The mean time-to-failure of some special series-parallel arrays

A method for finding the mean time-to-failure (MTTF) of parallel-series and series-parallel arrays is presented. The system itself is subject to two modes of failure, open and short, and all components states are mutually independent. Each item has the same failure-time distribution, and the probability of short failure of an item, given the failure of the item, is a constant. It is shown that the distribution of the lifetime of the system is a linear combination of the distributions of lifetimes of systems each of which is an ordinary series or parallel system of mutually independent components