Branch‐and‐bound‐based algorithm for solving the multi‐type component assignment problem in a consecutive‐k$k$‐out‐of‐n$n$:F system

Abstract

With the increasing scale and complexity of real‐world systems, it is crucial to improve system reliability in order to minimize occurrences of system failure. To achieve this, several prior studies have considered the component assignment problem for consecutive‐k$k$‐out‐of‐n$n$:F system models. This problem was extended to consider a system comprising multiple component types. This multi‐type component assignment problem (MCAP) aims to find an optimal component arrangement that achieves the maximum system reliability under the assumption that a component should be assigned only to a position of the same component type. A branch‐and‐bound (B&B) ‐based algorithm was developed to solve the MCAP in a consecutive‐k$k$‐out‐of‐n$n$:F system. The main principle of the proposed algorithm is the incorporation of the pruning conditions in the standard B&B framework to reduce the number of candidates for the optimal arrangement. It is experimentally demonstrated that the proposed algorithm can significantly improve the efficiency of the enumeration method in solving the MCAP. The proposed algorithm can obtain the optimal arrangement of a large system if the number of types is relatively large. The findings of this study can help in improving the reliability of any system that can be expressed as a consecutive‐k$k$‐out‐of‐n$n$:F system with multiple component types.