Summary
Optimum preventive maintenance policies for a two-unit standby redundant system are reviewed. Under the assumptions that all distributions are arbitrary, the first-passage time distributions, the transition probabilities, and the expected numbers of visits to a certain state are derived. Using the probabilistic quantities above, we discuss the optimum preventive maintenance policies maximizing or minimizing some criteria. We show that under suitable conditions there exist the optimum preventive maintenance policies which are given by the unique solutions of the equations. This paper concludes with numerical examples of such optimum preventive maintenance policies.
Zusammenfassung
In diesem Aufsatz werden optimale Strategien zur vorbeugenden Instandhaltung für ein System mit zwei Maschinen besprochen, wobei eine Maschine die Ersatzmaschine darstellt. Unter der Annahme willkürlicher Verteilungen werden die Verteilung der Zeit für den ersten Durchgang, die übergangswahrscheinlichkeiten und die erwartete Zahl des Erreichens eines bestimmten Zustandes abgeleitet. Anhand der oben erwähnten Wahrscheinlichkeitswerte werden optimale Strategien zur vorbeugenden Instandhaltung besprochen, die bestimmte Kriterien maximieren oder minimieren. Es wird gezeigt, daß bei entsprechenden Bedingungen optimale Strategien zur vorbeugenden Instandhaltung existieren, die man als eindeutige Lösung eines Gleichungssystems erhält. Am Ende des Aufsatzes werden numerische Beispiele für optimale Strategien gegeben.
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Nakagawa, T., Osaki, S. A summary of optimum preventive maintenance policies for a two-unit standby redundant system. Zeitschrift für Operations Research 20, 171–187 (1976). https://doi.org/10.1007/BF01920262
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DOI: https://doi.org/10.1007/BF01920262