Operational Behaviour of a Complex System Under Priority Repair Echelons

Abstract

A mathematical model is set up to evaluate the reliability of a complex system comprising two subsystems (with stand by redundancy in one subsystem). The failure and repair of units for both the subsystems follow exponential and general time distributions respectively. The switching over device for standby subsystem is not perfect and its repair is opportunistic. The repair for both subsystems is carried out under priority. The concept of waiting time for the repair of failed units in staidly subsystem has also been introduced. Supplementary variable and Laplace Transform techniques have been applied to obtain the transient state probabilities for such a system. From these pointwise availability has been evaluated. In the end, a particular case when repair follows exponential time distribution has been derived and asymptotic behaviour of such a system has also been examined.