On the Optimality of k-out-of-n:G Systems

Phillips proved that for i.i.d. components with opposite failure modes the k-out-of-n:G systems are the optimal s-coherent systems in terms of maximising reliability. This paper generalises that result to s-dependent components. Further, the proof provides corollaries in terms of: 1) necessary conditions for a system of s-identical components to be s-coherent, and 2) a method for efficiently evaluating the mean-time-to-failure of s-coherent systems of s-identical components.