Stochastic behaviour of a complex system with standby redundancy

Abstract

In this paper, the behaviour of a complex system consisting of two classes of components L 1 and L 2 has been considered. Class L 1 consists of N components connected in series in which the failure of any one of the N components completely breaks down the system as a whole. Class L 2 consists of two components one of which is in standby. The system works in a reduced efficiency only when both the components in this class fail. Further, it has been assumed that the repair of failed components of both the classes is carried under three different repair disciplines viz., head of line, preemptive resume and preemptive repeat. Laplace Transforms of various state probabilities have been obtained. Asymptotic behaviour of such a system has been examined. In the end some particular cases have also been derived from the general case.