Redundancy That Works: How k-out-of-n Logic Protects Supply Chains

Abstract

A comprehensive review of the k-out-of-n reliability framework is presented in this paper, and its potential for enhancing robustness in logistics and supply chain systems is demonstrated. Through an examination of a wide range of published research, it is shown that k-out-of-n models have evolved from simple binary formulations to sophisticated multi-state, dependent, and time-dependent structures capable of capturing real-world operational uncertainty. The flexibility of k-out-of-n logic in representing partial functionality, controlled redundancy, and minimum performance thresholds is highlighted, as these features are regarded as essential for modern logistics infrastructures. Applications of this modeling approach in fleet management, automated warehouses, distribution networks, supplier redundancy, and multimodal transportation are reviewed. Numerical examples are provided to illustrate how system-level availability can be quantified using k-out-of-n logic, thereby offering a transparent analytical basis for strategic and operational decisions. It is concluded that k-out-of-n modeling provides a unifying and versatile toolset for the design of supply chains intended to remain resilient despite component-level failures or disruptions.