Innage and Outage Intervals in Transmission Systems Composed of Links

This note is in the nature of an addendum to a recent paper of mine 011 satellite communication systems. 1 It is concerned with the same general problem, namely the reliability of transmission systems composed of links which fail independently. Various published results are reviewed and extended. A large part of these results is due to D. S. Palmer, 2 whose excellent work was overlooked in my satellite paper. The approach given here differs somewhat from that used by Palmer. Incidentally, questions similar to those discussed here have also appeared in connection with coincidences in counting devices. The notation to be followed is illustrated in Fig. 1. Suppose t h a t a link in a transmission system is always either in one or the other of two possible states, state (a) or state (b). For example, if the link is a satellite, (a) may be taken as the state of being out of sight and (b) the state of being visible. Again, if the link is one of a series of links in tandem making up a transmission line, we may choose (a) to be the state of workingorder and (b) the state of breakdown. In a satellite system the links are in parallel and in the transmission line they are in series. Fig. 1 applies to both cases. The light portions of the top line in Fig. 1 represent the intervals dur2267