs. OR Spektrum 5, 25–32 (1983). https://doi.org/10.1007/BF01720284
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DOI: https://doi.org/10.1007/BF01720284