In this paper we study the problem of computing the downtime distribution of a parallel system comprising stochastically identical components. It is assumed that the components are independent, with an exponential life-time distribution and an arbitrary repair time distribution. An exact formula is established for the distribution of the system downtime given a specific type of system failure scenario. It is shown by performing a Monte Carlo simulation that the portion of the system failures that occur as described by this scenario is close to one when we consider a system with quite available components, the most common situation in practice. Thus we can use the established formula as an approximation of the downtime distribution given system failure. The formula is compared with standard Markov expressions. Some possible extensions of the formula are presented.
An extended life time distribution: theory, properties and applications
