An exact algorithm for RAP with k-out-of-n subsystems and heterogeneous components under mixed and K-mixed redundancy strategies

Redundancy design is a widely used technique for enhancing system reliability across various industries, including aerospace and manufacturing. Consequently, the redundancy allocation problem (RAP) has attracted considerable attention in the field of reliability engineering. The RAP seeks to determine an optimal redundancy scheme for each subsystem under resource constraints to maximize system reliability. However, existing RAP models and exact algorithms are predominantly confined to simple 1-out-of-n subsystems or single optimization strategies, thereby limiting the optimization potential and failing to adequately address the engineering requirements. This paper introduces a model and an exact algorithm for RAP with k-out-of-n subsystems and heterogeneous components under mixed and K-mixed redundancy strategies. The model employs a continuous time Markov chain method to calculate subsystem reliability exactly. A dynamic programming (DP) algorithm based on super component and sparse node strategies is designed to obtain the exact solution for RAP. Numerical experiments confirm that all benchmark test problems reported in the literature are exactly solved by the proposed DP. The experiment results demonstrate that the proposed RAP model offers high flexibility and potential for reliability optimization. Additionally, owing to the generality of the problem considered, the proposed DP also exactly solves other RAP models with 1-out-of-n subsystems and simplified redundancy strategies, which provides a more generalized framework for redundancy optimization. Finally, the research's applicability in reliability engineering is validated through an optimization case study of a natural gas compressor pipeline system.