Reliability and profit analysis of a series repairable system with repairman vacation

This paper deals with an n-unit series repairable system with repairman vacation and replaceable facility. First, the uniqueness and existence of the system dynamic solution is discussed by using C₀-semigroup theory. It is followed by the presentation of the stability, especially the exponential stability of the system by analyzing the spectral distribution of the system operator and its quasi-compactness. In the end, some primary reliability indices are calculated from the eigenfunction point of view and the optimal system profit for repairman vacation and some other applications are provided.