Analysis of a Complex System Modelled by a Marked Point Process and Assuming Vacations for a Repairman

Abstract

In this paper a system consisting of two subsystems A and B is analyzed. A has only one unit while B has two units, B 1 and B 2 , connected in such a manner that B 2 is in hot standby with B 1 . The system is modelled by a marked point process. There are two repairmen namely a supervisor and a novice. The supervisor is always present, while the novice might be in vacation. Two types of failure of the components of B are considered. The model is analyzed under "preemptive-repeat repair discipline". By employing Laplace transformation and assuming the Gumbel-Hougaard copula, the state transition probabilities, reliability, availability and expected profit are obtained along with the steady state behaviour of the system. At the end some special cases of the system are investigated.