Optimal redundancy allocation using log-concave properties

Using log-concave properties, this paper presents an efficient linear-time algorithm to determine optimal redundancy allocations for different subsystems of non-repairable series systems with a single system-level resource constraint. Each subsystem in the system is modeled using a k-out-of-n warm standby redundancy that includes both active and cold standby redundancies as special cases. The key assumption used in the proposed method is that, within each subsystem, all components are identical, but they can have different operational and standby failure rates. However, the components belonging to different subsystems can be different, and they can have different failure rates and different resource consumption rates. The main contributions of this research work are: (1) proving the important log-concave properties associated with warm standby configurations, and (2) effectively utilizing these properties for finding the optimal solutions. The proposed algorithm and log-concave properties are illustrated using numerical examples.