Optimal design of linear consecutive-k-out-of-n systems

A linear consecutive-<i>k</i>-out-of-<i>n</i>:<i>F</i> system is an ordered sequence of <i>n</i> components that fails if and only if at least <i>k</i> consecutive components fail. A linear consecutive-<i>k</i>-out-of-<i>n</i>:<i>G</i> system is an ordered sequence of n components that works if and only if at least k consecutive components work. This chapter establishes necessary conditions for the variant optimal design and procedures to improve designs not satisfying these conditions for linear consecutive systems with 2<i>k</i> ¡Ü <i>n</i> ¡Ü 3<i>k</i>.