Optimal Consecutive-k-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. Suppose that all components are interchangeable, that component failures are s-independent, and that component failure probabilities need not be equal. When k = 2, a certain ordering of the components minimizes the probability of system failure regardless of the particular component failure probabilities. This paper characterizes all other values of k and n for which such an optimal configuration can be determined without knowledge of the component failure probabilities.