Maximizing system availability through joint decision on component redundancy and spares inventory

For a repairable k-out-of-n:G system consisting of line-replaceable units, its operational availability depends on component reliability, its redundancy level, and spare parts availability. As a result, it is important to consider redundancy allocation and spare parts provisioning simultaneously in maximizing the system's operational availability. In prior studies, however, these important aspects are often handled separately in the areas of reliability engineering and spare parts logistics. In this paper, we study a collection of operational availability maximization problems, in which the component redundancy and the spares stocking quantities are to be determined simultaneously under economic and physical constraints. To solve this type of problem, continuous-time Markov chain models are developed first for a single repairable k-out-of-n:G system under different shut-off rules, and some important properties of the corresponding operational availability and spare parts availability are derived. Then, we extend the models to series systems consisting of multiple repairable k-out-of-n:G subsystems. The related optimization problems are reformulated as binary integer linear programs and solved using a branch-and-bound method. Numerical examples, including a real-world application of automatic test equipment, are presented to illustrate this integrated product-service solution and to offer valuable managerial insights.