Application of discrete transforms in reliability of a parallel redundant system

This paper introduces the application of Discrete Transform in order to study the reliability of a redundant system consisting of more than one identical components that are connected in parallel. Successive failure times of each individual component are assumed to be positive random variables having a common general distribution, while the repair times of the system are governed by another independent general distribution. Further, it is assumed that the repair is carried out when all the components in the system have failed. TheLaplace Transform of the transient state probabilities associated with the system have been obtained. In the last section, the asymptotic behaviour of the system has also been examined.