Reliability theory for large linear systems with helping neighbors

Ways to model large systems, whose redundancy consists of the ability of neighbors to help (replace faulty units), at least for a degraded mode of operation, are shown. A general approach of determining and evaluating a fault-tree for such systems is given. One-dimensional (linear) arrays of components are emphasized, and linear consecutive quasi-3-out-of-n:F systems and circular consecutive 3-out-of- n:F systems are discussed. In all cases, explicit formulas-most of them recursive-are given for system unavailability and for mean system-failure frequency for nonidentical s-independent components. As to methodology, the good adaptation of the Shannon decomposition to finding recursive results is amply demonstrated