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.