Reliability Analysis of a Deteriorating System with Delayed Vacation of Repairman

In this paper, we discuss a deteriorating system with one repairman. In this system, it is assumed that the component cannot be repaired ”as good as new” after failures and the repairman takes a delayed vacation, the repair time is taken into account. Under these assumptions, we derive a model of partial differential equations by using the geometric process and supplementary variable technique. We get some reliability indices by the Laplace transform method. The working probability of the repairman, the delayed rate and the rate of occurrence of failures of the steady state of the system are explicitly given. In particular, the rate of occurrence of failures in the steady state satisfies mf 6= 0. Key–Words: deteriorating system, delayed vacation, Laplace transform, partial differential equation model, reliability.