Optimal Consecutive-2-out-of-n:F Component Sequencing

A consecutive-k-out-of-n:F system is an ordered linear arrangement of n components that fails if and only if at least k consecutive components fail. When the components are not necessarily equally likely to fail, the problem of interest is to assign components to positions in the system in a way that minimizes the probability of system failure. This paper shows that when k = 2 and component failures are s-independent, the optimal configuration can be determined without knowledge of the exact particular component-failure probabilities, but with knowledge of the component ranks (in terms of failure probability).