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A deteriorating system with its repairman having multiple vacations. (English) Zbl 1206.62164
Summary: This paper considers a repairable system with a repairman, who can take multiple vacations. If the system fails and the repairman is on vacation, it will wait for repair until the repairman is available. Assume that the system cannot be repaired “as good as new” after failures. Under these assumptions, using geometric process and supplementary variable techniques, some important reliability indexes are derived, such as the system reliability, availability, rate of occurrence of failures, etc. According to the renewal reward theorem, the explicit expression of the expected profit per unit time is obtained. Finally, a numerical example is given to illustrate that there exists an optimal replacement policy \(N^*\), which maximizes the value of the expected profit rate after a long time run.

MSC:
62N05 Reliability and life testing
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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