A GENERAL FORMULA FOR THE DOWNTIME DISTRIBUTION OF A PARALLEL SYSTEM

In this paper we study the problem of computing the downtime distribut ion of a parallel system comprising stochastically identical component s. It is assumed that the components are independent, with an exponent ial life-time distribution and an arbitrary repair time distribution. An exact formula is established for the distribution of the system dow ntime given a specific type of system failure scenario. It is shown by performing a Monte Carlo simulation that the portion of the system fa ilures that occur as described by this scenario is close to one when w e consider a system with quite available components, the most common s ituation in practice. Thus we can use the established formula as an ap proximation of the downtime distribution given system failure. The for mula is compared with standard Markov expressions. Some possible exten sions of the formula are presented.