Modeling of a deteriorating system with single vacation and reliability analysis

In this paper, we model a deteriorating system with one repairman having single vacation and its repair satisfying general distribution by methods of probability analysis. Here we suppose that if the system fails when the repairman is on vacation, it will wait for repair until the repairman is available and that the system cannot be repaired “as good as new” after failures, the repair time is taken into account. Under these assumptions, we derive a model of partial differential equations by using the geometric process and the supplementary variable technique. Moreover, we deduce some important indices of the system reliability such as the system availability, probability of the repairman working and the rate of occurrence of failures. In particular, the rate of occurrence of failures in the steady state satisfies m_f ≠ 0.