Optimum allocation of redundancy among subsystems connected in series

This analysis considers the optimum allocation of redundancy in a system of serially connected subsystems in which each subsystem is of the k-out-of-n type. Redundancy is optimally allocated when: (1) reliability is maximized for given costs; or (2) costs are minimized for given reliability. Several techniques are presented for achieving optimum allocation and their relative merits are discussed. Approximate solutions in closed form were attainable only for the special case of series-parallel systems and the efficacy of these approximations is discussed