The (k+1)-th component of linear consecutive-k-out-of-n systems

© Springer Science+Business Media, LLC 2009.A linear consecutive–k–out–of–n:F system is an ordered sequence of n components that fails if and only if at least k consecutive components fail. A linear consecutive–k–out–of–n:G system is an ordered sequence of n components that works if and only if at least k consecutive components work. The existing necessary conditions for the optimal design of systems with 2k ≤ n provide comparisons between reliabilities of components restricted to positions from 1 to k and positions from n to (n - k + 1). This chapter establishes necessary conditions for the variant optimal design that involve components at some other positions, including component (k+1). Procedures to improve designs not satisfying those conditions are also given.